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CAT 2023 Set-3 | Quantitative Aptitude | Question: 4
For a real number $x$, if $\frac{1}{2}, \frac{\log _{3}\left(2^{x}-9\right)}{\log _{3} 4}$, and $\frac{\log _{5}\left(2^{x}+\frac{17}{2}\right)}{\log _{5} 4}$ are in an a...
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 3
The sum of all possible values of $x$ satisfying the equation $2^{4 x^{2}}-2^{2 x^{2}+x+16}+2^{2 x+30}=0$, is$\frac{5}{2}$$\frac{1}{2}$$3$$\frac{3}{2}$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 21
If $p^2+q^2-29=2 p q-20=52-2 p q$, then the difference between the maximum and minimum possible value of $\left(p^3-q^3\right)$ is$486$$378$$243$$189$
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CAT 2023 Set-1 | Quantitative Aptitude | Question: 2
If $\sqrt{5 x+9}+\sqrt{5 x-9}=3(2+\sqrt{2})$, then $\sqrt{10 x+9}$ is equal to$3 \sqrt{7}$$4 \sqrt{5}$$3 \sqrt{31}$$2 \sqrt{7}$
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CAT 2023 Set-1 | Quantitative Aptitude | Question: 6
The equation $x^{3}+(2 r+1) x^{2}+(4 r-1) x+2=0$ has $-2$ as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of $r...
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CAT 2022 Set-3 | Quantitative Aptitude | Question: 2
If $c=\dfrac{16 x}{y}+\dfrac{49 y}{x}$ for some non-zero real numbers $x$ and $y,$ then $c$ cannot take the value$-60$ $-50$ $60$ $-70$
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CAT 2020 Set-3 | Question: 55
If $x_{1} = \;– 1$ and $x_{m} = x_{m+1} + (m + 1)$ for every positive integer $m, $ then $x_{100}$ equals $ – 5151 $$ – 5150 $$ – 5051 $$ – 5050 $
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CAT 2020 Set-3 | Question: 59
If $\text{a,b,c}$ are non-zero and $14^{a} = 36^{b} = 84^{c},$ then $6b \left( \frac{1}{c} \;– \frac{1}{a} \right)$ is equal to
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CAT 2020 Set-3 | Question: 69
How many pairs $(a,b)$ of positive integers are there such that $a \leq b$ and $ab = 4^{2017} \; ?$$2017$$2019$$2020$$2018$
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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{...
2 2 votes
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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}}$$\frac{1}{2}$
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CAT 2020 Set-2 | Question: 71
The number of integers that satisfy the equality $\left( x^{2} – 5x + 7 \right)^{x+1} = 1$ is $2$$3$$5$$4$
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CAT 2020 Set-1 | Question: 57
The number of real$-$valued of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ isinfinite$1$$0$$2$
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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$$4$
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CAT 2020 Set-1 | Question: 67
If $x=\left ( 4096 \right )^{7+4\sqrt{3}}$, then which of the following equals $64$?$\frac{x^{7}}{x^{2\sqrt{3}}}$$\frac{x^{7}}{x^{4\sqrt{3}}}$$\frac{x^\frac{7}{2}}{x^\fra...
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CAT 2020 Set-1 | Question: 69
If $a, b$ and $c$ are positive integers such that $ab=432, bc=96$ and $c<9,$ then the smallest possible value of $a+b+c$ is$56$$59$$49$$46$
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CAT 2020 Set-1 | Question: 72
A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of th...
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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
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NIELIT 2016 MAR Scientist D: 71
A certain number when added to $50\%$ of itself is $27$. What is the number?$7$$9$$11$$18$
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NIELIT 2016 MAR Scientist D: 70
Twelve less than $4$ times a number is $20$. What is the number?$2$$4$$6$$8$
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NIELIT 2016 MAR Scientist D: 69
The sum of a number and its double is $69$. What is the number?$46.6$$34.5$$23$$20$
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NIELIT 2019 Feb Scientist D - Section D: 3
A school has $378$ girls and $675$ boys. All the students divided into strictly boys and strictly girls students sections. All the sections in the school has same number ...
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NIELIT 2019 Feb Scientist D - Section D: 26
A dog at point $A$ goes in pursuit of a fox $30$ $m$ away. The dog makes $2$ $m$ and the fox, $1$ m long leaps. If the dog makes two leaps to the fox’s three, at what dis...
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NIELIT 2019 Feb Scientist D - Section D: 27
If $5$ spiders can catch $5$ files in $5$ minutes. How many files can $100$ spiders catch in $100$ minutes :$100$$1000$$500$$2000$
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NIELIT 2016 MAR Scientist C - Section A: 12
The expression $(11.98\times 11.98 + 11.98 \times x +0.02 \times 0.02)$ will be a perfect square for $x$ equal to:$2.02$$0.17$$0.04$$1.4$
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NIELIT 2016 MAR Scientist C - Section A: 15
The value of $\large\frac{(0.96)^3-(0.1)^3}{(0.96)^2+0.096+(0.1)^2}$ is :$0.86$$0.95$$0.97$$1.06$
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NIELIT 2019 Feb Scientist C - Section D: 15
The simplified form of $\left[ \left ( \left( \dfrac{a+1}{a-1}\right)^2+3 \right)\div \left( \left( \dfrac{a-1}{a+1}\right)^2+3\right) \right] \div \left [\left( \dfrac{a...
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NIELIT 2019 Feb Scientist C - Section D: 23
Rs.$6500$ were divided among a certain number of persons. If there had been $15$ more persons, each would have got $Rs.30$ less. Find the original number of persons.$50$$...
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NIELIT 2019 Feb Scientist C - Section D: 30
A charitable trust donates $28$ different books of Maths, $16$ different books of science and $12$ different books of social science to poor students. Each student is giv...
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NIELIT 2019 Feb Scientist C - Section C: 3
The factors of $(x^{2}+4y^{2}+4y-4xy-2x-8)$ are:$(x-2y-4)(x-2y+2)$$(x-y+2)(x-4y-4)$$(x+2y-4)(x+2y+2)$None of these
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NIELIT 2019 Feb Scientist C - Section C: 19
If $a^{x}=b, b^{y}=c$ and $c^{z}=a$, then $xyz$ equals:$abc$$\dfrac{1}{abc}$$1$None
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CAT 2019 Set-2 | Question: 86
What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer?$8$$12$$16$$6$
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CAT 2019 Set-2 | Question: 97
If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686$, then $x+y$ equals _______
3 3 votes
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CAT 2018 Set-1 | Question: 69
Given that $x^{2018}y^{2017}=1/2$ and $x^{2016}y^{2019}=8$, the value of $x^2+y^3$ is$35/4$$37/4$$31/4$$33/4$
2 2 votes
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CAT 2018 Set-1 | Question: 77
If $u^2+(u-2v-1)^2=-4v(u+v)$, then what is the value of $u+3v$ ?$1/4$$0$$1/2$$-1/4$
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CAT 2017 Set-2 | Question: 94
How many different pairs $(a,b)$ of positive integers are there such that $a\leq b$ and $1/a+1/b=1/9$None of these$2$$0$$1$
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CAT 2017 Set-2 | Question: 91
If $9^{\left ( x-1/2 \right )}-2^{\left ( 2x-2 \right )}=4^{x}-3^{\left (2x-3 \right )}$, then $x$ is$3/2$$2/5$$3/4$$4/9$
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CAT 2017 Set-1 | Question: 90
If $9^{2x-1}-81^{x-1}= 1944$ then $x$ is$3$$9/4$$4/9$$1/3$
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CAT 2017 Set-1 | Question: 88
If $x+1= x^{2}$ and $x 0$, then $2x^{4}$ is$6+4\sqrt{5}$$3+5\sqrt{5}$$5+3\sqrt{5}$$7+3\sqrt{5}$
1 1 vote
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CAT 2017 Set-1 | Question: 94
If $a, b, c$ and $d$ are integers such that $a+b+c+d=30$ , then the minimum possible value of $( a-b )^{2}+( a-c )^{2}+( a-d)^{2}$ is $1$$2$$5$$6$
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