MCQ

MCQ 11 Mark

If $0 < x < 1$ then which of the following is greatest

A
$x$
B
$x^2$
C
$\frac{1}{x}$
✓
$\frac{1}{x^2}$

Answer

Correct option: D.

$\frac{1}{x^2}$

(D) $\frac{1}{x^2}$
Explanation: $0 < x < 1$
between 0 and 1, $x^2$$< x < 1$
$\frac{1}{x^2}>\frac{1}{x}>1$, also, $1>x>0$$\quad$$\quad$ (given)
Therefore, $\frac{1}{x^2}>\frac{1}{x}>1>x>0$
Thus, $\frac{1}{x^2}$ is greatest.

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MCQ 21 Mark

If $\text{B} >\text{A},$ then which expression will have the highest value, given that A and B are positive integers.

A
$A - B$
B
$A\times B$
C
$A + B$
✓
Can't say

Answer

Correct option: D.

Can't say

(D) Can't say
Explanation: As, $B > A$
$\Rightarrow$ $A < B$
$\Rightarrow$ $A - B < 0$
$A + B > 0$ and $AB > 0$
If $A = 1, B = 4$ then, $AB < A + B$
If $A = 2, B = 4$ then, $AB > A + B$
Thus, we can't say which one of $A + B$ and $AB$ has higher value.

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MCQ 31 Mark

The solution set of the inequation $|x+2| \leq 5$ is:

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

Answer

Correct option: B.

[-7, 3]

(B) [-7,3]
Explanation: $|x+2| \leq 5$
$\Rightarrow$ $-5 \leq x+2 \leq 5$ $\quad$$[\because|x| \leq a$, then $-a \leq x \leq a]$
$\Rightarrow$ $-5-2 \leq x \leq 5-2$
$\Rightarrow$ $-7 \leq x \leq 3$
$\Rightarrow$ $x \in[-7,3]$

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MCQ 41 Mark

Pipe A can fill a tank 6 times faster than a pipe B. If B can fill a tank in 21 minutes, then the time taken by both the pipes together to fill the tank is:

✓
3 minutes
B
$4 \frac{1}{2}$ minutes
C
7 minutes
D
9 minutes

Answer

Correct option: A.

3 minutes

(A) 3 minutes
Explanation: Given, slower pipe filled the tank in 21 minutes.
Then faster pipe filled the tank in $\frac{21}{6}$ minutes
Thus, tank filled by both the pipes in 1 minute
$=\frac{1}{21}+\frac{6}{21}=\frac{7}{21}=\frac{1}{3}$
Hence, time taken by both pipes together to fill the tank is 3 minutes.

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MCQ 51 Mark

20 litres of a mixture contains milk and water in the ratio $3 : 1.$ The amount of milk, in litres, to be added to the mixture so as to have milk and water in the ratio $4 : 1,$ is:

A
7
B
4
✓
5
D
6

Answer

Correct option: C.

(C) 5
Explanation: In $20 l$ of mixture,
Quantity of milk = $\frac{3}{4} \times 20=15 l$
Quantity of water = $\frac{1}{4} \times 20=5 l$
Let the quantity of milk added be $x l$.
According to be question,
$\frac{15+x}{5}=\frac{4}{1}$
$\Rightarrow$ $15 + x = 20$
$\Rightarrow$ $x=5 l$

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MCQ 61 Mark

The solution of $\frac{x-3}{x+5}>0, x \neq-5, x \in R$ is:

A
$x>3$
B
$x<-5$
C
$x<-5$ or $x>3$
D
no solution

Answer

(C) $x < - 5$ or $x > 3$
Explanation: Given, $\frac{x-3}{x+5}>0, x \neq-5$
Multiply by $(x+5)^2$
$(x + 5)(x - 3) > 0$

$\therefore$ Solution $(-\infty,-5) \cup(3, \infty)$
$\text {or}\quad x < - 5$
$\quad\quad x > 3$

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MCQ 71 Mark

Pipe A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the time taken to fill the tank is:

A
2 hours
B
$2 \frac{3}{4}$ hours
C
3 hours
✓
$3 \frac{9}{17}$ hours

Answer

Correct option: D.

$3 \frac{9}{17}$ hours

(D) $3 \frac{9}{17}$ hours
Explanation: Here, LCM of 5, 6 and 12 is 60.
i.e., LCM(5, 6, 12) = 60
Suppose capacity of the tank is 60 $l$
Then, quantity filled by pipe A in $1 hr =\frac{60}{5}=12 l$
Quantity filled by pipe B in $1 hr =\frac{60}{6}=10 l$
Quantity emptied by pipe C in $1 hr =\frac{60}{12}=5 l$
So, quantity filled by all three pipes in 1 hr
$\begin{array}{l}=(12+10-5) l \\ =17 l\end{array}$
Required time $=\frac{60}{17}=3 \frac{9}{17}$ hours

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MCQ 81 Mark

In a 2 km race, P can give Q a start of 200 m and R a start of 560 m. Then in the same race, Q can give R a start of:

A
360 m
B
380 m
C
400 m
D
430 m

Answer

(C) 400 m
Explanation: Let P is complete the race 2000 m
and Q is at 1800 m
and R is at 1440 m
$\Rightarrow$ In a race of 1800 m

Q gives R a start at = 1800 $-$ 1440
= 360
$\Rightarrow$ 1 m race =$\frac{360}{1800}$
$\Rightarrow$ 2000 m race =$\frac{360}{1800} \times 2000$
= 400 m

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MCQ 91 Mark

If a man rows 32 km downstream and 14 km upstream in 6 hours each, then the speed of the stream is:

A
2 km/h
✓
1.5 km/h
C
2.5 km/h
D
2.25 km/h

Answer

Correct option: B.

1.5 km/h

(B) 1.5 km/h
Explanation: Upstream speed = $\frac{14}{6} km / h$
Downstream speed = $\frac{32}{6} km / h$
Speed of the stream = $\frac{\frac{32}{6}-\frac{14}{6}}{2}=\frac{\frac{18}{6}}{2}$
$=\frac{18}{6 \times 2}=\frac{3}{2}$
= 1.5km / h

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MCQ 101 Mark

In a 1000 m race, A can beat B by 100 m. In a race of 400 m, B can beat C by 40 m. In a race of 500 m by what margin will A beat C.

✓
95 m
B
85 m
C
75 m
D
55 m

Answer

Correct option: A.

95 m

(A) 95 m
Explanation: $A : B = 1000:900,$
$B : C = 400:360$
$= 100:90$
$= 900:810$
$\Rightarrow$ $A:B: C = 1000:900 : 810$
$\Rightarrow$ $A: C = 1000:810$
$\Rightarrow$ $A: C = 500:405$
$\Rightarrow$ In a 500 m race,
A beats C by $(500-405) \text{m} = 95$

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MCQ 111 Mark

In what ratio water is mixed with milk to gain $16 \frac{2}{3} \%$ on selling the mixture at cost price?

A
$1:6$
B
$6:1$
C
$2:3$
D
$3:2$

Answer

(A) $1:6$
Explanation: Let C.P. of 1 litre milk be ₹ 1.
S.P. of 1 litre of mixture = ₹ 1, Gain $=\frac{50}{3} \%$
$\therefore$ C.P. of 1 litre of mixture $=\left(100 \times \frac{3}{350} \times 1\right)$
$=\frac{6}{7}$

By the rule of alligation, we have
$\therefore$ Ratio of water and milk $=\frac{1}{7}: \frac{6}{7}=1: 6.$

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MCQ 121 Mark

The following graph represents the inequality.

A
$x > - 5$
B
$x < 5$
✓
$|x| < 5$
D
$|x| < - 5$

Answer

Correct option: C.

$|x| < 5$

(C) $|x| < 5$
Explanation: The given graph represents $x > - 5$ and $x < 5$ combining the two inequalities $|x| < 5.$

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MCQ 131 Mark

Speed of river is 6 km/hr. Speed of a motorboat in still water is 30 km/hr. How much distance can it cover downstream in 24 minutes?

A
9.8 km
B
12 km
C
12.8 km
✓
14.4 km

Answer

Correct option: D.

14.4 km

(D) $14.4$ km
Explanation: Distance $=$ Speed $\times$ Time
$X + Y = 30 + 6 = 36$ km/hr
$24$ minutes $=\frac{24}{60}$ hours
Distance $=36 \times \frac{24}{60}=14.4$ km

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MCQ 141 Mark

A and B can cover a 200 m race in 22 seconds and 25 seconds respectively. When A finished the race, the B is at what distance from the finishing line ?

✓
24 m
B
30 m
C
48 m
D
54 m

Answer

Correct option: A.

24 m

(A) 24 m
Explanation: Distance covered by B in 25 s
= 200m
Distance covered by B in 22 s
$=\left(\frac{200}{25} \times 22\right) m$
= 176m
$\therefore$ B was at a distance of $(200-176)$ m $= 24$ m from the finishing line.

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MCQ 151 Mark

In a one-kilometre race, A, B and C are three participants. A can give B start of 50 m and C a start of 69 m. The start, which B can allow C, is:

A
17 m
B
18 m
C
19 m
✓
20 m

Answer

Correct option: D.

20 m

(D) 20 m
Explanation: $A:B:C$
$= (1000 : (1000 - 50) : (1000 - 69)$
$= (1000:950) : 931$
In a 950 m race, B can give C a start of $(950-931)$ m
= 19 m
In a 1000 m race. B can give C a start of =$\left(\frac{19}{950} \times 1000\right)$
= 20 m

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MCQ 161 Mark

A team played 40 games in a season and won in 24 of them. What percent of games played did the team win?

A
$70\%$
B
$40\%$
✓
$60\%$
D
$35\%$

Answer

Correct option: C.

$60\%$

(C) $60\%$
Explanation: Number of games played $= 40$
Number of games won $= 24$
Percentage of games played
$=\left(\frac{24}{40} \times 100\right)$
$= 60\%$

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MCQ 171 Mark

There is a leak at the bottom of a cistern. Due to this it takes 8 hours to fill the cistern. Had there not been a leak, it would take one hour less to fill the cistern. How much time does it take for the leak to completely empty the cistern?

A
48 hours
B
$55 \frac{1}{3}$ hours
✓
56 hours
D
15 hours

Answer

Correct option: C.

56 hours

(C) 56 hours
Explanation: Normally, cistern gets filled in one hour less than 8 hours that means 7 hours.
So in 1 hour it fills $=\frac{1}{7}$ part
Due to leak, it takes 8 hours. So in 1 hour it actually fills $=\frac{1}{8}$ part
$\therefore$ Water removed by the leak in 1 hour
$=\frac{1}{7}-\frac{1}{8}=\frac{1}{56}$
$\therefore$ Leak empties the tank in 56 hours.

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MCQ 181 Mark

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains $25\%.$ The percentage of water in the mixture is:

A
$4\%$
B
$6\%$
✓
$20\%$
D
$25\%$

Answer

Correct option: C.

$20\%$

(C) $20\%$
Explanation: Let C.P. of 1 litre milk be ₹ 1
Then, S.P. of 1 litre of mixture = ₹ 1,
Gain $= 25\%$
C.P. of 1 litre mixture =₹$\left(\frac{100}{125} \times 1\right)=\frac{4}{5}$
By the rule of alligation, we have:

$\therefore$ Ratio of milk to water $=\frac{4}{5}: \frac{1}{5}=4: 1$
Hence, percentage of water in the mixture
$=\left(\frac{1}{5} \times 100\right) \%=20 \%.$

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MCQ 191 Mark

In what ratio must a grocer mix two varieties of pulses costing ₹ 15 and ₹ 20 per kg respectively so as to get a mixture worth ₹ 16.50 kg?

A
$3:7$
B
$5:7$
C
$7:3$
D
$7:5$

Answer

$\therefore$ Required rate $= 3.50:1.50= 7:3.$

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MCQ 201 Mark

If x is a real number and $|x| < 3,$ then

A
$x \geq 3$
✓
$-3 < x < 3$
C
$x \leq-3$
D
$-3 \leq x \leq 3$

Answer

Correct option: B.

$-3 < x < 3$

(B) $- 3 < x < 3$
Explanation: Given, $|x| < 3 \Rightarrow -3 < x < 3$
$[\text {Since,} |x| < a \Rightarrow -a < x < a]$

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MCQ 211 Mark

If $-3x + 17 < - 13,$ then

✓
$x \in(10, \infty)$
B
$x \in[10, \infty)$
C
$x \in(-\infty, 10)$
D
$x \in[-10,10)$

Answer

Correct option: A.

$x \in(10, \infty)$

(A) $x \in(10, \infty)$
Explanation: Given,
$- 3x + 17 < - 13$
$\Rightarrow$ $- 3x < - 17 - 13$
$\Rightarrow$ $- 3x < - 30$
$\Rightarrow$ $3x > 30$
$\Rightarrow$ $x > 10$
$\Rightarrow$ $x \in(10, \infty)$

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MCQ 221 Mark

If $x < 5,$ then

A
$- x < - 5$
B
$-x \leq-5$
✓
$- x > - 5$
D
$-x \leq-5$

Answer

Correct option: C.

$- x > - 5$

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MCQ 231 Mark

If $a$ and $b$ are positive integers and $\frac{a-b}{6.25}=\frac{8}{2.5},$then

A
$b > a$
✓
$b < a$
C
$b = a$
D
$b \geq a$

Answer

Correct option: B.

$b < a$

(B) $b < a$
Explanation: Given,
$\frac{a-b}{6.25}=\frac{8}{2.5}$
$a-b=\frac{6.25 \times 8}{2.5}$
$\Rightarrow$ $a - b = 20$
$\Rightarrow$ $a = 20 + b$
Hence, $a > b$ or $b < a$

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MCQ 241 Mark

If $p >= q$ and $r < 0,$ then which of the following is true?

✓
$pr < qr$
B
$p - r < q - r$
C
$p + r < q + r$
D
None of these

Answer

Correct option: A.

$pr < qr$

(A) $pr < qr$
Explanation: Since, given $p > q$ and $r < 0$
then $pr < qr$
(inequality sign is reversed when multiplied by a negative integer)

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MCQ 251 Mark

Two pipes A and B can fill a cistern in 8 hours and 12 hours respectively. The pipes when opened simultaneously takes 12 minutes more to fill the cistern due to leakage. Once the cistern is full, it will get emptied due to leakage in

A
5 hours
B
20 hours
C
60 hours
✓
120 hours

Answer

Correct option: D.

120 hours

(D) 120 hours
Explanation: Portion of cistern filled by both pipes in 1 hour
$=\frac{1}{8}+\frac{1}{12}$
$=\frac{5}{24}$.
Time taken by both pipes to fill the cistern
$= 4 ~\text{h}$ $48 ~\text {minutes}$
Time taken to fill tank due to leakage
$= 5~ \text{h}$
Cistern empty by leakage in $1 \text{h}$
$=\frac{5}{24}-\frac{1}{5}$
$=\frac{1}{120}$
Time taken by leakage to empty the cistern
$= 120 ~\text{h}$

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MCQ 261 Mark

A retailer buys 250 kg of rice, a part of which he sells at $10\%$ profit and the remaining at $5\%$ loss. If the net profit made by the retailer in the whole transaction is $7\%$, then the quantity of rice sold at $10\%$ profit is

✓
200 kg
B
150 kg
C
100 kg
D
50 kg

Answer

Correct option: A.

200 kg

(A) 200 kg
Explanation: $C = (- 5)\%\ d = 10\%,\ m = 7\%$
$(d-m): (m - c) = 1:4$
Quantity sold at $10\%$ profit
$=\frac{4}{5} \times 250$
= 200 kg

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MCQ 271 Mark

Two athletes Vijay and Samuel finish 100 meters race in 12 seconds and 16 seconds respectively. By how many meters does Vijay defeat Samuel?

A
10.2 meters
B
15 meters
✓
25 meters
D
33.3 meters

Answer

Correct option: C.

25 meters

(C) 25 meters
Explanation: Since Vijay is faster by 4 seconds.
$\therefore$ He beats Samuel by $=\frac{100}{16} \times 4$
= 25 meters

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MCQ 281 Mark

A person can row in still water at the rate of 8 km/h. If it takes him thrice as long to row upstream as to row downstream then the speed of the stream is:

A
2 km/h
B
3 km/h
✓
4 km/h
D
6 km/h

Answer

Correct option: C.

4 km/h

(C) 4 km/h
Explanation: Let x be the speed of the stream
$\frac{V_d}{t}=3 \frac{V_u}{t}$
$\therefore$ $8+ x = 3(8-x)$
$\Rightarrow$ $4x=16$
$\Rightarrow$ $x = 4$ km/h

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MCQ 291 Mark

For two distinct positive numbers x and y

✓
$x+y>2 \sqrt{x y}$
B
$\frac{x+y}{2}>x y$
C
$\sqrt{x y}>\frac{x+y}{2}$
D
$\frac{2 x y}{x+y}>\sqrt{x y}$

Answer

Correct option: A.

$x+y>2 \sqrt{x y}$

(A) $x+y>2 \sqrt{x y}$
Explanation: For distinct $x, y>0 ;$
$A.M. > G.M.$
$\Rightarrow$ $\frac{x+y}{2}>\sqrt{x y}$
$\Rightarrow$ $x+y>2 \sqrt{x y}$

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Applied Maths MCQ

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