MCQ 11 Mark
The mean proportional between 4 and 9 is:
Answer(b) 6
Explanation:
Mean proportional of 4 and 9
$=\sqrt{4 \times 9}=\sqrt{36}=6$ Ans.
View full question & answer→MCQ 21 Mark
The given table shows the distance covered and the time taken by a train moving at a uniform speed along a straight track:| Distance (in m) | 60 | 90 | y |
| Time(in sec) | 2 | X | 5 |
The values of $x$ and $y$ are: - A
$x=4, y=150$
- B
$x=3, y=100$
- C
$x=4, y=100$
- ✓
$x=3, y=150$
AnswerCorrect option: D. $x=3, y=150$
(d) $x=3, y=150$
Explanation:
It is a direction variation. If the speed is uniform then moving distance covered more will the time taken then,
$\begin{array}{l}\Rightarrow \frac{60}{2}=\frac{90}{x}-\frac{y}{5} \\ \Rightarrow x=\frac{90 \times 2}{60} \text { and } y=\frac{60 \times 5}{2} \\ =3=150 \\ \backslash x=3 \text { and } y=150\end{array}$
View full question & answer→MCQ 31 Mark
Statement (A): In alternendo, if $a: b:: c: d$ then $a: c:: b: d$
Statement (B): In componendo, if $a: b:: c: d$ then $(a+b): b::(c+d): d$.
Which of the statement is valid?
Answer(c) Both A and B
Explanation:
For statement A ,
Given $a: b:: c: d \Rightarrow \frac{a}{b}=\frac{c}{d} \Rightarrow a d=b c$
$\Rightarrow \frac{a}{c}=\frac{b}{d} \Rightarrow a: c:: b: d$
Statement A is correct
For statement $B$,
Given, $a: b:: c: d \Rightarrow \frac{a}{b}-\frac{c}{d}$
$\Rightarrow \frac{d}{b}+1=\frac{c}{d}+1$
$\Rightarrow \frac{a+b}{b}=\frac{c+d}{d}$
$\Rightarrow(a+b): b::(c+d): d$
Statement B is correct.
View full question & answer→MCQ 41 Mark
Statement (A): If $6: x:: 2: 13$, then $x$ is 39
Statement (B): The third proportional to 9 and 15 is 35 .
Which of the statement is valid?
Answer(a) Only A
Explanation:
For statement A ,
Given 6: $x: 2:: 13 \Rightarrow \frac{6}{x}-\frac{2}{13}$
$\Rightarrow 2 x=13 \times 6 \Rightarrow x=39$
Statement A is correct
For statement $B$,
Let the third proportional be $x$, then 9,15 and $x$ are in continued proportion,
$\frac{9}{15}-\frac{15}{x} \Rightarrow 9 x=15 \times 15 \Rightarrow x=25$
Statement B is incorrect.
View full question & answer→MCQ 51 Mark
Statement (A): If $a, b, c$ and d are in proportion then $\frac{d}{b}=\frac{c}{d} \Rightarrow a d=b c$
Statement (B): If $a, b$ and $c$ are in continued proportion, then, $b=\sqrt{a c}$
Which of the statement is valid?
Answer(c) Both A and B
Explanation:
If $a, b, c$ and $d$ are in propartion then, product of extreme terms $(a d)=$ product of middle terms $(b c)$.
And, if $a, b$ and $c$ are in continued propartion and $b$ is the mean propotional of $a$ and $c$, then
$\frac{a}{b}=\frac{b}{c} \Rightarrow b^2=a c$
$b=\sqrt{a c}$
View full question & answer→MCQ 61 Mark
Ratio A: Reciprocal ratio $3: 2$
Ratio B : $8: 15$
Ratio C : 11 : 12
Ratio D: Reciprocal ratio $16: 7$
Which of the above ratios has greatest and lowest?
- A
Ratio C is greatest and ratio A is lowest
- ✓
Ratio C is greatest and ratio D is lowest
- C
Ratio D is greatest and ratio C is lowest
- D
Ratio A greatest and ratio B is lowest
AnswerCorrect option: B. Ratio C is greatest and ratio D is lowest
(b) Ratio C is greatest and ratio D is lowest
Explanation:
Given ratios are $\frac{2}{3}, \frac{8}{15}, \frac{11}{12}$ and $\frac{7}{16}$
LCM of $3,15,12,16=240$
$\begin{array}{l}\frac{2}{3}=\frac{2}{3} \times \frac{80}{80}=\frac{160}{240} \\ \frac{8}{15}=\frac{8}{15} \times \frac{16}{16}=\frac{128}{240} \\ \frac{11}{12}=\frac{11}{12} \times \frac{20}{20}=\frac{220}{240} \\ \frac{7}{16}=\frac{7}{16} \times \frac{15}{15}=\frac{105}{240} \\ \frac{220}{240}>\frac{160}{240}>\frac{128}{240}>\frac{105}{240}\end{array}$
$\Rightarrow$ Ratio C $>$ Ratio $A >$ Ratio $B >$ Ratio D
View full question & answer→MCQ 71 Mark
The mean proportional between $\frac{1}{3}$ and 243 is:
Answer(b) 9
Explanation:
The mean proportional between
$\frac{1}{3}$ and 243 is given by
$\begin{array}{l}x=\sqrt{\frac{1}{3} \times 243} \\ x=\sqrt{81} \\ x=9\end{array}$
View full question & answer→MCQ 81 Mark
The third proportional to $\frac{36}{15}$ and 3 is :
AnswerCorrect option: C. $15 / 4$
(c) $15 / 4$
Explanation:
The third proportional to $\frac{36}{15}$ and 3 is given by
$\begin{array}{l}\frac{36}{15}: 3:: 3: x \\ \Rightarrow \frac{36}{15}+3=3 \div x \\ \Rightarrow \frac{36}{15 \times 3}-\frac{3}{x} \\ \Rightarrow x=\frac{3 \times 15 \times 3}{36} \\ \Rightarrow x=\frac{15}{4}\end{array}$
View full question & answer→MCQ 91 Mark
The ratio of number of edges of a cube to the number of its faces is:
- ✓
$2: 1$
- B
$1: 2$
- C
$3: 8$
- D
$8: 3$
AnswerCorrect option: A. $2: 1$
(a) $2: 1$
Explanation:
Number of edges of the cube $=12$
Number of faces $=6$
Ratio in edges a cube to the number of faces
= 12: 6=2: 1
View full question & answer→MCQ 101 Mark
When the number 350 is increased in the ratio $5: 7$, the new number is:
Answer(b) 490
Explanation:
350 is increased in the ratio $5: 7$ then new increased number will be $=350 \times \frac{7}{5}-490$
View full question & answer→MCQ 111 Mark
If $x, 12,8$ and 32 are in propartion, the value of $x$ is:
Answer(c) 3
Explanation:
$x, 12,8$ and 32 are in proportion, then product of extreme $=$ Product of means
$\begin{array}{l}x \times 32=12 \times 8 \\ x=\frac{12 \times 8}{32}=3\end{array}$
View full question & answer→MCQ 121 Mark
Two numbers are in the ratio $7: 9$. If the sum of the numbers is 288 , then the smaller number is:
Answer(a) 126
Explanation:
Ratio $=7: 9$
Sum of numbers $=288$
Sum of ratios $=7+9=16$
Smaller number $=\frac{288 \times 7}{16}=126$
View full question & answer→MCQ 131 Mark
The table shows the values of $x$ and $y$, where $x$ is proportional to $y$.What the values of M and N are: - A
$M =4, N=9$
- B
$M =9, N=3$
- ✓
$M =9, N=4$
- D
$M =12, N=0$
AnswerCorrect option: C. $M =9, N=4$
(c) $M=9, N=4$
Explanation:
According to question,
$\frac{x}{y}=\frac{6}{M}=\frac{12}{18}=\frac{N}{6}$
We take, $\frac{6}{M}=\frac{12}{18}$
$\Rightarrow M =\frac{6 \times 18}{12}=9$
Again we take,
$\begin{array}{l}\frac{12}{18}=\frac{N}{6} \\ \Rightarrow N=\frac{12 \times 6}{18}=4\end{array}$
Hence, we get,
M=9 and N=4
View full question & answer→MCQ 141 Mark
If $(x-2),(x+2),(2 x+1)$ and $(2 x+19)$ are in proportion, then the value of $x$ is:
Answer(d) 4
Explanation:
Since, $(x-2),(x+2),(2 x+1)$ and $(2 x+19)$ are in proportion.
$\therefore \frac{x-2}{x+2}=\frac{2 x+1}{2 x+19}$
$\begin{array}{l}\Rightarrow(x-2)(2 x+19)=(x+2)(2 x+1) \\ \Rightarrow 2 x^2+15 x-38=2 x^2+5 x+2 \\ \Rightarrow 10 x=40 \\ \Rightarrow x=4\end{array}$
View full question & answer→MCQ 151 Mark
If $\frac{\sqrt{5 x}+\sqrt{2 x-6}}{\sqrt{5 x}-\sqrt{2 x-6}}=4$, then the value of $x$ is:
Answer(c) 30
Explanation:
$\frac{\sqrt{5 x}+\sqrt{2 x-6}}{\sqrt{5 x}-\sqrt{2 x-6}}=4$
Applying componendo and dividendo, we get
$\begin{array}{l}\frac{2 \sqrt{5 x}}{2 \sqrt{2 x-6}}=\frac{4+1}{4-1} \\ \Rightarrow \frac{\sqrt{5 x}}{\sqrt{2 x-6}}=\frac{3}{3}\end{array}$
Squaring both sides, we get
$\frac{5 x}{2 x-6}=\frac{25}{9}$
$\begin{array}{l}\Rightarrow 45 x=50 x-150 \\ \Rightarrow 5 x=150 \\ \Rightarrow x=30\end{array}$
View full question & answer→MCQ 161 Mark
If $x+3$ is the mean proportion between $x+2$ and $x+9$, then the value of $x$ is:
- ✓
$-\frac{9}{5}$
- B
$\frac{9}{5}$
- C
$\frac{5}{9}$
- D
$-\frac{5}{9}$
AnswerCorrect option: A. $-\frac{9}{5}$
(a) $-\frac{9}{5}$
Explanation:
$x+3$ is the mean proportion $x+2$ and $x+9$,
$\therefore(x+3)^2=(x+2)(x+9)$
$\begin{array}{l}\Rightarrow x^2+6 x+9=x^2+11 x+18 \\ \Rightarrow-5 x=9 \\ \Rightarrow x=-\frac{9}{5}\end{array}$
View full question & answer→MCQ 171 Mark
The fourth proportional to $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ is:
- A
$\frac{3}{10}$
- ✓
$\frac{3}{20}$
- C
$\frac{3}{25}$
- D
AnswerCorrect option: B. $\frac{3}{20}$
(b) $\frac{3}{20}$
Explanation:
Let the fourth proportional be $x$.
Then $\frac{\frac{1}{3}}{4}=\frac{\frac{1}{5}}{\frac{x}{1}}$
$\begin{array}{l}\Rightarrow \frac{x}{3}=\frac{1}{20} \\ \Rightarrow x=\frac{3}{20}\end{array}$
View full question & answer→MCQ 181 Mark
If $x=\frac{\sqrt{a+1}+\sqrt{a-1}}{\sqrt{a+1}-\sqrt{a-1}}$, then $x^2-2 a x+1$ is equal to:
Answer(c) 0
Explanation:
We have,
$x=\frac{\sqrt{a+1}+\sqrt{a-1}}{\sqrt{a+1}-\sqrt{a-1}}$
Applying componendo and dividendo, we get
$\frac{x+1}{x-1}=\frac{2 \sqrt{a+1}}{2 \sqrt{a-1}}=\frac{\sqrt{a+1}}{\sqrt{a-1}}$
Squaring both sides, we get
$\frac{(x+1)^2}{(x-1)^2}=\frac{a+1}{a-1}$
$\begin{array}{l}\Rightarrow \frac{\left(x^2+2 x+1\right)}{x^2-2 x+1}=\frac{a+1}{a-1} \\ \Rightarrow(a-1)\left(x^2+2 x+1\right)=(a+1)\left(x^2-2 x+1\right) \\ \Rightarrow a x^2-x^2+2 a x-2 x+a-1 \\ =a x^2+x^2-2 a x-2 x+a+1 \\ \Rightarrow-2 x^2+4 a x-2=0 \\ \Rightarrow-2\left(x^2-2 a x+1\right)=0 \\ \Rightarrow x^2-2 a x+1=0\end{array}$
View full question & answer→MCQ 191 Mark
If 6 is the mean proportion between the two numbers $x$ and $y$, and 48 is the third proportion of $x$ and $y$, then the numbers $x$ and $y$ respectively, are:
Answer(a) 3,12
Explanation:
We have, $\sqrt{x y}=6$
$\begin{array}{l}\Rightarrow x y=36 \\ \Rightarrow x=\frac{36}{y} \ldots( i ) \\ \text { and } \frac{x}{y}=\frac{y}{48} \\ \Rightarrow 48 x=y^2 \\ \Rightarrow 48\left(\frac{36}{y}\right)=y^2[\text { Using }( i )] \\ \Rightarrow y^3=48 \times 36 \\ \Rightarrow y=\sqrt[3]{8 \times 6 \times 36}=2 \times 6=12\end{array}$
So, $x=\frac{36}{12}=3$
$\therefore x=3, y=12 \text {. }$
View full question & answer→MCQ 201 Mark
If $\frac{x^2+2 x}{2 x+4}-\frac{y^2+3 y}{3 y+9}$, then the value of $2 x: 3 y$ is:
- A
$16: 27$
- B
$1: 1$
- C
$2: 3$
- ✓
$4: 9$
AnswerCorrect option: D. $4: 9$
(d) $4: 9$
Explanation:
$\frac{x^2+2 x}{2 x+4}=\frac{y^2+3 y}{3 y+9}$
Applying componendo and dividendo,
$\begin{array}{l}\frac{x^2+2 x+2 x+4}{x^2+2 x-2 x-4}=\frac{y^2+3 y+3 y+9}{y^2+3 y-3 y-9} \\ \Rightarrow \frac{x^2+4 x+4}{x^2-4}=\frac{y^2+6 y+9}{y^2-9} \\ \Rightarrow \frac{(x+2)^2}{(x+2)(x-2)}=\frac{(y+3)^2}{(y+3)(y-3)} \\ \Rightarrow \frac{x+2}{x-2}=\frac{y+3}{y-3}\end{array}$
Again, applying componendo and dividendo,
$\begin{array}{l}\frac{x+2+x-2}{x+2-x+2}=\frac{y+3+y-3}{y+3-y+3} \\ \Rightarrow \frac{2 x}{4}=\frac{2 y}{6} \\ \Rightarrow \frac{x}{2}=\frac{y}{3} \\ \Rightarrow \frac{x}{y}=\frac{2}{3}\end{array}$
So, $\frac{2 x}{3 y}=\frac{2}{3} \times \frac{x}{y}=\frac{2}{3} \times \frac{2}{3}=\frac{4}{9}$
View full question & answer→MCQ 211 Mark
If $\frac{2 x+\sqrt{4 x^2-1}}{2 x-\sqrt{4 x^2-1}}=4$, then using the properties of proportion, the value of $x$ is:
- A
$\frac{1}{2}$
- ✓
$\frac{5}{8}$
- C
$\frac{8}{5}$
- D
$\frac{6}{5}$
AnswerCorrect option: B. $\frac{5}{8}$
(b) $\frac{5}{8}$
Explanation:
$\frac{2 x+\sqrt{4 r^2-1}}{2 x-\sqrt{4 x^2-1}}=4$
Applying componendo and dividendo, we get
$\begin{array}{l}\frac{2 x+\sqrt{4 x^2-1}+2 x-\sqrt{4 x^2-1}}{2 x+\sqrt{4 x^2-1}-2 x+\sqrt{4 x^2-1}}=\frac{4+1}{4-1} \\ \frac{4 x}{2 \sqrt{4 x^2-1}}=\frac{3}{3} \\ \Rightarrow \frac{2 x}{\sqrt{4 x^2-1}}=\frac{5}{3} \\ \Rightarrow \frac{4 x^2}{4 x^2-1}=\frac{25}{9} \\ \Rightarrow 36 x^2=100 x^2-25 \\ \Rightarrow 64 x^2=25 \\ \Rightarrow x^2=\frac{25}{64} \\ \Rightarrow x=\frac{5}{8}\end{array}$
View full question & answer→MCQ 221 Mark
If $a, b, c$ and $d$ are in proportional, then $\sqrt{\frac{3 a^2+8 b^2}{3 c^2+8 b^2}}$ is equal to:
- A
$\frac{c}{a}$
- ✓
$\frac{b}{d}$
- C
$\frac{a}{b}$
- D
$\frac{c}{d}$
AnswerCorrect option: B. $\frac{b}{d}$
(b) $\frac{b}{d}$
Explanation:
Since, $a, b, c$ and $d$ are in proportion.
$\therefore \frac{a}{b}=\frac{c}{d}=k \text { (say) }$
$\Rightarrow a=b k$ and $c=d k$
Now, $\sqrt{\frac{3 a^2+8 t^2}{3 c^2+8 d^2}}=\sqrt{\frac{3(b k)^2+8 b^2}{3(d k)^2+8 d^2}}$
$=\sqrt{\frac{b^2\left(3 k^2+8\right)}{d^2\left(3 k^2+8\right)}}=\sqrt{\frac{b^2}{d^2}}=\frac{b}{d}$
View full question & answer→MCQ 231 Mark
If $x: y=3: 4$ and $y: z=5: 2$, then $x: y: z$ is:
- A
$6: 20: 6$
- B
$3: 9: 2$
- C
$3: 20: 2$
- D
$15: 20: 8$
View full question & answer→MCQ 241 Mark
If $(9 x+10):(4 x+3)$ is the triplicate ratio of $4: 3$, then the value of $x$ is:
View full question & answer→MCQ 251 Mark
The reciprocal ratio of $\frac{1}{9}: 2$ is:
- A
$9: \frac{1}{2}$
- B
$18: 1$
- C
$9: 2$
- D
$2: 18$
View full question & answer→MCQ 261 Mark
The sub-duplicate ratio of $25: 16$ is:
- A
$16: 25$
- B
$23: 14$
- C
$\frac{25}{2}: 8$
- D
$5: 4$
View full question & answer→MCQ 271 Mark
The duplicate ratio of $\sqrt{3}: 7$ is
- A
$3: 49$
- B
$7: \sqrt{3}$
- C
$2 \sqrt{3}: 14$
- D
$(\sqrt{3}+2)=9$
View full question & answer→MCQ 281 Mark
If $\left(x^2+y^2\right):\left(x^2-y^2\right)=17: 8$, then $x: y$ is:
- A
$3: 7$
- B
$25: 9$
- C
$8: 17$
- D
$5: 3$
View full question & answer→MCQ 291 Mark
If $\left(2 x^2-5 y^2\right): x y=1: 3$, then $x: y$ is:
- A
$3: 2$
- B
$-5: 3$
- C
$5: 3$
- D
$-3: 2$
View full question & answer→MCQ 301 Mark
If $x^2+4 y^2=4 x y$, then $x: y$ is:
- A
$1: 4$
- B
$4: 1$
- C
$2: 1$
- D
$1: 2$
View full question & answer→MCQ 311 Mark
If $a: b=3: 2$, then $(a+b)^2:(a-b)^2$ is:
- A
$9: 4$
- B
$1: 25$
- C
$25: 1$
- D
$4: 9$
View full question & answer→MCQ 321 Mark
The ratio between $3 \cdot 6$ and 75 cm is:
- A
$18: 275$
- B
$24: 5$
- C
$6: 125$
- D
$4: 5$
View full question & answer→MCQ 331 Mark
The simplest form of the ratio $27: 81$ is:
- A
$1: 3$
- B
$3: 9$
- C
$27: 81$
- D
$9: 27$
View full question & answer→MCQ 341 Mark
If $x: y=2: 3$, then the value of $(7 x-4 y):(5 x+2 y)$ is:
- A
$1: 8$
- B
$2: 3$
- C
$4: 9$
- D
$5: 7$
View full question & answer→