# Recent questions tagged numerical-ability

1
A can is filled with $5$ paise coins. Another can is filled with $10$ paise coins. Another can is filled with $25$ paise coins. All the cans are given wrong labels. If the can labeled $25$ paise is not having the $10$ paise coins, what will the can, labeled $10$ paise have? $25$ paise $5$ paise $10$ paise cannot be determined
1 vote
2
Find the smallest number $y$ such that $y\times 162$ ($y$ multiplied by $162$) is a perfect cube $24$ $27$ $36$ $38$
1 vote
3
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 $26$ $24$ $20$ $22$
4
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_______. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$
5
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 $s_{0}$? $81$ $95$ $100$ $121$ $190$
6
A contiguous part, i.e., a set of adjacent sheets, is missing from Tharoor's GRE preparation book. The number on the first missing page is $183$, and it is known that the number on the last missing page has the same three digits, but in a different order. Note that every sheet ... one at the front and one at the back. How many pages are missing from Tharoor's book? $45$ $135$ $136$ $198$ $450$
7
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 $A(n)$.
8
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 $8$ $16$ $18$ $20$
9
The number of divisors of $6000$, where $1$ and $6000$ are also considered as divisors of $6000$ is $40$ $50$ $60$ $30$
1 vote
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
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.
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
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
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
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
16
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to $0$ $1$ $3$ $4$
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 $\lambda < \frac{4}{3}$ $\lambda > \frac{5}{3}$ $\lambda \in \big( \frac{4}{3}, \frac{5}{3}\big)$ $\lambda \in \big( \frac{1}{3}, \frac{5}{3}\big)$
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
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 $(2, -2)$ $(2\sqrt{2},-2)$ $(-2, 2\sqrt{2})$ $(2\sqrt{2}, -2\sqrt{2})$
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 $b \in \mathbb{R}$
21
If $l=1+a+a^2+ \dots$, $m=1+b+b^2+ \dots$, and $n=1+c+c^2+ \dots$, where $\mid a \mid <1, \: \mid b \mid < 1, \: \mid c \mid <1$ and $a,b,c$ are in arithmetic progression, then $l, m, n$ are in arithmetic progression geometric progression harmonic progression none of these
22
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 $\frac{n(4n^2-1)c^2}{6}$ $\frac{n(4n^2+1)c^2}{3}$ $\frac{n(4n^2-1)c^2}{3}$ $\frac{n(4n^2+1)c^2}{6}$
1 vote
23
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 $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$
24
Let $y=[\:\log_{10}3245.7\:]$ where $[ a ]$ denotes the greatest integer less than or equal to $a$. Then $y=0$ $y=1$ $y=2$ $y=3$
The number of integer solutions for the equation $x^2+y^2=2011$ is $0$ $1$ $2$ $3$
The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to $18$ $720$ $360$ $36$
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