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1 votes
1 answer
322
CAT 2020 Set-2 | Question: 75
For the same principal amount, the compound interest for two years at $5\%$ per annum exceeds the simple interest for three years at $3\%$ per annum by $\text{Rs } 1125.$ Then the principal amount in rupees is
For the same principal amount, the compound interest for two years at $5\%$ per annum exceeds the simple interest for three years at $3\%$ per annum by $\text{Rs } 1125.$...
2 votes
1 answer
323
CAT 2020 Set-2 | Question: 76
In a group of $10$ students, the mean of the lowest $9$ scores is $42$ while the mean of the highest $9$ scores is $47.$ For the entire group of $10$ students, the maximum possible mean exceeds the minimum possible mean by $4$ $3$ $5$ $6$
In a group of $10$ students, the mean of the lowest $9$ scores is $42$ while the mean of the highest $9$ scores is $47.$ For the entire group of $10$ students, the maximu...
1 votes
1 answer
324
CAT 2020 Set-1 | Question: 51
How many $3-$digit numbers are there, for which the product of their digits is more than $2$ but less than $7$?
How many $3-$digit numbers are there, for which the product of their digits is more than $2$ but less than $7$?
1 votes
1 answer
327
CAT 2020 Set-1 | Question: 54
On a rectangular metal sheet of area $135$ ... $4\sqrt{\pi }\left ( 3+\frac{9}{\pi} \right )$
On a rectangular metal sheet of area $135$ sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thir...
2 votes
1 answer
328
CAT 2020 Set-1 | Question: 55
If $\log_4 5=\left ( \log _{4}y \right )\left ( \log _{6}\sqrt{5} \right )$, then $y$ equals
If $\log_4 5=\left ( \log _{4}y \right )\left ( \log _{6}\sqrt{5} \right )$, then $y$ equals
1 votes
1 answer
330
CAT 2020 Set-1 | Question: 57
The number of real$-$valued of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is infinite $1$ $0$ $2$
The number of real$-$valued of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ isinfinite$1$$0$$2$
1 votes
1 answer
331
CAT 2020 Set-1 | Question: 58
If $y$ is a negative number such that $2^{y^{2}\log _{2}3}=5^{\log_{2}3}$, then $y$ equals $\log _{2}\left ( \frac{1}{3} \right )$ $-\log _{2}\left ( \frac{1}{3} \right )$ $\log _{2}\left ( \frac{1}{5} \right )$ $-\log _{2}\left ( \frac{1}{5} \right )$
If $y$ is a negative number such that $2^{y^{2}\log _{2}3}=5^{\log_{2}3}$, then $y$ equals$\log _{2}\left ( \frac{1}{3} \right )$$-\log _{2}\left ( \frac{1}{3} \right )$$...
1 votes
1 answer
332
CAT 2020 Set-1 | Question: 59
How many distinct positive integer-valued solutions exist to the equation $\left ( x^{2}-7x+11 \right )^{(x^{2}-13x+42)} =1$? $6$ $8$ $2$ $4$
How many distinct positive integer-valued solutions exist to the equation $\left ( x^{2}-7x+11 \right )^{(x^{2}-13x+42)} =1$?$6$$8$$2$$4$
1 votes
1 answer
333
CAT 2020 Set-1 | Question: 60
A person spent Rs $50000$ to produce a desktop computer and a laptop computer. He sold the desktop at $20\%$ profit and the laptop at $10\%$ loss. If overall he made a $2\%$ profit then the purchase price, in rupees, of the desktop is
A person spent Rs $50000$ to produce a desktop computer and a laptop computer. He sold the desktop at $20\%$ profit and the laptop at $10\%$ loss. If overall he made a $2...
1 votes
1 answer
334
CAT 2020 Set-1 | Question: 61
The area of the region satisfying the inequilities $\left | x \right |-y\leq 1,y\geq 0$ and $y\leq 1$ is
The area of the region satisfying the inequilities $\left | x \right |-y\leq 1,y\geq 0$ and $y\leq 1$ is
1 votes
1 answer
336
CAT 2020 Set-1 | Question: 63
Among $100$ students, $x_{1}$ have birthdays in January, $x_{2}$ have birthdays in February, and so on. If $x_{0}= \text{max}\left ( x_{1},x_{2},\dots,x_{12} \right ),$ then the smallest possible value of $x_{0}$ is $9$ $10$ $8$ $12$
Among $100$ students, $x_{1}$ have birthdays in January, $x_{2}$ have birthdays in February, and so on. If $x_{0}= \text{max}\left ( x_{1},x_{2},\dots,x_{12} \right ),$ t...
1 votes
1 answer
337
CAT 2020 Set-1 | Question: 64
The mean of all $4-$digit even natural numbers of the form $\text{‘}aabb\text{’},$ where $a>0,$ is $5050$ $4466$ $5544$ $4864$
The mean of all $4-$digit even natural numbers of the form $\text{‘}aabb\text{’},$ where $a>0,$ is$5050$$4466$$5544$$4864$
2 votes
1 answer
340
CAT 2020 Set-1 | Question: 67
If $x=\left ( 4096 \right )^{7+4\sqrt{3}}$, then which of the following equals $64$? $\frac{x^{7}}{x^{2\sqrt{3}}}$ $\frac{x^{7}}{x^{4\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x\frac{4}{\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x^{2\sqrt{3}}}$
If $x=\left ( 4096 \right )^{7+4\sqrt{3}}$, then which of the following equals $64$?$\frac{x^{7}}{x^{2\sqrt{3}}}$$\frac{x^{7}}{x^{4\sqrt{3}}}$$\frac{x\frac{7}{2}}{x\frac{...
1 votes
1 answer
341
CAT 2020 Set-1 | Question: 68
If $f\left ( 5+x \right )= f\left ( 5-x \right )$ for every real $x,$ and $f\left ( x \right )=0$ has four distinct real roots, then the sum of these roots is $0$ $40$ $10$ $20$
If $f\left ( 5+x \right )= f\left ( 5-x \right )$ for every real $x,$ and $f\left ( x \right )=0$ has four distinct real roots, then the sum of these roots is$0$$40$$10$$...
1 votes
1 answer
342
CAT 2020 Set-1 | Question: 69
If $a, b$ and $c$ are positive integers such that $ab=432, bc=96$ and $c<9,$ then the smallest possible value of $a+b+c$ is $56$ $59$ $49$ $46$
If $a, b$ and $c$ are positive integers such that $ab=432, bc=96$ and $c<9,$ then the smallest possible value of $a+b+c$ is$56$$59$$49$$46$
1 votes
1 answer
343
CAT 2020 Set-1 | Question: 70
In a group of people, $28\%$ of the members are young while the rest are old. If $65\%$ of the members are literates, and $25\%$ of the literates are young, then the percentage of old people among the illiterates is nearest to $62$ $55$ $66$ $59$
In a group of people, $28\%$ of the members are young while the rest are old. If $65\%$ of the members are literates, and $25\%$ of the literates are young, then the perc...
1 votes
1 answer
344
CAT 2020 Set-1 | Question: 71
A circle is inscribed in a rhombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is $\frac{5\pi }{18}$ $\frac{6\pi }{25}$ $\frac{3\pi }{25}$ $\frac{2\pi }{15}$
A circle is inscribed in a rhombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is $\frac{5\pi }{18}$ $\frac{6\pi }{25}$ $\f...
1 votes
1 answer
348
CAT 2020 Set-1 | Question: 75
The number of distinct real roots of the equation $\left ( x+\frac{1}{x}\right )^{2}-3\left ( x+\frac{1}{x} \right )+2= 0$ equals
The number of distinct real roots of the equation $\left ( x+\frac{1}{x}\right )^{2}-3\left ( x+\frac{1}{x} \right )+2= 0$ equals
0 votes
2 answers
350
The single discount equivalent to two successive discount 10% and 20% will be
0 votes
1 answer
355
NIELIT 2016 MAR Scientist D: 61
A man rowed $3$ miles upstream in $90$ minutes. If the river flowed with a current of $2$ miles per hour, how long did the man’s return trip take? $20$ minutes $30$ minutes $45$ minutes $60$ minutes
A man rowed $3$ miles upstream in $90$ minutes. If the river flowed with a current of $2$ miles per hour, how long did the man’s return trip take?$20$ minutes$30$ minut...
0 votes
1 answer
357
NIELIT 2016 MAR Scientist D: 66
Two bicyclists travel in opposite directions. One travels $5$ miles per hour faster than the other. In $2$ hours they are $50$ miles apart. What is the rate of the faster bicyclist? $11.25$ mph $15$ mph $20$ mph $22.5$ mph
Two bicyclists travel in opposite directions. One travels $5$ miles per hour faster than the other. In $2$ hours they are $50$ miles apart. What is the rate of the faster...
0 votes
1 answer
358
NIELIT 2016 MAR Scientist D: 64
What is the area of a semicircle with a diameter of $16$ inches? $32 \pi$ square inches $64 \pi$ square inches $128 \pi$ square inches $256 \pi$ square inches
What is the area of a semicircle with a diameter of $16$ inches?$32 \pi$ square inches$64 \pi$ square inches$128 \pi$ square inches$256 \pi$ square inches
0 votes
1 answer
360
NIELIT 2016 MAR Scientist D: 63
A circular garden twenty feet in diameter is surrounded by a path three feet wide. What is the area of the path? $51 \pi$ square feet $60 \pi$ square feet $69 \pi$ square feet $90 \pi$ square feet
A circular garden twenty feet in diameter is surrounded by a path three feet wide. What is the area of the path?$51 \pi$ square feet$60 \pi$ square feet$69 \pi$ square fe...
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