MCQ

MCQ 11 Mark

Choose the correct answer. If $x$ is a real number and $|x| < 3,$ then:

A
$\text{x}\geq3$
✓
$-3<\text{x}<3$
C
$\text{x}\leq-3$
D
$-3\leq\text{x}\leq3$

Answer

Correct option: B.

$-3<\text{x}<3$

Given that $|x| < 3$
$\Rightarrow -3 < x < 3 | x | < a$
$\Rightarrow -a < x < a.$
$-3<\text{x}<3$

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MCQ 21 Mark

If $−5\leq\frac{5 – 3\text{x}}{2}\leq8, $ then $\text{x}\in$

✓
$\big[\frac{11}{3},5\big]$
B
$\big[-5,5\big]$
C
$\big[\frac{-11}{3},\infty\big]$
D
$\big(-\infty,\infty\big)$

Answer

Correct option: A.

$\big[\frac{11}{3},5\big]$

$\big[\frac{11}{3},5\big]$

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MCQ 31 Mark

The solution of $\Big|\frac{2}{(\text{x} – 4)}\Big|>1$ where $\text{x}\neq4$ is:

A
$(2, 6)$
✓
$(2, 4)\cup(4, 6)$
C
$(2, 4)\cup(4,\infty)$
D
$(-\infty, 4)\cup(4, 6)$

Answer

Correct option: B.

$(2, 4)\cup(4, 6)$

Given,$\Big|\frac{2}{(\text{x} – 4)}\Big|>1$
$\Rightarrow2 > |\text{x} – 4|$
$\Rightarrow |\text{x} – 4|<2$
$\Rightarrow-2<\text{x}-4<2$
$\Rightarrow-2+4 < \text{x} < 2+4$
$\Rightarrow2<\text{x}<6$
$\Rightarrow\text{x}\in(2, 6), $ where $\text{x}\neq4$
$\Rightarrow\text{x}\in(2, 4)\cup(4, 6)$

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MCQ 41 Mark

Write the solution of inequality $\frac{1}{5}\bigg(\frac{3\text{x}}{5}+4\bigg)\geq\frac{1}{3}(\text{x}-6).$

✓
$\text{x}\leq\frac{105}{8}$
B
$\text{x}\geq\frac{105}{8}$
C
$\text{x}\geq120$
D
$\text{x}\leq120$

Answer

Correct option: A.

$\text{x}\leq\frac{105}{8}$

$\frac{1}{5}\big(\frac{3\text{x}}{5}+4\big)\geq\frac{1}{3}(\text{x}-6).$
$\Rightarrow3\big(\frac{3\text{x}}{5}+4\big)\geq5\big(\text{x}-6\big)$
$\Rightarrow\big(\frac{9\text{x}}{5}+12\big)\geq5\text{x}-6$
$\Rightarrow(30+12)\geq-\frac{9\text{x}}{5}+5\text{x}$
$\Rightarrow42\geq\frac{-9\text{x}+25\text{x}}{5}$
$\Rightarrow42\geq\frac{16\text{x}}{5}$
$\Rightarrow\frac{42\times5}{16}\geq\text{x}$
$\text{x}\leq\frac{105}{8}$
Therefore option (1) is the correct answere.

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MCQ 51 Mark

If the roots of the equation $x^2-b x+c=0$ be two consecutive integers, then $b^2-4 c$ equals:

✓
1
B
2
C
3
D
-2

Answer

Correct option: A.

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MCQ 61 Mark

The length of a rectangle is three times the breadth.If the minimum perimeter of the rectangle is 160cm, then:

A
breadth > 20cm
B
length < 20cm
✓
breadth x ≥ 20cm
D
length ≤ 20cm

Answer

Correct option: C.

breadth x ≥ 20cm

Let x be the breadth of a rectangle.
So, length = 3x
Given that the minimum perimeter of a rectangle is 160cm.
Thus, $2(3\text{x}+\text{x})\geq160$
$\Rightarrow4\text{x}\geq80$
$\Rightarrow\text{x}\geq20$

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MCQ 71 Mark

Which of the following points lie in the solution set?

A
(1, 1)
✓
(1, 2)
C
(2, 1)
D
(3, 2)

Answer

Correct option: B.

(1, 2)

(1, 2)

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MCQ 81 Mark

The value of a for which the sum of the squares of the roots of the equation $x^2-(a-2) x-a-1=0$ the least value is:

A
2
B
3
C
0
✓
1

Answer

Correct option: D.

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MCQ 91 Mark

If x is a whole number and $10\text{x}\leq50$ then find solution set of x.

✓
{0,1, 2, 3, 4, 5}
B
{1, 2, 3, 4, 5}
C
{1, 2, 3, 4}
D
{0, 1, 2, 3, 4}

Answer

Correct option: A.

{0,1, 2, 3, 4, 5}

$10\text{x}\leq50$
Dividing by 10 on both sides, $\text{x}\leq\Big(\frac{50}{10}\Big)=\Rightarrow\text{x}\leq5$
Since x is a whole number so x = 0, 1, 2, 3, 4, 5.

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MCQ 101 Mark

If the sum of the roots of the quadratic equation $ \text{ax}^2+\text{bx}+\text{c}=0$ is equal to the sum of the squares of their reciprocals, then $\frac{\text{a}}{\text{c}}, \frac{\text{b}}{\text{a}}$ and $\frac{\text{c}}{\text{b}}$ are in:

A
arithmetic progression
B
geometric progression
✓
harmonic progression
D
arithmetico-geometric progression

Answer

Correct option: C.

harmonic progression

harmonic progression

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MCQ 111 Mark

The quadratic equations $x^2-6 x+a=0$ and $x^2-c x+6=0$ have one root in common. The other roots of the first and second equations are integers in the ratio $4: 3$. Then, the common root is:

✓
2
B
1
C
4
D
3

Answer

Correct option: A.

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MCQ 121 Mark

Solution of $|3\text{x}+2| <1$ is:

A
$\big[-1,\frac{-1}{3}\big]$
B
$\big(\frac{-1}{3},-1\big)$
✓
$\big(-1,\frac{-1}{3}\big)$
D
$\text{None of these}$

Answer

Correct option: C.

$\big(-1,\frac{-1}{3}\big)$

$\big(-1,\frac{-1}{3}\big)$

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MCQ 131 Mark

A solution is to be kept between $77^\circ$ F and $86^\circ$ F.What is the range in temperature in degree Celsius (C) if the $\frac{\text{Celsius}}{\text{Fahrenheit}}$(F) conversion formula is given by $\text{F}=\frac{9}{5\text{c}}+32^\circ$

A
$\big[15^\circ, 20^\circ\big]$
B
$\big[20^\circ, 25^\circ\big]$
✓
$\big[25^\circ, 30^\circ\big]$
D
$\big[30^\circ, 35^\circ\big]$

Answer

Correct option: C.

$\big[25^\circ, 30^\circ\big]$

$\text{F}=\frac{9}{5\text{c}}+32^\circ$
$\text{C}=\text{F}-32^\circ\times\frac{5}{9}$
$77^\circ\leq\text{F}\leq86^\circ$
$\Rightarrow77^\circ-32^\circ\leq\text{F}-32^\circ\leq86^\circ -32^\circ$
$\Rightarrow45^\circ\leq\text{F}-32^\circ\leq54^\circ$
$\Rightarrow45^\circ\times\frac{5}{9}\leq(\text{F}-32^\circ)\times\frac{5}{9}\leq54^\circ\times\frac{5}{9}$
$\Rightarrow25^\circ\leq\text{C}\leq30^\circ$

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MCQ 141 Mark

The graph of the inequations x ≤ 0, y ≤ 0, and 2x + y + 6 ≥ 0 is:

A
exterior of a triangle
✓
a triangular region in the 3rd quadrant
C
in the 1st quadrant
D
none of these

Answer

Correct option: B.

a triangular region in the 3rd quadrant

Given inequalities x ≥ 0, y ≥ 0, 2x + y + 6 ≥ 0
Now take x = 0, y = 0 and 2x + y + 6 = 0
when x = 0, y = -6
when y = 0, x = -3
So, the points are A(0, 0), B(0, -6) and C(-3, 0)

So, the graph of the inequations x ≤ 0, y ≤ 0, and 2x + y + 6 ≥ 0 is a triangular region in the 3rd quadrant.

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MCQ 151 Mark

If $4\text{x} + 3<6\text{x} + 7$, then$\text{ x}\in$

A
$\big(2,\infty\big)$
✓
$\big(-2,\infty\big)$
C
$\big(-\infty,2\big)$
D
$\big(-\infty,\infty\big)$

Answer

Correct option: B.

$\big(-2,\infty\big)$

$\big(-2,\infty\big)$

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MCQ 161 Mark

If |x−1| x - 1 > 5, then:

A
$\text{x}\in(-4,6)$
B
$\text{x}\in[-4,6]$
✓
$\text{x}\in(-\infty,-4)\cup(6,\infty)$
D
$\text{x}\in(-\infty,-4)\cup[6,\infty)$

Answer

Correct option: C.

$\text{x}\in(-\infty,-4)\cup(6,\infty)$

|x−1| > 5
⇒ x − 1 > 5 or x − 1 < −5
⇒ x > 5 + 1 or x < −5 + 1
⇒ x > 6 or x < −4
$\Rightarrow\text{x}\in(-\infty,-4)\cup(6,\infty)$

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MCQ 171 Mark

If x is a natural number and $20\text{x}\leq100$ then find solution set of x.

A
{0, 1, 2, 3, 4, 5}
✓
{1, 2, 3, 4, 5}
C
{1, 2, 3, 4}
D
{0, 1, 2, 3, 4}

Answer

Correct option: B.

{1, 2, 3, 4, 5}

$20\text{x}\leq100$
Dividing by 20 on both sides, $\text{x}\leq\frac{100}{20}\Rightarrow\text{x}\leq5$
Since x is a natural number so x = 1, 2, 3, 4, 5.

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MCQ 181 Mark

If − 3x + 17 < -13, then:

✓
$\text{x}\in(10,\infty)$
B
$\text{x}\in[10,\infty)$
C
$\text{x}\in(-\infty,10]$
D
$\text{x}\in[-10,10)$

Answer

Correct option: A.

$\text{x}\in(10,\infty)$

− 3x + 17 < −13
Subtracting 17 on both sides, we get
⇒ −3x + 17 − 17 < −13 − 17
⇒ −3x < − 30
Dividing −3 on both sides, we get
$\Rightarrow\frac{-3\text{x}}{-3}>\frac{-30}{-3}$
$\Rightarrow\text{x}>10$
$\Rightarrow\text{x}\in(10,\infty)$

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MCQ 191 Mark

The graph of the inequalities x ≥ 0, y ≥ 0, 2x + y + 6 ≤ 0 is:

A
a square
B
a triangle
✓
{}
D
none of these

Answer

Correct option: C.

{}

Given inequalities x ≥ 0, y ≥ 0, 2x + y + 6 ≤ 0
Now take x = 0, y = 0 and 2x + y + 6 = 0
when x = 0, y = -6
when y = 0, x = -3
So, the points are A(0, 0), B(0, -6) and C(-3, 0)

Since region is outside from the line 2x + y + 6 = 0
So, it does not represent any figure.

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MCQ 201 Mark

If $\frac{|\text{x}-2|}{\text{x}-2}\geq0,$ then:

A
$\text{x}\in[2,\infty)$
✓
$\text{x}\in(2,\infty)$
C
$\text{x}\in(-\infty,2)$
D
$\text{x}\in(-\infty,2]$

Answer

Correct option: B.

$\text{x}\in(2,\infty)$

- For $x-2>0$ (i.e., $x>2$ ):
$|x-2|=x-2, \text { so } \frac{x-2}{x-2}=1 \geq 0 \text { (True) }$
- For $x-2=0$ (i.e., $x=2$ ):
$|x-2|=0$, so $\frac{0}{0}$ is undefined.
- For $x-2<0$ (i.e., $x<2$ ):
$|x-2|=-(x-2)=2-x$, so $\frac{2-x}{x-2}=\frac{-(x-2)}{x-2}=-1 \geq 0$ (False)
$\text{x}\in(2,\infty)$

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MCQ 211 Mark

If x is a real number and |x| < 5, then:

A
$\text{x}\geq5$
✓
$-5<\text{x}<5$
C
$\text{x}\leq-5$
D
$-5\leq\text{x}\leq5$

Answer

Correct option: B.

$-5<\text{x}<5$

If x is a real number.
|x| < 5
⇒ -5 < x < 5

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MCQ 221 Mark

If $|\text{x} + 3|\geq10,$ then:

A
$\text{x}\in\big(-13, 7\big] $
B
$\text{x}\in\big(–13, 7\big)$
✓
$\text{x}\in\big(-\infty,-13\big]\cup\big[7,\infty\big)$
D
$\text{x}\in\big(-\infty,-13\big)\cup\big[7,\infty\big)$

Answer

Correct option: C.

$\text{x}\in\big(-\infty,-13\big]\cup\big[7,\infty\big)$

$\text{x}\in\big(-\infty,-13\big]\cup\big[7,\infty\big)$

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MCQ 231 Mark

The solution of the inequality $\frac{3(\text{x}-2)}{5}\geq\frac{5(2-\text{x})}{3}$ is:

A
$\text{x}\in(2,\infty)$
B
$\text{x}\in\big[-2,\infty)$
C
$\text{x}\in\big[\infty,2)$
✓
$\text{x}\in\big[2,\infty)$

Answer

Correct option: D.

$\text{x}\in\big[2,\infty)$

Given, $\frac{3(\text{x}-2)}{5}\geq\frac{5(2-\text{x})}{3}$
$\Rightarrow3(\text{x} – 2)\times3\geq5(2 – \text{x})\times5$
$\Rightarrow9(\text{x} – 2)\geq25(2 – \text{x})$
$\Rightarrow9\text{x} – 18\geq50 – 25\text{x}$
$\Rightarrow9\text{x} – 18 + 25\text{x}\geq50$
$\Rightarrow34\text{x}-18\geq50$
$\Rightarrow34\text{x}\geq50+18$
$\Rightarrow34\geq68$
$\Rightarrow\text{x}\geq\frac{68}{34}$
$\Rightarrow\text{x}\geq2$
$\Rightarrow\text{x}\in\big[2,\infty)$

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MCQ 241 Mark

If the equstion $\text{a}_\text{n}\text{x}^\text{n}+\text{a}_\text{n-1}\text{x}^\text{n-1}+...+\text{a}_1\text{x}=0,$ $\text{a}_1\neq0,\text{n}\geq2,$ has positive root $\text{x}=\alpha$ then the eqestions $\text{na}_\text{n}\text{x}^\text{n-1}+(\text{n-1})\text{a}_\text{n-1}\text{x}^\text{n-2}+...+\text{a}_1=0$ has a positive root, which is:

A
equal to $\alpha$
B
greater than or equal to $\alpha$
✓
smaller than $\alpha$
D
greater than $\alpha$

Answer

Correct option: C.

smaller than $\alpha$

smaller than $\alpha$

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MCQ 251 Mark

Question: If one root of the equation $\text{x}^2+\text{px}+12=0$ is 4, while the equation $\text{x}^2+\text{px}+\text{q}=0$ has equal roots, then the value of q is:

✓
$\frac{49}{4}$
B
$12$
C
$3$
D
$4$

Answer

Correct option: A.

$\frac{49}{4}$

$\frac{49}{4}$

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MCQ 261 Mark

Solution of $\bigg|\text{x}+\frac{1}{\text{x}}\bigg|<4 $ is:

✓
$\big(2-3, 2+3\big)\cup\big(-2-3-2+3\big)$
B
$\text{R}\big(2-3, 2+3\big)$
C
$\text{R}-\big(-2-3-2 + 3\big)$
D
$\text{None of these}$

Answer

Correct option: A.

$\big(2-3, 2+3\big)\cup\big(-2-3-2+3\big)$

$\big(2-3, 2+3\big)\cup\big(-2-3-2+3\big)$

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MCQ 271 Mark

The number of the real solutions of the equation $x^2-3|x|+2=0$ is:

A
2
✓
4
C
1
D
3

Answer

Correct option: B.

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MCQ 281 Mark

If the difference between the roots of the equation $\text{x}^2 +\text{ax}+1=0$ is less than $\sqrt{5},$ then the set of possible values of a is:

✓
$(-3,3)$
B
$(-3,\infty)$
C
$(3,\infty)$
D
$(-\infty,-3)$

Answer

Correct option: A.

$(-3,3)$

$(-3,3)$

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MCQ 291 Mark

All the values of $m$ for which both roots of the equation $x^2-2 m x+m^2-1=0$ are greater than -2 but less than 4 lie in the interval:

A
$m>3$
✓
$-1<m<3$
C
$1<\mathrm{m}<4$
D
$-2<m<0$

Answer

Correct option: B.

$-1<m<3$

$-1<m<3$

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MCQ 301 Mark

If $ 7\text{x} + 3 < 5\text{x} + 9$ then$\text{x}\in$

A
$\big(-\infty, 3\big]$
B
$\big(\infty,\infty\big)$
✓
$\big(-\infty,3\big)$
D
$\big[3,\infty\big)$

Answer

Correct option: C.

$\big(-\infty,3\big)$

$\big(-\infty,3\big)$

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MCQ 311 Mark

The inequality representing the following graph is:

✓
$|\text{x}|<5$
B
$|\text{x}|\leq5$
C
$|\text{x}|>5$
D
$|\text{x}|\geq5$

Answer

Correct option: A.

$|\text{x}|<5$

$|\text{x}|<5$

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MCQ 321 Mark

ax + b > 0 is, ___________________?

A
double inequality
B
quadratic inequality
C
numerical inequality
✓
linear inequality

Answer

Correct option: D.

linear inequality

Since it has highest power of x ‘1’ and has inequality sign so, it is called linear inequality.
It is not numerical inequality as it does not have numbers on both sides of inequality.
It does not have two inequality signs so it is not double inequality.

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MCQ 331 Mark

If $\text{|x}+2|\leq9,$ then:

A
$\text{x}\in(-7,11)$
✓
$\text{x}\in[-11,7]$
C
$\text{x}\in(-\infty,-7)\cup(11,\infty)$
D
$\text{x}\in(-\infty,-7)\cup[11,\infty)$

Answer

Correct option: B.

$\text{x}\in[-11,7]$

$|\text{x}+2|\leq9$
$\Rightarrow-9\leq\text{x}+2\leq9$
$\Rightarrow-9-2\leq\text{x}+2-2\leq9-2$
$\Rightarrow-11\leq\text{x}\leq7$
$\Rightarrow\text{x}\in[-11,7]$

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MCQ 341 Mark

$a x^2+b x+c>0$ is, _____________________?

A
double inequality
✓
quadratic inequality
C
numerical inequality
D
linear inequality

Answer

Correct option: B.

quadratic inequality

quadratic inequality

Solution:
Since it has highest power of x ‘2’ and has inequality sign so, it is called quadratic inequality.
It is not numerical inequality as it does not have numbers on both sides of inequality.
It does not have two inequality signs so it is not double inequality.

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MCQ 351 Mark

Solution of $|\text{x} – 1|\geq|\text{x}-3| $ is:

A
$\text{x}\leq2$
✓
$\text{x}\geq2$
C
$\big[1, 3\big]$
D
$\text{None of these}$

Answer

Correct option: B.

$\text{x}\geq2$

$\text{x}\geq2$

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MCQ 361 Mark

If $(1-p)$ is a root of quadratic equation $x^2+p x+(1-p)=0$, then its roots are:

A
0, 1
B
– 1, 1
✓
0, -1
D
– 1, 2

Answer

Correct option: C.

0, -1

0, -1

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MCQ 371 Mark

If $–3\text{x}+17<-13, $ then:

✓
$\text{x}\in\big(10,\infty\big)$
B
$\text{x}\in\big[10,\infty\big)$
C
$\text{x}\in\big(-\infty,10\big)$
D
$\text{x}\in\big[-10,10\big)$

Answer

Correct option: A.

$\text{x}\in\big(10,\infty\big)$

$\text{x}\in\big(10,\infty\big)$

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MCQ 381 Mark

If $|\text{x}+3|\geq10,$ then:

A
$\text{x}\in(-12,7]$
B
$\text{x}\in(-13,7)$
C
$\text{x}\in(\infty,-13)\cup(7,\infty)$
✓
$\text{x}\in(-\infty,-13]\cup[7,\infty)$

Answer

Correct option: D.

$\text{x}\in(-\infty,-13]\cup[7,\infty)$

$|\text{x}+3|\geq10$
$\Rightarrow\text{x}+3\geq10\text{ or }\text{x}+3;\leq-10$
$\Rightarrow\text{x}\geq10-3\text{ or }\text{x}\leq-10-3$
$\Rightarrow\text{x}\geq7\ \text{or}\ \text{x}\leq-13$
$\Rightarrow\text{x}\in(-\infty,-13)\cup[7,\infty)$

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MCQ 391 Mark

Choose the correct answer. If x < 5, then.

A
$-\text{x} < – 5 $
B
$-\text{x}\leq-5$
✓
$-\text{x} > – 5 $
D
$-\text{x}\leq-5$

Answer

Correct option: C.

$-\text{x} > – 5 $

If x > 5 then - x > - 5.

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MCQ 401 Mark

If $|\text{x} – 1|>5,$ then

A
$\text{x}\in\big(-4, 6\big)$
B
$\text{x}\in\big[–4, 6\big]$
✓
$\text{x}\in\big(-\infty, –4\big)\cup\big(6,\infty\big)$
D
$\text{x}\in\big(-\infty, –4\big)\cup\big[6,\infty\big)$

Answer

Correct option: C.

$\text{x}\in\big(-\infty, –4\big)\cup\big(6,\infty\big)$

$\text{x}\in\big(-\infty, –4\big)\cup\big(6,\infty\big)$

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MCQ 411 Mark

The solution set of the inequation $|\text{x}+2|\leq5$ is:

A
(-7, 5)
✓
[-7, 3]
C
[-5, 5]
D
(-7, 3)

Answer

Correct option: B.

[-7, 3]

$|\text{x}+2|\leq5$
$\Rightarrow-5\leq\text{x}+2\leq5$
$\Rightarrow-5-2\leq\text{x}+2-2\leq5-2$
$\Rightarrow-7\leq\text{x}\leq3$
$\Rightarrow\text{x}\in[-7,3]$

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MCQ 421 Mark

The inequality representing the following graph is:

✓
|x| < 5
B
|x| ≤ 5
C
|x| > 5
D
|x| ≥ 5

Answer

Correct option: A.

|x| < 5

The given graph shows the shaded region corresponding to x > – 5 and x < 5.
Therefore, by combining the above two inequalities, we get |x| < 5.

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MCQ 431 Mark

Choose correct option which suitably represents value of $\text{x.x}<5,\text{x}\in\text{N}$

A
{0, 1, 2, 3, 4}
✓
{1, 2, 3, 4}
C
{1, 2, 3, 4, 5}
D
{0, 1, 2, 3, 4, 5}

Answer

Correct option: B.

{1, 2, 3, 4}

Given, $\text{x}<5$ and $\text{x}\in\text{N}$ Natural numbers are counting numbers whose set is.
N = {1, 2, 3, ..} Therefore, {1, 2, 3, 4} represents $\text{x}<5$

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MCQ 441 Mark

Solutions of the inequalities comprising a system in variable x are represented on number lines as given below, then 36

A
$\text{x}\in\big(-\infty,-4\big]\cup\big[3,\infty\big)$
✓
$\text{x}\in\big[–3, 1\big]$
C
$\text{x}\in\big(-\infty, -4\big)\cup\big[3,\infty\big)$
D
$\text{x}\in\big[–4, 3\big]$

Answer

Correct option: B.

$\text{x}\in\big[–3, 1\big]$

$\text{x}\in\big[–3, 1\big]$

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MCQ 451 Mark

Solution of $(\text{x}-1) 2 (\text{x}+4)<0$ is:

A
$(-\infty, 1)$
✓
$(\infty, –4)$
C
$(– 1, 4)$
D
$(1, 4)$

Answer

Correct option: B.

$(\infty, –4)$

$(\infty, –4)$

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MCQ 461 Mark

If x < 7, then:

A
$-\text{x}<-7$
B
$-\text{x}\leq-7$
✓
$-\text{x}>-7$
D
$-\text{x}\geq-7$

Answer

Correct option: C.

$-\text{x}>-7$

x < 7
subtracting x on both sides, we get
⇒ x − x < 7 − x
⇒ 0 < 7 − x
subtracting 7 on both sides, we get
⇒ 0 − 7 < 7 − x − 7
⇒ −7 < − x
⇒ − x > −7

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MCQ 471 Mark

If the roots of the equation $b x^2+c x+a=0$ be imaginary, then for all real values of $x$, the expression $3 b^2 x^2+6 b c x+$ $2 \mathrm{c}^2$

A
greater than 4ab
B
less than 4ab
✓
greater than -4ab
D
less than -4ab

Answer

Correct option: C.

greater than -4ab

greater than -4ab

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MCQ 481 Mark

IQ of a person is given by the formula. $\text{IQ}=\Big(\frac{\text{MA}}{\text{CA}}\Big)\times100$ where MA is mental age and CA is chronological age. If $40\leq\text{IQ}\leq120$ for a group of 10 years old children, find the range of their mental age.

A
$\big(9,16\big)$
B
$\big[9,16\big]$
C
$\big(4,12\big)$
✓
$\big[4,12\big]$

Answer

Correct option: D.

$\big[4,12\big]$

$\text{IQ}=\Big(\frac{\text{MA}}{\text{CA}}\Big)\times100$
$\Rightarrow\text{MA}=\text{IQ}\times\frac{\text{CA}}{100}$ Given, $\text{CA}=10$ years
$40\leq\text{IQ}\leq120$
$\Rightarrow40\times\text{CA}\leq\text{IQ}\times\text{CA}\leq120\times\text{CA}$
$\Rightarrow40\times10\leq\text{IQ}\times\text{CA}\leq120\times10$
$\Rightarrow40\times10100\leq\text{Q}\times\text{CA}100\leq120\times10100$
$\Rightarrow40\leq\text{MA}\leq120$

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MCQ 491 Mark

If $|3 – 4\text{x}|\geq9, $ then$\text{x}\in$

A
$\big(-\infty –3\big)\cup\big(3,\infty\big)$
B
$\big(\infty,\frac{ -3}{2}\big]\cup\big(3 ,\infty\big)$
C
$\big(−\infty ,\frac{-3}{2}\big]\cup\big(0,\infty\big)$
✓
$\big(-\infty,\frac{-3}{2}\big]\cup\big[3,\infty\big)$

Answer

Correct option: D.

$\big(-\infty,\frac{-3}{2}\big]\cup\big[3,\infty\big)$

$\big(-\infty,\frac{-3}{2}\big]\cup\big[3,\infty\big)$

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MCQ 501 Mark

The solution of the $15<\frac{3(\text{x} – 2)}{5}<0$ is:

✓
$27 <\times< 2$
B
$27 <\times< -2$
C
$-27 <\times< 2$
D
$27 <\times< -2$

Answer

Correct option: A.

$27 <\times< 2$

Given inequality is:
$15<\frac{3(\text{x} – 2)}{5}<0$
$\Rightarrow15\times5<3(\text{x} – 2)<0 × 5$
$\Rightarrow75<3(\text{x} – 2)<0$
$\Rightarrow\frac{75}{3}<\text{x} – 2<0$
$\Rightarrow25<\text{x}-2<0$
$\Rightarrow25 + 2 <\text{x}<0 + 2$
$\Rightarrow27 <\times< 2$

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MCQ 511 Mark

The longest side of a triangle is 2 times the shortest side and the third side is 4cm shorter than the longest side.If the perimeter of the triangle is at least 61cm, find the minimum length of the shortest side.

A
7
B
9
C
11
✓
13

Answer

Correct option: D.

Let shortest side be x.Then longest side $=2\text{x}.$
Third side $=2\text{x}-4.$
Given, perimeter of triangle is at least 61cm
$\Rightarrow\text{x}+2\text{x}+2\text{x} - 4\geq61\Rightarrow5\text{x}\geq65=\text{x}\geq13.$
Minimum length of the shortest side is 13cm.

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MCQ 521 Mark

$\text{x} + 2\text{y}\leq8$

$\text{x}\geq0, \text{y}\geq0$
$\text{x}\leq0,\text{y}\leq0$
$ 2\text{x} + \text{y}\leq8$
$4\text{x}+5\text{y}\geq40$

A
(i), (iii) and (v)
B
(i), (iv) and (v)
C
(i), (iii) and (iv)
✓
(i), (ii) and (iv)

Answer

Correct option: D.

(i), (ii) and (iv)

(i), (ii) and (iv)

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MCQ 531 Mark

The solution of the inequality $\frac{\text{x}}{4}>\frac{\text{x}}{2}+1$ will be:

A
$\text{x}>4$
B
$\text{x}>-4$
✓
$\text{x}<-4$
D
$-4 <\text{ x} >4$

Answer

Correct option: C.

$\text{x}<-4$

Given: $\frac{\text{x}}{4}>\frac{\text{x}}{2}+1$
$\Rightarrow\frac{\text{x}}{4}-\frac{\text{x}}{2}>1$
$\Rightarrow\frac{\text{x}-2\text{x}}{4}>1$
$\Rightarrow\frac{\text{-x}}{4}>1$
$\Rightarrow-\text{x}>4$
$\Rightarrow\text{x}<-4$

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MCQ 541 Mark

$3\text{x}-6\geq0$ are, ____________?

A
right side with dotted x = 2
B
left side with dotted x = 2
✓
right side with complete line x = 2
D
left side with complete line x = 2

Answer

Correct option: C.

right side with complete line x = 2

$3\text{x}-6\geq0\Rightarrow\text{x}\geq2.$
(0, 0) does not satisfy te equation so region is right side of x = 2 with complete line x = 2 due to presence of equality sign along with inequality sign.

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MCQ 551 Mark

Choose the correct answer. Solution of a linear inequality in variable x is represented on number line.

✓
$\text{x}\in\big(-\infty,\frac{7}{2}\big)$
B
$\text{x}\in\big(\infty,\frac{7}{2}\big]$
C
$\text{x}\in\big(\frac{7}{2},-\infty\big)$
D
$\text{x}\in\big(\frac{7}{2},\infty\big)$

Answer

Correct option: A.

$\text{x}\in\big(-\infty,\frac{7}{2}\big)$

The given graph all real values of $x$ greater than and equal $\frac{7}{2}$ on real number line.
So, $\text{x}\in\big(-\infty,\frac{7}{2}\big)$

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MCQ 561 Mark

The value of x for which $|\text{x} + 1|+\sqrt{(\text{x} – 1)} = 0$

A
0
B
1
C
-1
✓
No value of x

Answer

Correct option: D.

No value of x

Given, $|\text{x} + 1| +\sqrt{(\text{x} – 1)}= 0, $where each term is non - negative.
So, $ |\text{x} + 1| = 0 $ and $\sqrt{\text{(x-1})}=0$ should be zero simultaneously.
$\text{i}.\text{e}. \text{x} = -1 $ and $\text{x}=1,$ which is not possible.
So, there is no value of x for which each term is zero simultaneously.

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MCQ 571 Mark

Solution of $ |\text{x}^2 – 10|\leq6$ is:

A
$\big(2, 4\big)$
B
$\big(– 4, – 2\big)$
C
$\big(– 4, – 2\big)\cup\big(2, 4\big)$
✓
$\big[– 4, – 2\big]\cup\big[2, 4\big]$

Answer

Correct option: D.

$\big[– 4, – 2\big]\cup\big[2, 4\big]$

$\big[– 4, – 2\big]\cup\big[2, 4\big]$

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MCQ 581 Mark

Sum of two rational numbers is, ______ number:

✓
rational
B
irrational
C
Integer
D
Both 1, 2 and 3

Answer

Correct option: A.

rational

The sum of two rational numbers is a rational number.
Ex: Let two rational numbers are $\frac{1}{2}$ and $\frac{1}{3}$Now, $\frac{1}{2}+\frac{1}{3}=\frac{5}{6}$ which is a rational number:

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MCQ 591 Mark

Solution of $2\text{x}-\frac{3}{3\text{x}}-5\geq3$ is:

A
$\big[1,\frac{12}{7}\big]$
✓
$\big(\frac{5}{3},\frac{12}{7}\big]$
C
$\big(-\infty,\frac{5}{3}\big)$
D
$\big[\frac{2}{7},\infty\big)$

Answer

Correct option: B.

$\big(\frac{5}{3},\frac{12}{7}\big]$

$\big(\frac{5}{3},\frac{12}{7}\big]$

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MCQ 601 Mark

If $|2\text{x} – 3|<|\text{x} + 5|,$ then x belongs to:

A
$\big(–3, 5\big)$
B
$\big(5, 9\big)$
✓
$\big(\frac{-2}{3} ,8\big)$
D
$\big(\frac{-8}{2} ,3\big)$

Answer

Correct option: C.

$\big(\frac{-2}{3} ,8\big)$

$\big(\frac{-2}{3} ,8\big)$

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MCQ 611 Mark

If α and $\beta$ are the roots of the equation $\text{x}^2-\text{x}+1=0,$ then a $2009+\beta^{2009}$ is equal to:

A
-2
B
-1
✓
1
D
2

Answer

Correct option: C.

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MCQ 621 Mark

Solution of $\bigg|\text{x}+\frac{1}{\text{x}}\bigg|>2$ is:

A
R – (0)
✓
R – (–1, 0, 1)
C
R – (1)
D
R – (–1, 1)

Answer

Correct option: B.

R – (–1, 0, 1)

R – (–1, 0, 1)

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MCQ 631 Mark

If the cube roots of unity are $1,\omega$ and $\omega^2$, then the roots of the equation $(\text{x} -1)3+8=0,$ are:

A
$-1,1+2\omega,1+2\omega^2$
✓
$-1,1+2\omega,1-2\omega^2$
C
$-1,-1,-1$
D
$-1,-1+2\omega-1-2\omega^2$

Answer

Correct option: B.

$-1,1+2\omega,1-2\omega^2$

$-1,1+2\omega,1-2\omega^2$

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MCQ 641 Mark

Solve: $|\text{x}-1|\leq 5, |\text{x}|\geq2$

A
$[2, 6]$
B
$[-4, -2]$
✓
$[-4, -2]\cup[2, 6]$
D
$\text{None of these}$

Answer

Correct option: C.

$[-4, -2]\cup[2, 6]$

Given, $|\text{x}-1|\leq 5, |\text{x}|\geq2$
$\Rightarrow-(5\leq(\text{x} – 1)\leq5), (\text{x}\leq -2 \text{or} \text{x} \geq 2)$
$\Rightarrow-(4\leq\text{x}\leq6), (\text{x}\leq-2 \text{or}\text{x}\geq 2)$
Now, required solution is.
$\text{x}\in[-4, -2]\cup[2, 6]$

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MCQ 651 Mark

Ordered pair that satisfy the equation x + y + 1 < 0 is:

A
(0, -1)
B
(-2,0)
C
(2, -4)
✓
Both (B) and (C)

Answer

Correct option: D.

Both (B) and (C)

Given inequation is x + y + 1 < 0
From option A, 0 + (-1) + 1 < 0
⇒ 0 < 0 which is false
Hence, (0, -1) is not a solution.
From option B, -2 + 0 + 1 < 0
⇒-1 < 0 which is true
Hence, (-2,0) there is a solution.
From option C, 2 - 4 + 1 < 0
⇒ -1 < 0 which is true.
Hence, (2,-4) is a solution.

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MCQ 661 Mark

Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 40.

✓
(11, 13), (13, 15), (15, 17), (17, 19)
B
(11, 13), (13, 15), (15, 17)
C
(21, 23), (23, 25), (25, 27), (27, 29)
D
(15, 17), (17, 19), (19, 21), (21, 23)

Answer

Correct option: A.

(11, 13), (13, 15), (15, 17), (17, 19)

(11, 13), (13, 15), (15, 17), (17, 19)

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MCQ 671 Mark

Observe the figure given below:

The interval at which the value of x lies is:

A
$\text{x}\in(-\infty,-2)$
✓
$\text{x}\in(-\infty,-2\big]$
C
$\text{x}\in(-2,\infty\big]$
D
$\text{x}\in\big[-2,\infty)$

Answer

Correct option: B.

$\text{x}\in(-\infty,-2\big]$

In the given figure, the circle is filled with dark colour at -2 which means -2 is included and the highlighted is towards the left of -2.
So, $\text{x}\in(-\infty,-2\big]$

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MCQ 681 Mark

If a is an irrational number which is divisible by b then the number b:

A
Must be rational
✓
Must be irrational
C
May be rational or irrational
D
None of these

Answer

Correct option: B.

Must be irrational

If a is an irrational number which is divisible by b then the number b must be irrational.
Ex: Let the two irrational numbers are $\sqrt{2}$ and $\sqrt{3}$ Now, $\sqrt{2}\sqrt{3}=\sqrt{\Big(\frac{2}{3}}\Big)$

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MCQ 691 Mark

If x > 7 then which is impossible?

A
x > 4
✓
x < 6
C
x > 9
D
x < 14

Answer

Correct option: B.

x < 6

x > 7 and 7 > 4 ⇒ x > 7 > 4 => x > 4.
If x > 7 then x cannot be less than 6.
If x = 11 then x > 7 and x > 9.
If x = 11 then x > 7 and x < 14.

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MCQ 701 Mark

Choose the correct answer. If $|\text{x}+2|\leq9,$ then:

A
$\text{x}\in(-7,11)$
✓
$\text{x}\in[-11, 7]$
C
$\text{x}\in[-\infty,-7)\cup(11,\infty) $
D
$\text{x}\in(-\infty,-7)\cup[11,\infty) $

Answer

Correct option: B.

$\text{x}\in[-11, 7]$

Given that $|\text{x}+2|\leq9$
$\Rightarrow-9\leq\text{x}+2\leq9$
$\Rightarrow-9-2\leq\text{x}\leq9-2[|\text{x}\leq\text{a}|]$
$\Rightarrow-11\leq\text{x}\leq7$
$\Rightarrow\text{x}\in[-11, 7]$

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MCQ 711 Mark

Inequations involved in the given region are____________?

A
$2\text{x}+\text{y}\geq6,\text{x}\geq0,\text{y}\geq0$
B
$2\text{x}+\text{y}>,\text{x}\geq0,\text{y}\geq0$
C
$2\text{x}+\text{y}<6,\text{x}\geq0,\text{y}\geq0$
✓
$2\text{x}+\text{y}\leq6,\text{x}\geq0,\text{y}\geq0$

Answer

Correct option: D.

$2\text{x}+\text{y}\leq6,\text{x}\geq0,\text{y}\geq0$

$2\text{x}+\text{y}\leq6,\text{x}\geq0,\text{y}\geq0$

Solution:
Since region involves $1^{st}$ quadrant so $\text{x}\geq0,\text{y}\geq0.$
Two points on line are $(0,6)$ and$(3,0)$
$\frac{(\text{y}-6)}{(0-6)} =\frac{(\text{x}-0)}{(3-0)}$
$\Rightarrow\frac{(\text{y}-6)}{(-6)}=\frac{\text{x}}{3}$
$\Rightarrow\text{y}-6=2\text{x}\Rightarrow2\text{x}+\text{y}=6$
$2\text{x}+\text{y}\leq6$ since $(0,0) $ should also satisfy.
So, $ 2\text{x}+\text{y}\leq6, \text{x}\geq0, \text{y}\geq0.$

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MCQ 721 Mark

If the expression $\big(\text{mx} – 1 +\frac{1}{\text{x}}\big)$is always nonnegative, then the minimum value of m must be:

A
$\frac{-1}{2}$
B
$0$
✓
$\frac{1}{4}$
D
$\frac{1}{2}$

Answer

Correct option: C.

$\frac{1}{4}$

$\frac{1}{4}$

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MCQ 731 Mark

The solution of the function f(x) = |x| > 0 is:

A
R
✓
R – (0)
C
R – (1)
D
R – (-1)

Answer

Correct option: B.

R – (0)

Given, f(x) = |x| > 0
We know that modulus is non negative quantity.
So, x ∈ R except that x = 0
$\Rightarrow\text{x}\in\text{R}-(0)$
This is the required solution

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MCQ 741 Mark

The point which does not belong to the feasible region of the LPP: Minimize: $\text{Z}=60\text{x}+10\text{y}$ subject to $3\text{x}+\text{y}\geq18$ $2\text{x}+2\text{y}\geq12$ $\text{x}+2\text{y}\geq10$ $\text{x,y}\geq0$ is.

A
$(0,8)$
✓
$(4,2)$
C
$(6,2)$
D
$(10,0)$

Answer

Correct option: B.

$(4,2)$

We test whether the inequalities are satishfied or not
$(0,8),3(0)+8\geq 83(0)+8\geq8 8\geq8$ is true.
$2(0)+2(8)=16\geq12$ is true.
$0+2(8)=16\geq10$ is true.
$\therefore(0,8)$ is in the feasible region.
$(4,2), 3(4)+2=14\geq 83(4)+2=14\geq8$
$2(4)+2(2)=16\geq12$
$4+2(2)=8\geq10$ is not true.
$\therefore(4,2)$ is not a point in the feasible region.
$\therefore(2)$ is correct.

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MCQ 751 Mark

If $|\text{x} – 1| > 5$ then:

A
$\text{x}\in(-4,6)$
B
$\text{x}\in\big[-4,6\big]$
✓
$\text{x}\in(-\infty,-4)\cup(6,\infty)$
D
$\text{x}\in\big[-\infty,-4)\cup\big[6,\infty)$

Answer

Correct option: C.

$\text{x}\in(-\infty,-4)\cup(6,\infty)$

$|\text{x} – 1| > 5$
$\text{x} – 1 < - 5 $ and $\text{x} – 1 > - 5 $
$\text{x} < -4 $ and $\text{x} > 6 $
$\therefore\text{x}\in(-\infty,-4)\cup(6,\infty)$

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MCQ 761 Mark

Choose the correct answer. The inequality representing the following graph is:

✓
$|\text{x}|>5$
B
$|\text{x}|\leq5$
C
$|\text{x}|>5$
D
$|\text{x}|\geq5$

Answer

Correct option: A.

$|\text{x}|>5$

The given graph represents
x > -5 and x < 5
Combining the two inequalities
|x| > 5.

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MCQ 771 Mark

If $4\text{x}+3<6\text{x}+7$ then x belongs to the interval:

A
$(2,\infty)$
✓
$(-2,\infty)$
C
$(-\infty, 2)$
D
$(-4,\infty)$

Answer

Correct option: B.

$(-2,\infty)$

$4\text{x}+3<6\text{x}+7$
Subtracting 3 from both sides,
$4\text{x}+3<6\text{x}+7-3$
$\Rightarrow4\text{x}<6\text{x}+4$
Subtracting 6x from both sides,
$4\text{x} – 6\text{x} <6\text{x} + 4 – 6\text{x}$
$\Rightarrow– 2\text{x}<4$ or
$\Rightarrow\text{x}>-2\text{ i.e..,}$ all the real numbers greater than –2, are the solutions of the given inequality.
Hence, the solution set is $(–2,\infty), \text{i}.\text{e}.\text{x}\in(-2,\infty)$

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MCQ 781 Mark

If x and a are real numbers such that a > 0 and |x| > a, then:

A
$\text{x}\in(-\text{a},\infty)$
B
$\text{x}\in[-\infty,\text{a}]$
C
$\text{x}\in(-\text{a},\text{a})$
✓
$\text{x}\in(-\infty,-\text{a})\cup(\text{a},\infty)$

Answer

Correct option: D.

$\text{x}\in(-\infty,-\text{a})\cup(\text{a},\infty)$

If x and a are real numbers such that a > 0.
|x| > a
⇒ x > a or x < −a
$\Rightarrow\text{x}\in(-\infty,-\text{a})\cup(\text{a},\infty)$

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MCQ 791 Mark

If |x| < -5 then the value of x lies in the interval:

A
$(-\infty,-5)$
B
$(\infty,5)$
C
$(-5,\infty)$
✓
$\text{No Solution}$

Answer

Correct option: D.

$\text{No Solution}$

Given, |x| < -5
Now, LHS ≥ 0 and RHS < 0
Since LHS is non-negative and RHS is negative
So, |x| < -5 does not posses any solution

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MCQ 801 Mark

If$(\text{x} – 1)(\text{x}^2 – 5\text{x} + 7)<(\text{x} – 1), $ then x belongs to:

A
$\big(1, 2\big)\cup\big(3,\infty\big)$
B
$\big(2, 3\big)$
✓
$\big(-\infty,1)\cup\big(2, 3\big)$
D
$\text{None of these}$

Answer

Correct option: C.

$\big(-\infty,1)\cup\big(2, 3\big)$

$\big(-\infty,1)\cup\big(2, 3\big)$

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MCQ 811 Mark

The value of a for which one root of the quadratic equation $(\text{a}^2-5\text{a}+3) \text{x}^2+3\text{a}-1)\text{x}+2$ is twice as large as the other, is:

✓
$\frac{2}{3}$
B
$\frac{-2}{3}$
C
$\frac{1}{3}$
D
$\frac{-1}{3}$

Answer

Correct option: A.

$\frac{2}{3}$

$\frac{2}{3}$

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MCQ 821 Mark

The linear inequality representing the solution set given in Fig. is:

A
$\text{|x|}<5$
B
$\text{|x|}>5$
✓
$\text{|x|}\geq5$
D
$\text{|x|}\geq5$

Answer

Correct option: C.

$\text{|x|}\geq5$

As according to the graph,
$x$ lies between $(-\infty,-5]$ and $[5,\infty)$
$\Rightarrow\text{x}\geq5$ or $\text{x}\leq-5$
$\Rightarrow|\text{x}|\geq5$

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MCQ 831 Mark

Solve: $ 1\leq|\text{x} – 1|\leq3$

A
$\big[-2,0\big]$
B
$\big[2,4\big]$
✓
$\big[-2,0\big]\cup\big[2,4\big]$
D
$\text{None of these}$

Answer

Correct option: C.

$\big[-2,0\big]\cup\big[2,4\big]$

Given, $ 1\leq|\text{x} – 1|\leq3$
$\Rightarrow-3\leq(\text{x} – 1)\leq-1 $ or $1\leq(\text{x}-1)\leq3$
i.e. the distance covered is between 1 unit to 3 unit.
$\Rightarrow-2\leq \text{x}\leq0$ or $2\leq\text{x}\leq4$
Hence, the solution set of the given inequality is.
$\text{x}\in\big[-2, 0\big]\cup\big[2, 4\big]$

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MCQ 841 Mark

If $|\text{x} + 2|\leq9,$ then:

A
$\text{x}\in\big(–7, 11\big)$
✓
$\text{x}\in\big[–11, 7\big]$
C
$\text{x}\in\big(-\infty, –7\big)\cup\big(11,\infty\big)$
D
$\text{x}\in\big(-\infty, -7\big)\cup\big[11,\infty\big)$

Answer

Correct option: B.

$\text{x}\in\big[–11, 7\big]$

$\text{x}\in\big[–11, 7\big]$

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MCQ 851 Mark

Given that x, y and b are real numbers and x < y, b < 0, then:

✓
$\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$
B
$\frac{\text{x}}{\text{b}}\leq\frac{\text{y}}{\text{b}}$
C
$\frac{\text{x}}{\text{b}}>\frac{\text{y}}{\text{b}}$
D
$\frac{\text{x}}{\text{b}}\geq\frac{\text{y}}{\text{b}}$

Answer

Correct option: A.

$\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$

$\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$

Solution:
Given that x, y and b are real numbers and x < y, b < 0.
Consider, x < y
Divide both sides of the inequality by “b”
$\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}(\text{since, b<0})$

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MCQ 861 Mark

Solution of $\frac{\text{x}-7}{\text{x}+3}>2$ is:

A
$(– 3,\infty)$
B
$\big(-\infty, –13\big)$
✓
$(-13, –3)$
D
$(– 13, 3)$

Answer

Correct option: C.

$(-13, –3)$

$(-13, –3)$

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MCQ 871 Mark

What is the solution set for $0<−\frac{\text{x}}{2} < 3$

A
$(−6, 6)$
✓
$(−6, 0)$
C
$(0, 6)$
D
$(-\infty, -6)$

Answer

Correct option: B.

$(−6, 0)$

Given: $0<−\frac{\text{x}}{2} < 3$
Multiply by 2 in above inequality (Here 2 is a positive number so the direction of the inequality does not change)
$\Rightarrow0 <-\text{x}<6$
$\Rightarrow−6 <\text{x}<0$
$\therefore\text{x}$ lies in $(−6, 0)$

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MCQ 881 Mark

If $\text{x}\in\text{l},$ the solution set of the inequation $-2\leq\text{x}<3$ is:

✓
−2, −1, 0, 1, 2
B
−1, 0, 1, 2, 3
C
0, 1, 2, 3
D
0, 1, 2

Answer

Correct option: A.

−2, −1, 0, 1, 2

$\text{x}\in\text{l},$ solution set $-2\leq\text{x}<3$
= −2, −1, 0, 1, 2

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MCQ 891 Mark

Solve the following in equations $\frac{2\text{x}+4}{\text{x}-1}\geq5$

A
$\big(1,2\big]$
B
$\big(1,3\big)$
✓
$\big(1,3\big]$
D
$\big(1,4\big]$

Answer

Correct option: C.

$\big(1,3\big]$

$\frac{2\text{x}+4}{\text{x}-1}\geq5$
$\Rightarrow\frac{2\text{x}+4}{\text{x}-1}-5\geq0$
$\Rightarrow\frac{2\text{x}+4-5(\text{x-1})}{\text{x-1}}\geq0$
$\Rightarrow\frac{2\text{x}+4-\text{5x+5}}{\text{x-1}}\geq0$
$\Rightarrow\frac{9-3\text{x}}{\text{x-1}}\geq0$
$\Rightarrow\frac{-3\text{(x-3)}}{\text{x}-1}\geq0$
Multiplying each side of an inequality by a negative number $\big(\frac{-1}{3}\big)$ reverses the direction of the inequality symbol.
$\Rightarrow\frac{(\text{x}-3)}{\text{x}-1}\leq0$ Here $\text{x}-1\neq0\Rightarrow\text{x}\neq1$

Hence the solution set of the given in equations is $\big(1, 3\big]$

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MCQ 901 Mark

Solution of 2x – 1 = |x + 7| is:

A
– 2
✓
8
C
– 2, 8
D
None of these

Answer

Correct option: B.

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MCQ 911 Mark

Let two numbers have arithmetic mean $9$ and geometric mean $4$.Then, these numbers are the roots of the quadratic equation:

A
$x^2+18 x+16=0$
✓
$x^2-18 x+16=0$
C
$x^2+18 x-16=0$
D
$x^2-18 x-16=0$

Answer

Correct option: B.

$x^2-18 x+16=0$

$x^2-18 x+16=0$

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MCQ 921 Mark

Find all pairs of consecutive odd positive integers both of which are smaller than 8 such that their sum is more than 10.

✓
(5, 7)
B
(3, 5), (5, 7)
C
(3, 5), (5, 7), (7, 9)
D
(5, 7), (7, 9)

Answer

Correct option: A.

(5, 7)

Let two numbers be x and x + 2.
x + x + 2 > 10 ⇒ 2x > 8 ⇒ x > 4 and x < 8 and x + 2 < 8 ⇒ x < 6.
4 < x < 6 ⇒ x can be 5.
For x = 5, x + 2 = 7
So, Pairs of odd consecutive positive integers are (5, 7).

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MCQ 931 Mark

The quantity of A and B in one day for which profit will be maximum is:

A
25, 30
B
30, 35
C
25, 25
✓
30, 30

Answer

Correct option: D.

30, 30

30, 30

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MCQ 941 Mark

If both the roots of the quadratic equation $\text{x}^2 -2\text{kx}+\text{k}^2-5=0 $ are less than 5, than k lies in the interval:

A
$\big[4,5\big]$
✓
$\big(-\infty,4\big)$
C
$\big(6,\infty\big)$
D
$\big(5,6\big]$

Answer

Correct option: B.

$\big(-\infty,4\big)$

$\big(-\infty,4\big)$

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MCQ 951 Mark

Given that x, y and b are real numbers and x < y, b > 0, then:

✓
$\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$
B
$\frac{\text{x}}{\text{b}}\leq\frac{\text{y}}{\text{b}}$
C
$\frac{\text{x}}{\text{b}}>\frac{\text{y}}{\text{b}}$
D
$\frac{\text{x}}{\text{b}}\geq\frac{\text{y}}{\text{b}}$

Answer

Correct option: A.

$\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$

Given that x, y and b are real numbers and x < y, b > 0.
Both sides of an inequality can be multiplied or divided by the same positive number.
$\therefore\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$

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MCQ 961 Mark

If – 3x + 17 < – 13, then:

✓
$\text{x}\in(10,\infty)$
B
$\text{x}\in\big[10,\infty)$
C
$\text{x}\in(-\infty,10\big]$
D
$\text{x}\in\big[-10,10)$

Answer

Correct option: A.

$\text{x}\in(10,\infty)$

Given,
-3x + 17 < -13
Subtracting 17 from both sides,
-3x + 17 – 17 < -13 – 17
$\Rightarrow$ -3x < -30
$\Rightarrow$ x > 10 (since the division by negative number inverts the inequality sign)
$\Rightarrow\text{x}\in(10,\infty)$

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MCQ 971 Mark

All the values of $m$ for which both roots of the equation $x^2-2 m x+m^2-1=0$ are greater than -2 but less than 4 lie in the interval:

A
m > 3
✓
-1 < m < 3
C
1 < m < 4
D
– 2 < m < 0

Answer

Correct option: B.

-1 < m < 3

-1 < m < 3

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MCQ 981 Mark

A pack of coffee powder contains a mixture of x gms of coffee and y gms of choco. The amount of coffee powder is greater than that of chocolate and each pack weights at least 10g. Which of the followinginequalities describe the given condition?

A
$\text{x}<\text{y}$
✓
$\text{x}+\text{y}\geq10$
C
$\text{x}+\text{y}\leq10$
D
$\text{x}>\text{y}$

Answer

Correct option: B.

$\text{x}+\text{y}\geq10$

The coffee powder is greater than choco.
hence, $\text{x}>\text{y}$
each pack is at least 10gm.

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MCQ 991 Mark

Solution of $|3-\text{x}| = 3-\text{x} $ is:

A
$\text{x}<3$
B
$\text{x}>3$
C
$\text{x}\geq3$
✓
$\text{x}\leq3$

Answer

Correct option: D.

$\text{x}\leq3$

$\text{x}\leq3$

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MCQ 1001 Mark

If x - 1 > -x + 7 then which is true?

✓
x > 4
B
x < 4
C
x > 2
D
x < 2

Answer

Correct option: A.

x > 4

x - 1 > -x + 7
⇒ 2x > 8 ⇒ x > 4.

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MCQ 1011 Mark

x and b are real numbers.If $\text{b}>0$ and $|\text{x}|>\text{b},$ then:

A
$\text{x}\in\big(–\text{b},\infty\big)$
B
$\text{x}\in\big(-\infty,\text{b}\big)$
C
$\text{x}\in\big(–\text{b}, \text{b}\big)$
✓
$\text{x}\in(-\infty, –\text{b}\big)\cup\big(\text{b},\infty\big)$

Answer

Correct option: D.

$\text{x}\in(-\infty, –\text{b}\big)\cup\big(\text{b},\infty\big)$

$\text{x}\in(-\infty, –\text{b}\big)\cup\big(\text{b},\infty\big)$

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MCQ 1021 Mark

If $–8\leq5\text{x} – 3<7,$ then $\text{x}\in$

A
$\big(–1, 2\big)$
✓
$\big[–1, 2\big)$
C
$\big[–2,\infty\big)$
D
$\big[-2,0\big)$

Answer

Correct option: B.

$\big[–1, 2\big)$

$\big[–1, 2\big)$

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MCQ 1031 Mark

If Ram has x rupees and he pay 40 rupees to shopkeeper then find range of x if amount of money left with Ram is at least 10 rupees is given by inequation, ___?

A
x ≥ 10
B
x ≤ 10
C
x ≤ 50
✓
x ≥ 50

Answer

Correct option: D.

x ≥ 50

Amount left is at least 10 rupees i.e.amount left ≥ 10.
x - 40 ≥ 10 ⇒ x ≥ 50.

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MCQ 1041 Mark

Consider the linear inequations and solve them graphically: $3\text{x−y}-2>0,\text{x+y}\leq4:\text{x}>0\text{y}\geq0$ Which of the following points belong to the feasible solution region?

A
$\Big(\frac{1}{2},0\Big)$
B
$\Big(\frac{1}{2},\frac{1}{2}\Big)$
C
$\Big(\frac{3}{2},\frac{5}{2}\Big)$
✓
$\text{None of the above }$

Answer

Correct option: D.

$\text{None of the above }$

$\text{None of the above }$

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MCQ 1051 Mark

Choose the correct answer. If |x - 1| > 5, then:

A
$\text{x}\in(-4, 6)$
B
$\text{x}\in[-4,6]$
✓
$\text{x}\in[-\infty,-4)\cup(6,\infty) $
D
$\text{x}\in[-\infty,-4)\cup[6,\infty) $

Answer

Correct option: C.

$\text{x}\in[-\infty,-4)\cup(6,\infty) $

Given that |x - 1| > 5
⇒ (x - 1) < -5 or (x - 1) > 5
⇒ x < -5 + 1 or x > 5 + 1
⇒ x < -4 or x > 6
$\Rightarrow\text{x}\in[-\infty,-4)\cup(6,\infty) $

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MCQ 1061 Mark

The inequality $\frac{2}{\text{x}}<3$ is true, when x belongs to:

A
$\big[\frac{2}{3},\infty\big) $
B
$\big(-\infty,\frac{2}{3}\big)$
✓
$\big(-\infty ,0\big)\cup\big(\frac{2}{3},\infty\big) $
D
$\text{None of these}$

Answer

Correct option: C.

$\big(-\infty ,0\big)\cup\big(\frac{2}{3},\infty\big) $

$\big(-\infty ,0\big)\cup\big(\frac{2}{3},\infty\big) $

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MCQ 1071 Mark

If $7\text{x}+3<5\text{x}+9$ then $\text{x}\in$

A
$\big(-\infty, 3\big]$
B
$\big(-\infty,\infty\big)$
✓
$\big(-\infty, 3\big)$
D
$\big[3,\infty\big)$

Answer

Correct option: C.

$\big(-\infty, 3\big)$

$\big(-\infty, 3\big)$

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MCQ 1081 Mark

If $\frac{\text{x} – 2}{\text{x} + 5}> 2 ,$ then $\text{x}\in$

A
(–12, 5)
✓
(–12, –5)
C
(–5, 12)
D
(5, 12)

Answer

Correct option: B.

(–12, –5)

(–12, –5)

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MCQ 1091 Mark

Solution of $\text{l}1 +\frac{3}{\text{xl}}> 2 $ is:

A
$\big(0, 3\big]$
B
$\big[-1,0\big)$
✓
$\big(-1, 0\big)\cup\big(0, 3\big)$
D
$\text{None of these}$

Answer

Correct option: C.

$\big(-1, 0\big)\cup\big(0, 3\big)$

$\big(-1, 0\big)\cup\big(0, 3\big)$

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MCQ 1101 Mark

Solving $ – 8 \leq 5\text{x} – 3<7, $ we get:

A
$\frac{–1}{2}\leq \text{x}\leq 2$
B
$1\leq \text{x}<2$
✓
$ –1\leq\text{x}<2$
D
$ –1<\text{x}\leq2$

Answer

Correct option: C.

$ –1\leq\text{x}<2$

Given,
$-8\leq5\text{x}-3$ and $5\text{x}-3<7$
Let us solve these two inequalities simultaneously.
$-8\leq5\text{x}-3$ and $5\text{x}-3<7$ can be written as:
$– 8\leq5\text{x} –3 < 7$
Adding 3, we get
$– 8 + 3\leq5\text{x}-3+3<7+3$
$–5\leq5\text{x}<10$
Dividing by 5, we get
$–1\leq\text{x}<2$

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MCQ 1111 Mark

The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160cm, then:

A
breadth > 20cm
B
length < 20cm
✓
breadth ≥ 20cm
D
length ≤ 20cm

Answer

Correct option: C.

breadth ≥ 20cm

breadth ≥ 20cm

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MCQ 1121 Mark

Number of integral solutions satisfy inequality $|\text{x-3}|-|2\text{x}+5|\geq|\text{x}+8|$

A
5
✓
6
C
7
D
8

Answer

Correct option: B.

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MCQ 1131 Mark

If $x>7$ then $-x>-7$ is, ___________?

A
possible
✓
certainly false
C
certainly true
D
depend on x

Answer

Correct option: B.

certainly false

certainly false

Solution:
If we multiply by negative number on both sides of inequality then,
sign of inequality will change i.e. if $x>7$ then $(-1) x<(-1)^7 \Rightarrow-x<-7$.

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MCQ 1141 Mark

If the equations $\text{x}^2+2\text{x}+3=0 $ and $\text{ax}^2+\text{bx}+\text{c}=0,\text{abc}\in\text{R},$ I have a common root, then a : b : c is.

✓
1 : 2 : 3
B
3 : 2 : 1
C
1 : 3 : 2
D
3 : 1 : 2

Answer

Correct option: A.

1 : 2 : 3

1 : 2 : 3

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MCQ 1151 Mark

If $\frac{\text{lx}-2\text{l}}{\text{x}-2}\geq0$ then, $\text{x}\in$

A
$\big[2,\infty\big)$
✓
$\big(2,\infty\big)$
C
$\big(\infty, 2\big)$
D
$\big(-\infty, 2\big]$

Answer

Correct option: B.

$\big(2,\infty\big)$

$\big(2,\infty\big)$

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MCQ 1161 Mark

If x is a positive integer and 20 x < 100 then find solution set of x.

A
(0, 1, 2, 3, 4, 5)
B
(1, 2, 3, 4, 5)
✓
(1, 2, 3, 4)
D
(0, 1, 2, 3, 4)

Answer

Correct option: C.

(1, 2, 3, 4)

$20\text{x}<100$
Dividing by 20 on both sides, $\text{x}<\Big(\frac{100}{20}\Big)\Rightarrow\text{x}<5$
Since x is a positive integer so x = 1, 2, 3, 4.

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MCQ 1171 Mark

Choose the correct answer. x and b are real numbers. If b > 0 and |x| > b, then:

A
$\text{x}\in(-\text{b},\infty)$
B
$\text{x}\in(\infty,-\text{b})$
C
$\text{x}\in(-\text{b},\text{b})$
✓
$\text{x}\in(-\infty,-\text{b})\cup(\text{b},\infty)$

Answer

Correct option: D.

$\text{x}\in(-\infty,-\text{b})\cup(\text{b},\infty)$

Given that |x| > b, b > 0
⇒ x < -b or x > b
$\Rightarrow\text{x}\in(-\infty,-\text{b})\cup(\text{b,}\infty)$

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MCQ 1181 Mark

Solve: $2\text{x}+1>3$

A
$\big[-1,\infty\big]$
✓
$(1,\infty)$
C
$(\infty,\infty)$
D
$(\infty,1)$

Answer

Correct option: B.

$(1,\infty)$

Given, $2\text{x}+1>3$
$\Rightarrow2\text{x}>3-1$
$\Rightarrow2\text{x}>2$
$\Rightarrow\text{x}>1$
$\Rightarrow\text{x}\in(1,\infty)$

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MCQ 1191 Mark

If 2x + 1 > 5 then which is true?

A
x > 4
B
x < 4
✓
x > 2
D
x < 2

Answer

Correct option: C.

x > 2

2x + 1 > 5
⇒ 2x > 5 - 1
⇒ 2x > 4 ⇒ x > 2.

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MCQ 1201 Mark

If $1\leq|\text{x} -2|\leq3,$ then $\text{x}\in$

A
$\big[–1, 5\big]$
✓
$\big[–1, 1\big]\cup\big[3, 5\big]$
C
$\big(–1, 0\big)\cup\big(2, 5\big)$
D
$\big(–1, 5\big)$

Answer

Correct option: B.

$\big[–1, 1\big]\cup\big[3, 5\big]$

$\big[–1, 1\big]\cup\big[3, 5\big]$

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MCQ 1211 Mark

If $x^2<4$ then the value of $x$ is:

A
(0, 2)
✓
(-2, 2)
C
(-2, 0)
D
None of these

Answer

Correct option: B.

(-2, 2)

(-2, 2)

Solution:
$\text { Given, } x^2<4$
$\Rightarrow x^2-4<0$
$\Rightarrow(x-2) \times(x+2)<0$
$\Rightarrow-2<x<2$
$\Rightarrow x \in(-2,2)$

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MCQ 1221 Mark

Solve: $\frac{-1}{(|\text{x}| – 2)}\geq1$ where $\text{x}\in\text{R}, \text{x}\neq\pm2$

A
$(-2, -1)$
B
$(-2, 2)$
✓
$(-2, -1)\cup(1, 2)$
D
$\text{None of these}$

Answer

Correct option: C.

$(-2, -1)\cup(1, 2)$

Given, $\frac{-1}{(|\text{x}| – 2)}\geq1$
$\Rightarrow\frac{-1}{(|\text{x}|-2) -1}\geq0$
$\Rightarrow\frac{-1 – (|\text{x}| – 2)}{(|\text{x}| – 2)}\geq0$
$\Rightarrow\frac{1 – |\text{x}|}{(|\text{x}| – 2)}\geq0$
$\Rightarrow\frac{-(|\text{x}| – 1)}{(|\text{x}| – 2)}\geq0$

Using number line rule:
$1\leq |\text{x}|<2$
$\Rightarrow\text{x}\in(-2, -1)\cup(1, 2)$

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MCQ 1231 Mark

Which of the following statements is correct:

✓
If x > y and b < 0, then bx < by
B
If x > y, then x > 0 and y < 0
C
If xy < 0, then x > 0 and y > 0
D
All of these

Answer

Correct option: A.

If x > y and b < 0, then bx < by

If x > y and b < 0, then bx < by

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MCQ 1241 Mark

Rahul obtained 20 and 25 marks in first two tests.Find the minimum marks he should get in the third test to have an average of at least 30 marks.

A
60
B
35
C
180
✓
45

Answer

Correct option: D.

Average is at least 30 marks.
Let x be the marks in $3^\text{rd}$ test.
Average $=\frac{(20+25+\text{x})}{3}\geq30$
$\Rightarrow45+\text{x}\geq90\Rightarrow\text{x}\geq90-45\Rightarrow\text{x}\geq45.$
Minimum marks in $3^\text{rd}$ test should be 45.

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MCQ 1251 Mark

If $|\text{x}| = -5$ then the value of x lies in the interval:

A
$(-5,\infty)$
B
$(5,\infty)$
C
$(\infty,-5)$
✓
$\text{No Solution}$

Answer

Correct option: D.

$\text{No Solution}$

Given, |x| = -5
Since |x| is always positive or zero.
So, it can not be negative.
Hence, given inequality has no solution.

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MCQ 1261 Mark

If $-2<2\text{x}-1<2$ then the value of x lies in the interval:

A
$\Big(\frac{1}{2},\frac{3}{2}\Big)$
✓
$\Big(\frac{-1}{2},\frac{3}{2}\Big)$
C
$\Big(\frac{3}{2},\frac{1}{2}\Big)$
D
$\Big(\frac{3}{2},\frac{-1}{2}\Big)$

Answer

Correct option: B.

$\Big(\frac{-1}{2},\frac{3}{2}\Big)$

Given, $-2<2\text{x}-1<2$
$\Rightarrow2+1< 2\text{x}<2+1$
$\Rightarrow-1<2\text{x}<3$
$\Rightarrow\frac{-1}{2}<\text{x}<\frac{3}{2}$
$\Rightarrow\text{x}\in\Big(\frac{-1}{2},\frac{3}{2}\Big)$

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MCQ 1271 Mark

If the roots of the quadratic equation $x^2+p x+q=0$ are $\tan 30^{\circ}$ and $\tan 15^{\circ}$ then the value of $2+q-p$ is:

✓
3
B
0
C
1
D
2

Answer

Correct option: A.

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MCQ 1281 Mark

Consider the linear inequations and solve them graphically: $3\text{x−y}-2>0,\text{x+y}\leq4:\text{x}>0\text{y}\geq0$ Which of the following points belong to the feasible solution region?

A
$\Big(\frac{1}{2},0\Big)$
B
$\Big(\frac{1}{2},\frac{1}{2}\Big)$
C
$\Big(\frac{3}{2},\frac{5}{2}\Big)$
✓
$\text{None of the above }$

Answer

Correct option: D.

$\text{None of the above }$

$\text{None of the above }$

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MCQ 1291 Mark

If $\frac{\text{lx}-2\text{l}}{\text{x}-2}\geq0$ then, $\text{x}\in$

A
$\big[2,\infty\big)$
✓
$\big(2,\infty\big)$
C
$\big(\infty, 2\big)$
D
$\big(-\infty, 2\big]$

Answer

Correct option: B.

$\big(2,\infty\big)$

$\big(2,\infty\big)$

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MCQ 1301 Mark

The marks obtained by a student of Class XI in first and second terminal examination are 62 and 48, respectively.Find the minimum marks he should get in the annual examination to have an average of at least 60 marks.

A
50
B
60
✓
70
D
80

Answer

Correct option: C.

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MCQ 1311 Mark

The inequality representing the following graph is:

A
$\text{|x|}<3$
✓
$\text{|x|}\leq3$
C
$\text{|x|}>3$
D
$\text{|x|}\geq3$

Answer

Correct option: B.

$\text{|x|}\leq3$

As according to the graph,
x lies between −3 and 3
$\Rightarrow-3\leq\text{x}\leq3$
$\Rightarrow|\text{x}|\leq3$

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MCQ 1321 Mark

Solution of $0<|3\text{x}+1\big|<\frac{1}{3} $ is:

A
$\bigg(\frac{-4}{9},\frac{2}{9}\bigg)$
B
$\bigg[\frac{-4}{9},\frac{-2}{9}\bigg]$
✓
$\bigg(\frac{-4}{9},\frac{2}{9}\bigg)-\bigg(\frac{-1}{3}\bigg)$
D
$\bigg[\frac{-4}{9},\frac{-2}{9}\bigg]-\bigg(\frac{-1}{3}\bigg)$

Answer

Correct option: C.

$\bigg(\frac{-4}{9},\frac{2}{9}\bigg)-\bigg(\frac{-1}{3}\bigg)$

$\bigg(\frac{-4}{9},\frac{2}{9}\bigg)-\bigg(\frac{-1}{3}\bigg)$

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MCQ 1331 Mark

Choose the correct answer. Given that x, y and b are real numbers and x < y, b < 0, then:

A
$\frac{\text{x}}{\text{b}}<\frac{\text{y}}{\text{b}}$
B
$\frac{\text{x}}{\text{b}}\leq\frac{\text{y}}{\text{b}}$
✓
$\frac{\text{x}}{\text{b}}>\frac{\text{y}}{\text{b}}$
D
$\frac{\text{x}}{\text{b}}\geq\frac{\text{y}}{\text{b}}$

Answer

Correct option: C.

$\frac{\text{x}}{\text{b}}>\frac{\text{y}}{\text{b}}$

Given that x < y, b < 0
$\Rightarrow\frac{\text{x}}{\text{b}}>\frac{\text{y}}{\text{b}},\text{b}<0$

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MCQ 1341 Mark

The sum of four numbers in $AP$ is $20.$ The numbers are such that the ratio of the product of first and fourth is to the product of second and third as $2 : 3.$ The greatest number is:

✓
$8$
B
$7$
C
$14$
D
$4$

Answer

Correct option: A.

$8$

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MCQ 1351 Mark

The set of values of x which satisfy the inequations $5\text{x}+2<3\text{x}+8$ and $\text{x}+\frac{\text{x}+2}{\text{x}-1}<4$ is:

A
$(-\infty, 1)$
B
$(2, 3)$
C
$\big(-\infty, 3)$
✓
$(-\infty, 1)\cup(2, 3)$

Answer

Correct option: D.

$(-\infty, 1)\cup(2, 3)$

$(-\infty, 1)\cup(2, 3)$

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MCQ 1361 Mark

If $\text{x}^2<-4$ then the value of x is:

A
$(-2,2)$
B
$(2,\infty)$
C
$(-2,\infty)$
✓
$\text{No solution}$

Answer

Correct option: D.

$\text{No solution}$

Given, $\text{x}^2<-4$
$\Rightarrow\text{x}^2+4<0$
Which is not possible.
So, there is no solution.

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MCQ 1371 Mark

If $\frac{\big[\text{x} – 7\big]}{(\text{x} – 7)\geq 0}$ then:

A
$\text{x}\in\big[7,\infty)$
✓
$\text{x}\in(7,\infty)$
C
$\text{x}\in(\infty, 7)$
D
$\text{x}\in(-\infty, 7)$

Answer

Correct option: B.

$\text{x}\in(7,\infty)$

Given,
$\frac{|\text{x}-7|}{(\text{x}-7)}\geq0$
This is possible when $\text{x}-7\geq0,$ and $\text{x}-7\neq0.$
Here, $\text{x}\geq7$ but $\text{x}\neq7$
Therefore, $\text{x}> 7, \text{i}.\text{e}. \text{x}\in(7,\infty).$

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MCQ 1381 Mark

If $3\text{x}-7<5+\text{x},11-5\text{x}\leq1,$, then $\text{x}\in$

A
$\big[2, 6\big]$
B
$\big[–2, 6\big]$
✓
$\big[2,6\big)$
D
$\big(-2,6\big)$

Answer

Correct option: C.

$\big[2,6\big)$

$\big[2,6\big)$

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MCQ 1391 Mark

If $|\text{x} + 3|\geq10,$ then:

A
$\text{x}\in(-13,7\big)$
B
$\text{x}\in(-13,7\big]$
C
$\text{x}\in(-\infty -13\big]\cup \big[7,\infty)$
✓
$\text{x}\in\big[-\infty -13\big]\cup \big[7,\infty)$

Answer

Correct option: D.

$\text{x}\in\big[-\infty -13\big]\cup \big[7,\infty)$

$|\text{x} + 3|\geq10$
$\Rightarrow\text{x} + 3\leq-10$ or $\text{x}+3\geq10$
$\Rightarrow\text{x}\leq -13 $ or $\text{x}\geq7$
$\Rightarrow\text{x}\in\big[-\infty -13\big]\cup \big[7,\infty)$

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MCQ 1401 Mark

The cost and revenue functions of a product are given by C(x) = 20x + 4000 and R(x) = 60x + 2000, respectively, where x is the number of items produced and sold. How many items must be sold to realise some profit?

A
Less than 40
✓
More than 50
C
Less than 50
D
Exactly 50

Answer

Correct option: B.

More than 50

More than 50

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MCQ 1411 Mark

Choose the correct answer. If – 3x + 17 < – 13, then:

✓
$\text{x}\in(10, \infty)$
B
$\text{x}\in[10, \infty)$
C
$\text{x}\in(-\infty\text{j},10]$
D
$\text{x}\in[-10, 10)$

Answer

Correct option: A.

$\text{x}\in(10, \infty)$

Given that - 3x + 17 < - 13
⇒ - 3x < - 17 - 13
⇒ -3x < - 30
⇒ 3x > 30
⇒ x > 10
$\Rightarrow\text{x}\in(10, \infty)$

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MCQ 1421 Mark

Solve: $2\text{x}+1>3$

A
$\big[1,1\big)$
✓
$\big(1,\infty\big)$
C
$\big(\infty,\infty\big)$
D
$\big(\infty, 1\big)$

Answer

Correct option: B.

$\big(1,\infty\big)$

Given, $2\text{x}+1>3$
$\Rightarrow2\text{x}>3-1$
$\Rightarrow2\text{x}>2$
$\Rightarrow\text{x}>1$
$\Rightarrow\text{x}\in\big(1,\infty\big)$

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MCQ 1431 Mark

y < -2 involves region are, ____________?

A
above dotted line y = -2
✓
below dotted line y = -2
C
above complete line y = -2
D
below complete line y = -2

Answer

Correct option: B.

below dotted line y = -2

y < -2 does not satisfy (0, 0) so, region is below y = -2.
Since only inequality sign given, so dotted line y = -2.

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MCQ 1441 Mark

Value of i(iota) is, ____________?

A
$-1$
B
$1$
✓
$(-1)^\frac{1}{2}$
D
$(-1)^\frac{1}{4}$

Answer

Correct option: C.

$(-1)^\frac{1}{2}$

Explanation: Iota is used to denote complex number.
The value of i (iota) is $\sqrt{-1}\text{ i.e.}(-1)^\frac{1}{2}$

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MCQ 1451 Mark

Find the number of real numbers in the solution set of following $\frac{2\text{x}}{5}+1<-3.$

A
10
B
11
C
9
✓
Infinite

Answer

Correct option: D.

Infinite

$\frac{2\text{x}}{5}+1<-3.$
$\frac{2\text{x}}{5}<-3-1$
$2\text{x}<-4\times5$
$\text{x}<-\frac{20}{2}$
$\text{x}<-10$
As we know the number of rational numbers on either side of a number on the number line is infinite.
$\therefore$ set x = (infinite number of integers which are < - 10)

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MCQ 1461 Mark

Formulate the equations for the above problem.(x and y are the number of units of A and B manufactured in a day respectively)

A
$15\text{x}+5\text{y}\leq10:24\text{x}+14\text{y}\geq1000$
✓
$15\text{x}+5\text{y}\leq600:24\text{x}+14\text{y}\geq1000$
C
$15\text{x}+15\text{y}\leq600:24\text{x}+14\text{y}\geq1000$
D
$15\text{x}+15\text{y}\leq10:24\text{x}+14\text{y}\geq1000$

Answer

Correct option: B.

$15\text{x}+5\text{y}\leq600:24\text{x}+14\text{y}\geq1000$

$15\text{x}+5\text{y}\leq600:24\text{x}+14\text{y}\geq1000$

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MCQ 1471 Mark

x > 5 is, _____________________?

A
double inequality
B
quadratic inequality
C
numerical inequality
✓
literal inequality

Answer

Correct option: D.

literal inequality

Since a variable ‘x’ is compared with number ‘5’ with inequality sign so it is called literal inequality.

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