Register

Recent questions tagged quantitative-aptitude

2 votes
1 answer
164
CAT 2020 Set-2 | Question: 56
If $\textsf{x}$ and $\textsf{y}$ are positive real numbers satisfying $\textsf{x+y = 102},$ then the minimum possible value of $\textsf{2601} \left( 1 + \frac{1}{\textsf{x}} \right) \left( 1 + \frac{1}{\textsf{y}} \right)$ is
If $\textsf{x}$ and $\textsf{y}$ are positive real numbers satisfying $\textsf{x+y = 102},$ then the minimum possible value of $\textsf{2601} \left( 1 + \frac{1}{\textsf{...
3 votes
1 answer
165
CAT 2020 Set-2 | Question: 57
The value of $\log_{a} \left( \frac {a}{b} \right) + \log_{b} \left( \frac{b}{a} \right),$ for $ 1 < a \leq b$ cannot be equal to $ – 0.5$ $1$ $0$ $ – 1$
The value of $\log_{a} \left( \frac {a}{b} \right) + \log_{b} \left( \frac{b}{a} \right),$ for $ 1 < a \leq b$ cannot be equal to $ – 0.5$$1$$0$$ – 1$
0 votes
0 answers
166
CAT 2020 Set-2 | Question: 58
In how many ways can a pair of integers $\textsf{(x , a)}$ be chosen such that $x^{2} – 2 |x| + |a-2| = 0 ?$ $4$ $5$ $6$ $7$
In how many ways can a pair of integers $\textsf{(x , a)}$ be chosen such that $x^{2} – 2 |x| + |a-2| = 0 ?$$4$ $5$$6$$7$
2 votes
1 answer
168
CAT 2020 Set-2 | Question: 60
For real $\textsf{x}$ , the maximum possible value of $ \frac{x}{\sqrt{1+x^{4}}}$ is $ \frac{1}{\sqrt{3}}$ $1$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$
For real $\textsf{x}$ , the maximum possible value of $ \frac{x}{\sqrt{1+x^{4}}}$ is $ \frac{1}{\sqrt{3}}$$1$$\frac{1}{\sqrt{2}}$$\frac{1}{2}$
2 votes
1 answer
173
CAT 2020 Set-2 | Question: 65
How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before $3.$
How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before $3.$
1 votes
1 answer
174
CAT 2020 Set-2 | Question: 66
The number of pairs of integers $(x,y)$ satisfying $ x \geq y \geq – 20 $ and $ 2x + 5y = 99 $ is
The number of pairs of integers $(x,y)$ satisfying $ x \geq y \geq – 20 $ and $ 2x + 5y = 99 $ is
2 votes
1 answer
175
CAT 2020 Set-2 | Question: 67
If $\textsf{x}$ and $\textsf{y}$ are non-negative integers such that $\textsf{x+9=z, y+1=z}$ and $\textsf{x+y<z+5},$ then the maximum possible value of $\textsf{2x+y}$ equals
If $\textsf{x}$ and $\textsf{y}$ are non-negative integers such that $\textsf{x+9=z, y+1=z}$ and $\textsf{x+y<z+5},$ then the maximum possible value of $\textsf{2x+y}$ eq...
3 votes
1 answer
179
CAT 2020 Set-2 | Question: 71
The number of integers that satisfy the equality $\left( x^{2} – 5x + 7 \right)^{x+1} = 1$ is $2$ $3$ $5$ $4$
The number of integers that satisfy the equality $\left( x^{2} – 5x + 7 \right)^{x+1} = 1$ is $2$$3$$5$$4$
2 votes
1 answer
180
CAT 2020 Set-2 | Question: 72
Let $f(x) = x^{2} + ax + b $ and $g(x) = f(x+1) – f(x-1).$ If $ f(x) \geq 0 $ for all real $x,$ and $ g(20) = 72,$ then the smallest possible value of $b$ is $1$ $16$ $0$ $4$
Let $f(x) = x^{2} + ax + b $ and $g(x) = f(x+1) – f(x-1).$ If $ f(x) \geq 0 $ for all real $x,$ and $ g(20) = 72,$ then the smallest possible value of $b$ is $1$$16$$0$...
1 votes
1 answer
183
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
184
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
185
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
188
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
189
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
191
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
192
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
193
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$$4$
1 votes
1 answer
194
CAT 2020 Set-1 | Question: 60
A person spent Rs $50000$ to produce a desktop computer and a laptop computer. He sold the desktop at $20\%$ profit and the laptop at $10\%$ loss. If overall he made a $2\%$ profit then the purchase price, in rupees, of the desktop is
A person spent Rs $50000$ to produce a desktop computer and a laptop computer. He sold the desktop at $20\%$ profit and the laptop at $10\%$ loss. If overall he made a $2...
1 votes
1 answer
195
CAT 2020 Set-1 | Question: 61
The area of the region satisfying the inequilities $\left | x \right |-y\leq 1,y\geq 0$ and $y\leq 1$ is
The area of the region satisfying the inequilities $\left | x \right |-y\leq 1,y\geq 0$ and $y\leq 1$ is
1 votes
1 answer
197
CAT 2020 Set-1 | Question: 63
Among $100$ students, $x_{1}$ have birthdays in January, $x_{2}$ have birthdays in February, and so on. If $x_{0}= \text{max}\left ( x_{1},x_{2},\dots,x_{12} \right ),$ then the smallest possible value of $x_{0}$ is $9$ $10$ $8$ $12$
Among $100$ students, $x_{1}$ have birthdays in January, $x_{2}$ have birthdays in February, and so on. If $x_{0}= \text{max}\left ( x_{1},x_{2},\dots,x_{12} \right ),$ t...
1 votes
1 answer
198
CAT 2020 Set-1 | Question: 64
The mean of all $4-$digit even natural numbers of the form $\text{‘}aabb\text{’},$ where $a>0,$ is $5050$ $4466$ $5544$ $4864$
The mean of all $4-$digit even natural numbers of the form $\text{‘}aabb\text{’},$ where $a>0,$ is$5050$$4466$$5544$$4864$
1 votes
1 answer
200
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...
Page: