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Recent questions tagged numerical-ability

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Recent questions tagged numerical-ability

3 votes
4 answers
1
GATE2020-CS-GA-9
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_______. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$
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_______. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$
asked Feb 12 in Numerical Ability Arjun 1.5k views
0 votes
2 answers
2
TIFR2020-A-15
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 $s_{0}$? $81$ $95$ $100$ $121$ $190$
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 $s_{0}$? $81$ $95$ $100$ $121$ $190$
asked Feb 11 in Numerical Ability Lakshman Patel RJIT 144 views
0 votes
1 answer
3
TIFR2020-A-9
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 ... at the front and one at the back. How many pages are missing from Tharoor's book? $45$ $135$ $136$ $198$ $450$
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? $45$ $135$ $136$ $198$ $450$
asked Feb 11 in Verbal Ability Lakshman Patel RJIT 88 views
0 votes
1 answer
4
TIFR2020-A-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 $A(n)$.
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 $A(n)$.
asked Feb 10 in Numerical Ability Lakshman Patel RJIT 68 views
4 votes
6 answers
5
ISRO2020-55
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 $8$ $16$ $18$ $20$
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 $8$ $16$ $18$ $20$
asked Jan 13 in Numerical Ability Satbir 623 views
4 votes
3 answers
6
ISI2014-DCG-10
The number of divisors of $6000$, where $1$ and $6000$ are also considered as divisors of $6000$ is $40$ $50$ $60$ $30$
The number of divisors of $6000$, where $1$ and $6000$ are also considered as divisors of $6000$ is $40$ $50$ $60$ $30$
asked Sep 23, 2019 in Numerical Ability Arjun 321 views
1 vote
2 answers
7
ISI2014-DCG-16
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
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
asked Sep 23, 2019 in Numerical Ability Arjun 179 views
1 vote
2 answers
8
ISI2014-DCG-22
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 ... $c$ has the opposite sign. $a$ and $c$ have the same sign. $a$, $b$ and $c$ have the same sign.
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.
asked Sep 23, 2019 in Numerical Ability Arjun 111 views
2 votes
2 answers
9
ISI2014-DCG-23
The sum of the series $\:3+11+\dots +(8n-5)\:$ is $4n^2-n$ $8n^2+3n$ $4n^2+4n-5$ $4n^2+2$
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 Arjun 153 views
1 vote
1 answer
10
ISI2014-DCG-26
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
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
asked Sep 23, 2019 in Numerical Ability Arjun 107 views
1 vote
1 answer
11
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
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 Arjun 91 views
1 vote
1 answer
12
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
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 Arjun 95 views
0 votes
1 answer
13
ISI2014-DCG-54
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to $0$ $1$ $3$ $4$
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to $0$ $1$ $3$ $4$
asked Sep 23, 2019 in Numerical Ability Arjun 144 views
0 votes
1 answer
14
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 $\lambda < \frac{4}{3}$ $\lambda > \frac{5}{3}$ $\lambda \in \big( \frac{4}{3}, \frac{5}{3}\big)$ $\lambda \in \big( \frac{1}{3}, \frac{5}{3}\big)$
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 Arjun 68 views
0 votes
1 answer
15
ISI2014-DCG-56
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 $4$ $3$ $-4$ $-3$
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 $4$ $3$ $-4$ $-3$
asked Sep 23, 2019 in Numerical Ability Arjun 64 views
1 vote
1 answer
16
ISI2014-DCG-58
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 $(2, -2)$ $(2\sqrt{2},-2)$ $(-2, 2\sqrt{2})$ $(2\sqrt{2}, -2\sqrt{2})$
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 $(2, -2)$ $(2\sqrt{2},-2)$ $(-2, 2\sqrt{2})$ $(2\sqrt{2}, -2\sqrt{2})$
asked Sep 23, 2019 in Numerical Ability Arjun 134 views
0 votes
1 answer
17
ISI2014-DCG-60
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 $b \in \mathbb{R}$
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 $b \in \mathbb{R}$
asked Sep 23, 2019 in Numerical Ability Arjun 58 views
0 votes
1 answer
18
ISI2014-DCG-61
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
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
asked Sep 23, 2019 in Numerical Ability Arjun 122 views
0 votes
1 answer
19
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 $\frac{n(4n^2-1)c^2}{6}$ $\frac{n(4n^2+1)c^2}{3}$ $\frac{n(4n^2-1)c^2}{3}$ $\frac{n(4n^2+1)c^2}{6}$
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 Arjun 65 views
1 vote
0 answers
20
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 $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$
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 Arjun 104 views
0 votes
1 answer
21
ISI2014-DCG-67
Let $y=[\:\log_{10}3245.7\:]$ where $[ a ]$ denotes the greatest integer less than or equal to $a$. Then $y=0$ $y=1$ $y=2$ $y=3$
Let $y=[\:\log_{10}3245.7\:]$ where $[ a ]$ denotes the greatest integer less than or equal to $a$. Then $y=0$ $y=1$ $y=2$ $y=3$
asked Sep 23, 2019 in Numerical Ability Arjun 55 views
0 votes
1 answer
22
ISI2014-DCG-68
The number of integer solutions for the equation $x^2+y^2=2011$ is $0$ $1$ $2$ $3$
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 Arjun 60 views
1 vote
1 answer
23
ISI2014-DCG-69
The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to $18$ $720$ $360$ $36$
The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to $18$ $720$ $360$ $36$
asked Sep 23, 2019 in Numerical Ability Arjun 94 views
0 votes
1 answer
24
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
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 Arjun 184 views
1 vote
1 answer
25
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
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 Arjun 126 views
0 votes
1 answer
26
ISI2015-MMA-12
Consider the polynomial $x^5+ax^4+bx^3+cx^2+dx+4$ where $a,b,c,d$ are real numbers. If $(1+2i)$ and $(3-2i)$ are two two roots of this polynomial then the value of $a$ is $-524/65$ $524/65$ $-1/65$ $1/65$
Consider the polynomial $x^5+ax^4+bx^3+cx^2+dx+4$ where $a,b,c,d$ are real numbers. If $(1+2i)$ and $(3-2i)$ are two two roots of this polynomial then the value of $a$ is $-524/65$ $524/65$ $-1/65$ $1/65$
asked Sep 23, 2019 in Numerical Ability Arjun 114 views
0 votes
1 answer
27
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
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 Arjun 97 views
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