Hot questions in Numerical Ability

Syllabus: Numerical computation, Numerical estimation, Numerical reasoning and data interpretation

$$\small{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&2&3&2&3&1&2&1&2.2&3
\\\hline\textbf{2 Marks Count}&3&4&4&4&3&3&3&3.5&4
\\\hline\textbf{Total Marks}&8&11&10&11&7&8&\bf{7}&\bf{9.2}&\bf{11}\\\hline
\end{array}}}$$

0 votes

1 answer

ISI2015-MMA-28
In a triangle $ABC$, $AD$ is the median. If length of $AB$ is $7$, length of $AC$ is $15$ and length of $BC$ is $10$ then length of $AD$ equals $\sqrt{125}$ $69/5$ $\sqrt{112}$ $\sqrt{864}/5$

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 18 views

0 votes

2 answers

ISI2017-DCG-17
If $\cos ^{2}x+ \cos ^{4} x=1$, then $\tan ^{2} x+ \tan ^{4} x$ is equal to $1$ $0$ $2$ none of these

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 17 views

+2 votes

1 answer

ISI2015-DCG-29
The condition that ensures that the roots of the equation $x^3-px^2+qx-r=0$ are in $H.P.$ is $r^2-9pqr+q^3=0$ $27r^2-9pqr+3q^3=0$ $3r^3-27pqr-9q^3=0$ $27r^2-9pqr+2q^3=0$

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 28 views

0 votes

1 answer

ISI2015-MMA-13
The number of real roots of the equation $2 \cos \left( \frac{x^2+x}{6} \right) = 2^x +2^{-x} \text{ is }$ $0$ $1$ $2$ infinitely many

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 19 views

+2 votes

4 answers

GATE2017 CE-2: GA-4
What is the value of $x$ when $81\times\left (\frac{16}{25} \right )^{x+2}\div\left (\frac{3}{5} \right )^{2x+4}=144?$ $1$ $-1$ $-2$ $\text{Can not be determined}$

asked May 18, 2019 in Numerical Ability by Lakshman Patel RJIT Veteran (58.9k points) | 135 views

+1 vote

2 answers

ISI2016-DCG-19
The expression $3^{2n+1}+2^{n+2}$ is divisible by $7$ for all positive integer values of $n$ all non-negative integer values of $n$ only even integer values of $n$ only odd integer values of $n$

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 25 views

+1 vote

1 answer

ISI2017-DCG-9
The solution of $\log_5(\sqrt{x+5}+\sqrt{x})=1$ is $2$ $4$ $5$ none of these

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 28 views

+1 vote

1 answer

ISI2015-MMA-17
Let $X=\frac{1}{1001} + \frac{1}{1002} + \frac{1}{1003} + \cdots + \frac{1}{3001}$. Then, $X \lt1$ $X\gt3/2$ $1\lt X\lt 3/2$ none of the above holds

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 24 views

+1 vote

1 answer

ISI2014-DCG-36
Consider any integer $I=m^2+n^2$, where $m$ and $n$ are odd integers. Then $I$ is never divisible by $2$ $I$ is never divisible by $4$ $I$ is never divisible by $6$ None of the above

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 40 views

+1 vote

1 answer

ISI2015-MMA-11
The number of positive integers which are less than or equal to $1000$ and are divisible by none of $17$, $19$ and $23$ equals $854$ $153$ $160$ none of the above

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 18 views

+1 vote

1 answer

ISI2014-DCG-23
The sum of the series $\:3+11+\dots +(8n-5)\:$ is $4n^2-n$ $8n^2+3n$ $4n^2+4n-5$ $4n^2+2$

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 58 views

+2 votes

6 answers

UGCNET-June-2019-I-23
If $152$ is divided into four parts proportional at $3$, $4$, $5$ and $7$, then the smallest part is $29$ $26$ $25$ $24$

asked Jul 2, 2019 in Numerical Ability by Arjun Veteran (431k points) | 158 views

+1 vote

1 answer

ISI2014-DCG-30
Consider the equation $P(x) =x^3+px^2+qx+r=0$ where $p,q$ and $r$ are all real and positive. State which of the following statements is always correct. All roots of $P(x) = 0$ are real The equation $P(x)=0$ has at least one real root The equation $P(x)=0$ has no negative real root The equation $P(x)=0$ must have one positive and one negative real root

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 38 views

0 votes

1 answer

ISI2014-DCG-68
The number of integer solutions for the equation $x^2+y^2=2011$ is $0$ $1$ $2$ $3$

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 23 views

+1 vote

1 answer

ISI2014-DCG-11
Let $x_1$ and $x_2$ be the roots of the quadratic equation $x^2-3x+a=0$, and $x_3$ and $x_4$ be the roots of the quadratic equation $x^2-12x+b=0$. If $x_1, x_2, x_3$ and $x_4 \: (0 < x_1 < x_2 < x_3 < x_4)$ are in $G.P.,$ then $ab$ equals $64$ $5184$ $-64$ $-5184$

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 62 views

+1 vote

2 answers

ISI2015-DCG-20
The total number of factors of $3528$ greater than $1$ but less than $3528$ is $35$ $36$ $34$ None of these

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 27 views

0 votes

1 answer

ISI2017-DCG-16
If $\cos x = \dfrac{1}{2}$, the value of the expression $\dfrac{\cos 6x+6 \cos 4x+15 \cos 2x +10}{\cos 5x+5 \cos 3x +10 \cos x}$ is $\frac{1}{2}$ $1$ $\frac{1}{4}$ $0$

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 15 views

0 votes

1 answer

ISI2014-DCG-55
If $a,b,c$ are sides of a triangle $ABC$ such that $x^2-2(a+b+c)x+3 \lambda (ab+bc+ca)=0$ has real roots then $\lambda < \frac{4}{3}$ $\lambda > \frac{5}{3}$ $\lambda \in \big( \frac{4}{3}, \frac{5}{3}\big)$ $\lambda \in \big( \frac{1}{3}, \frac{5}{3}\big)$

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 33 views

+1 vote

1 answer

ISI2016-DCG-9
The $5000$th term of the sequence $1,2,2,3,3,3,4,4,4,4,\cdots$ is $98$ $99$ $100$ $101$

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 33 views

0 votes

1 answer

ISI2015-MMA-2
If $a,b$ are positive real variables whose sum is a constant $\lambda$, then the minimum value of $\sqrt{(1+1/a)(1+1/b)}$ is $\lambda \: – 1/\lambda$ $\lambda + 2/\lambda$ $\lambda+1/\lambda$ None of the above

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 51 views

+1 vote

1 answer

ISI2015-DCG-65
The value of $\sin ^2 5^{\circ} + \sin ^2 10^{\circ} + \sin ^2 15^{\circ} + \dots + \sin^2 90^{\circ}$ is $8$ $9$ $9.5$ None of these

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 27 views

+1 vote

0 answers

ISI2014-DCG-65
The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n-1)^2} + \cdots \cdots$ is $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 52 views

+1 vote

1 answer

ISI2015-DCG-61
The value of $\sin^6 \frac{\pi}{81} + \cos^6 \frac{\pi}{81}-1+3 \sin ^2 \frac{\pi}{81} \cos^2 \frac{\pi}{81}$ is $\tan ^6 \frac{\pi}{81}$ $0$ $-1$ None of these

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 25 views

+1 vote

2 answers

UGCNET-June-2019-I-32
Consider the following table that shows the number (in lakhs) of different sizes of LED television sets sold by a company over the last seven years from $2012$ to $2018$. Answer the question based on the data contained in the table: Sale of LED Television ... seven years the maximum? $22$ - inch Television $24$ - inch Television $32$ - inch Television $49$ - inch Television

asked Jul 2, 2019 in Numerical Ability by Arjun Veteran (431k points) | 41 views

+1 vote

1 answer

ISI2015-DCG-6
The coefficient of $x^2$ in the product $(1+x)(1+2x)(1+3x) \dots (1+10x)$ is $1320$ $1420$ $1120$ None of these

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 44 views

+1 vote

1 answer

ISI2016-DCG-25
If $\alpha$ and $\beta$ be the roots of the equation $x^{2}+3x+4=0,$ then the equation with roots $(\alpha+\beta)^{2}$ and $(\alpha-\beta)^{2}$ is $x^{2}+2x+63=0$ $x^{2}-63x+2=0$ $x^{2}-2x-63=0$ None of these

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 22 views

+1 vote

1 answer

ISI2015-DCG-39
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b)$, $B(0,0)$ and $C(a,0)$ are mutually perpendicular if $b=\sqrt{2}a$ $b=\pm \sqrt{2}b$ $b= – \sqrt{2}a$ $b=a$

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 20 views

+1 vote

1 answer

ISI2016-DCG-20
The total number of factors of $3528$ greater than $1$ but less than $3528$ is $35$ $36$ $34$ None of these

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 18 views

0 votes

1 answer

ISI2014-DCG-62
If the sum of the first $n$ terms of an arithmetic progression is $cn^2$, then the sum of squares of these $n$ terms is $\frac{n(4n^2-1)c^2}{6}$ $\frac{n(4n^2+1)c^2}{3}$ $\frac{n(4n^2-1)c^2}{3}$ $\frac{n(4n^2+1)c^2}{6}$

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (431k points) | 22 views

+1 vote

2 answers

CMI2018-A-2
Akash, Bharani, Chetan and Deepa are invited to a party. If Bharani and Chetan attend, then Deepa will attend too. If Bharani does not attend, then Akash will not attend. If Deepa does not attend, which of the following is true? Chetan does not attend Akash does not attend either (A) or (B) none of the above

asked Sep 13, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 53 views

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