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

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

# Recent questions in Numerical Ability

0 votes
4 answers
1
Find the smallest number $y$ such that $y\times 162$ ($y$ multiplied by $162$) is a perfect cube $24$ $27$ $36$ $38$
0 votes
2 answers
2
When the sum of all possible two digit numbers formed from three different one digit natural numbers are divided by sum of the original three numbers, the result is $26$ $24$ $20$ $22$
3 votes
4 answers
3
Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, then $\alpha + \beta$ is_______. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$
0 votes
2 answers
4
The sequence $s_{0},s_{1},\dots , s_{9}$ is defined as follows: $s_{0} = s_{1} + 1$ $2s_{i} = s_{i-1} + s_{i+1} + 2 \text{ for } 1 \leq i \leq 8$ $2s_{9} = s_{8} + 2$ What is $s_{0}$? $81$ $95$ $100$ $121$ $190$
0 votes
1 answer
5
A ball is thrown directly upwards from the ground at a speed of $10\: ms^{-1}$, on a planet where the gravitational acceleration is $10\: ms^{-2}$. Consider the following statements: The ball reaches the ground exactly $2$ seconds after it is thrown up The ball travels a ... Statement $3$ is correct None of the Statements $1,2$ or $3$ is correct All of the Statements $1,2$ and $3$ are correct
0 votes
1 answer
6
What is the maximum number of regions that the plane $\mathbb{R}^{2}$ can be partitioned into using $10$ lines? $25$ $50$ $55$ $56$ $1024$ Hint: Let $A(n)$ be the maximum number of partitions that can be made by $n$ lines. Observe that $A(0) = 1, A(2) = 2, A(2) = 4$ etc. Come up with a recurrence equation for $A(n)$.
4 votes
6 answers
7
If $x+2y=30$, then $\left(\dfrac{2y}{5}+\dfrac{x}{3} \right) + \left (\dfrac{x}{5}+\dfrac{2y}{3} \right)$ will be equal to $8$ $16$ $18$ $20$
4 votes
3 answers
8
The number of divisors of $6000$, where $1$ and $6000$ are also considered as divisors of $6000$ is $40$ $50$ $60$ $30$
1 vote
1 answer
9
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 $64$ $5184$ $-64$ $-5184$
1 vote
2 answers
10
The sum of the series $\dfrac{1}{1.2} + \dfrac{1}{2.3}+ \cdots + \dfrac{1}{n(n+1)} + \cdots$ is $1$ $1/2$ $0$ non-existent
1 vote
2 answers
11
The conditions on $a$, $b$ and $c$ under which the roots of the quadratic equation $ax^2+bx+c=0 \: ,a \neq 0, \: b \neq 0$ and $c \neq 0$, are unequal magnitude but of the opposite signs, are the following: $a$ and $c$ have the same sign while $b$ has the opposite sign ... $b$ have the same sign while $c$ has the opposite sign. $a$ and $c$ have the same sign. $a$, $b$ and $c$ have the same sign.
2 votes
2 answers
12
The sum of the series $\:3+11+\dots +(8n-5)\:$ is $4n^2-n$ $8n^2+3n$ $4n^2+4n-5$ $4n^2+2$
1 vote
1 answer
13
Let $x_1 > x_2>0$. Then which of the following is true? $\log \big(\frac{x_1+x_2}{2}\big) > \frac{\log x_1+ \log x_2}{2}$ $\log \big(\frac{x_1+x_2}{2}\big) < \frac{\log x_1+ \log x_2}{2}$ There exist $x_1$ and $x_2$ such that $x_1 > x_2 >0$ and $\log \big(\frac{x_1+x_2}{2}\big) = \frac{\log x_1+ \log x_2}{2}$ None of these
1 vote
1 answer
14
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
1 vote
1 answer
15
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
0 votes
1 answer
16
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to $0$ $1$ $3$ $4$
0 votes
1 answer
17
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 $\lambda < \frac{4}{3}$ $\lambda > \frac{5}{3}$ $\lambda \in \big( \frac{4}{3}, \frac{5}{3}\big)$ $\lambda \in \big( \frac{1}{3}, \frac{5}{3}\big)$
0 votes
1 answer
18
Two opposite vertices of a rectangle are $(1,3)$ and $(5,1)$ while the other two vertices lie on the straight line $y=2x+c$. Then the value of $c$ is $4$ $3$ $-4$ $-3$
1 vote
1 answer
19
Consider a circle with centre at origin and radius $2\sqrt{2}$. A square is inscribed in the circle whose sides are parallel to the $X$ an $Y$ axes. The coordinates of one of the vertices of this square are $(2, -2)$ $(2\sqrt{2},-2)$ $(-2, 2\sqrt{2})$ $(2\sqrt{2}, -2\sqrt{2})$
0 votes
1 answer
20
The equation of any circle passing through the origin and with its centre on the $X$-axis is given by $x^2+y^2-2ax=0$ where $a$ must be positive $x^2+y^2-2ax=0$ for any given $a \in \mathbb{R}$ $x^2+y^2-2by=0$ where $b$ must be positive $x^2+y^2-2by=0$ for any given $b \in \mathbb{R}$