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1
ISI2014DCG54
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
in
Numerical Ability
by
Arjun
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isi2014dcg
numericalability
trigonometry
roots
0
votes
0
answers
2
ISI2014DCG61
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
in
Numerical Ability
by
Arjun
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424k
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14
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isi2014dcg
numericalability
progression
+1
vote
0
answers
3
ISI2014DCG65
The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n1)^2} + \cdots \cdots$ is $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$
asked
Sep 23
in
Numerical Ability
by
Arjun
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424k
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isi2014dcg
numericalability
summation
series
0
votes
0
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4
ISI2015MMA27
Let $\cos ^6 \theta = a_6 \cos 6 \theta + a_5 \cos 5 \theta + a_4 \cos 4 \theta + a_3 \cos 3 \theta + a_2 \cos 2 \theta + a_1 \cos \theta +a_0$. Then $a_0$ is $0$ $1/32$ $15/32$ $10/32$
asked
Sep 23
in
Numerical Ability
by
Arjun
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424k
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12
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isi2015mma
numericalability
trigonometry
nongate
0
votes
0
answers
5
ISI2015MMA29
The set $\{x \: : \begin{vmatrix} x+\frac{1}{x} \end{vmatrix} \gt6 \}$ equals the set $(0,32\sqrt{2}) \cup (3+2\sqrt{2}, \infty)$ $( \infty, 32\sqrt{2}) \cup (3+2 \sqrt{2}, \infty)$ $( \infty, 32\sqrt{2}) \cup (3+2\sqrt{2}, \infty)$ $( \infty, 32\sqrt{2}) \cup (3+2 \sqrt{2},32\sqrt{2}) \cup (3+2 \sqrt{2}, \infty )$
asked
Sep 23
in
Numerical Ability
by
Arjun
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424k
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10
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isi2015mma
numbersystem
nongate
0
votes
0
answers
6
ISI2015DCG40
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) represent a circle a parabola an ellipse a hyperbola
asked
Sep 18
in
Numerical Ability
by
gatecse
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16.8k
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41
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isi2015dcg
numericalability
trigonometry
geometry
0
votes
0
answers
7
ISI2015DCG53
Four squares of sides $x$ cm each are cut off from the four corners of a square metal sheet having side $100$ cm. The residual sheet is then folded into an open box which is then filled with a liquid costing Rs. $x^2$ with $cm^3$. The value of $x$ for which the cost of filling the box completely with the liquid is maximized, is $100$ $50$ $30$ $10$
asked
Sep 18
in
Numerical Ability
by
gatecse
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16.8k
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9
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isi2015dcg
numericalability
geometry
squares
0
votes
0
answers
8
ISI2015DCG60
Which of the following relations is true for the following figure? $b^2 = c(c+a)$ $c^2 = a(a+b)$ $a^2=b(b+c)$ All of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
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16.8k
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12
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isi2015dcg
numericalability
geometry
triangles
0
votes
0
answers
9
ISI2015DCG62
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is $1$ $2$ $3$ more than $3$
asked
Sep 18
in
Numerical Ability
by
gatecse
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16.8k
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11
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isi2015dcg
numericalability
trigonometry
0
votes
0
answers
10
ISI2016DCG13
For all the natural number $n\geq 3,\: n^{2}+1$ is divisible by $3$ not divisible by $3$ divisible by $9$ None of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
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16.8k
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8
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isi2016dcg
numericalability
numbersystem
remaindertheorem
0
votes
0
answers
11
ISI2016DCG18
The value of $(1.1)^{10}$ correct to $4$ decimal places is $2.4512$ $1.9547$ $2.5937$ $1.4512$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
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16.8k
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7
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isi2016dcg
numericalability
numbersystem
+1
vote
0
answers
12
ISI2016DCG29
The condition that ensures that the roots of the equation $x^{3}px^{2}+qxr=0$ are in H.P. is $r^{2}9pqr+q^{3}=0$ $27r^{2}9pqr+3q^{3}=0$ $3r^{3}27pqr9q^{3}=0$ $27r^{2}9pqr+2q^{3}=0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
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16.8k
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9
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isi2016dcg
numericalability
quadraticequations
roots
0
votes
0
answers
13
ISI2016DCG51
Four squares of sides $x\: cm$ each are cut off from the four corners of a square metal sheet having side $10\: cm.$ The residual sheet is then folded into an open box which is then filled with a liquid costing Rs. $x^{2}$ per $cm^{3}.$ The value of $x$ for which the cost of filling the box completely with the liquid is maximized, is $100$ $50$ $30$ $10$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
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16.8k
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5
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isi2016dcg
numericalability
geometry
0
votes
0
answers
14
ISI2016DCG70
Water pours into a rectangular tank of $20\:metres$ depth which was initially halffilled. The rate at which the height of the water rises is inversely proportional to the height of the water at that instant. If the height of the water after an hour is observed to be $12\:metres$, ... hours, will be required to fill up the tank? $\frac{75}{11}$ $\frac{125}{11}$ $\frac{25}{3}$ $5$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
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16.8k
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12
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isi2016dcg
numericalability
worktime
0
votes
0
answers
15
ISI2017DCG13
The value of $\dfrac{x}{1x^2} + \dfrac{x^2}{1x^4} + \dfrac{x^4}{1x^8} + \dfrac{x^8}{1x^{16}}$ is $\frac{1}{1x^{16}}$ $\frac{1}{1x^{12}}$ $\frac{1}{1x} – \frac{1}{1x^{16}}$ $\frac{1}{1x} – \frac{1}{1x^{12}}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
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16.8k
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11
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isi2017dcg
numericalability
series
summation
0
votes
0
answers
16
ISI2017DCG18
If $a,b,c$ are the sides of $\Delta ABC$, then $\tan \frac{BC}{2} \tan \frac{A}{2}$ is equal to $\frac{b+c}{bc}$ $\frac{bc}{b+c}$ $\frac{cb}{c+b}$ none of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
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16.8k
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7
views
isi2017dcg
numericalability
trigonometry
geometry
0
votes
0
answers
17
ISI2017DCG19
The angle between the tangents drawn from the point $(1, 7)$ to the circle $x^2+y^2=25$ is $\tan^{1} (\frac{1}{2})$ $\tan^{1} (\frac{2}{3})$ $\frac{\pi}{2}$ $\frac{\pi}{3}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
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6
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isi2017dcg
numericalability
geometry
circle
trigonometry
+1
vote
0
answers
18
ISI2018DCG11
The sum of $99^{th}$ power of all the roots of $x^71=0$ is equal to $1$ $2$ $1$ $0$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
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16.8k
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17
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isi2018dcg
numericalability
polynomials
roots
0
votes
0
answers
19
ISI2018DCG19
The area of the region formed by line segments joining the points of intersection of the circle $x^2+y^210x6y+9=0$ with the two axes in succession in a definite order (clockwise or anticlockwise) is $16$ $9$ $3$ $12$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
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10
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isi2018dcg
circle
intersection
nongate
+1
vote
0
answers
20
Aptitude Self Doubt
If altitude of equilateral triangle is given, then what is formula to find area of it??
asked
Jun 2
in
Numerical Ability
by
srestha
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117k
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82
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numericalability
0
votes
0
answers
21
TrigonometryDoubt
$1)$What is the value of $\sin 15^{o}$ $\sin 15^{o}=\sin \left ( 60^{o}45^{o} \right )$ $=\sin 60^{o}.\cos 45^{o}\cos 60^{o}.\sin 45^{o}$ ... $=\frac{\sqrt{3}1}{2\sqrt{2}}=0.258$ Is it correct? $2)$ $\sin 80^{o}$ value=_____________ Is it possible to do?
asked
May 28
in
Numerical Ability
by
srestha
Veteran
(
117k
points)

57
views
generalaptitude
0
votes
0
answers
22
Aptitude(Recruitment Ques)
The value of $\sin 120^{o}+\sin 780^{o}\cos 360^{o}$ $=(\sin (90^{o}\times 2)60^{o})+\left ( \sin \left ( 90^{o}\times 8 \right )+60^{o} \right )\left ( \cos (90^{o}\times 4)+0^{o} \right )$ $=\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}1=0.73$ right??
asked
May 28
in
Numerical Ability
by
srestha
Veteran
(
117k
points)

44
views
generalaptitude
+1
vote
0
answers
23
ISI2018PCBA3
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r1$ divides $n^s1$ if and only if $r$ divides $s$.
asked
May 12
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.9k
points)

18
views
isi2018pcba
generalaptitude
numericalability
descriptive
0
votes
0
answers
24
ISI2018PCBA2
Let there be a pile of $2018$ chips in the center of a table. Suppose there are two players who could alternately remove one, two or three chips from the pile. At least one chip must be removed, but no more than three chips can be removed in a ... game, that is, whatever moves his opponent makes, he can always make his moves in a certain way ensuring his win? Justify your answer.
asked
May 12
in
Numerical Ability
by
akash.dinkar12
Boss
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41.9k
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16
views
isi2018pcba
generalaptitude
numericalability
logicalreasoning
descriptive
0
votes
0
answers
25
ISI2018MMA23
For $n\geq 1$, let $a_n=\frac{1}{2^2} + \frac{2}{3^2}+ \dots +\frac{n}{(n+1)^2}$ and $b_n=c_0 + c_1r + c_2r^2 + \dots + c_nr^n$,where $\mid c_k \mid \leq M$ for all integer $k$ and $\mid r \mid <1$. Then both $\{a_n\}$ ... $\{a_n\}$ is not a Cauchy sequence,and $\{b_n\}$ is Cauchy sequence neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.9k
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13
views
isi2018mma
generalaptitude
numericalability
0
votes
0
answers
26
ISI2018MMA22
The $x$axis divides the circle $x^2 + y^2 − 6x − 4y + 5 = 0$ into two parts. The area of the smaller part is $2\pi1$ $2(\pi1)$ $2\pi3$ $2(\pi2)$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.9k
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17
views
isi2018mma
generalaptitude
numericalability
0
votes
0
answers
27
ISI2018MMA21
The angle between the tangents drawn from the point $(1, 4)$ to the parabola $y^2 = 4x$ is $\pi /2$ $\pi /3$ $\pi /4$ $\pi /6$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.9k
points)

9
views
isi2018mma
generalaptitude
numericalability
0
votes
0
answers
28
ISI2018MMA8
Let $a$ and $b$ be two positive integers such that $a = k_1b + r_1$ and $b = k_2r_1 + r_2,$ where $k_1,k_2,r_1,r_2$ are positive integers with $r_2 < r_1 < b$ Then $\text{gcd}(a, b)$ is same as $\text{gcd}(r_1,r_2)$ $\text{gcd}(k_1,k_2)$ $\text{gcd}(k_1,r_2)$ $\text{gcd}(r_1,k_2)$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.9k
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18
views
isi2018mma
generalaptitude
numericalability
0
votes
0
answers
29
ISI2018MMA5
One needs to choose six real numbers $x_1, x_2, . . . , x_6$ such that the product of any five of them is equal to other number. The number of such choices is $3$ $33$ $63$ $93$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.9k
points)

15
views
isi2018mma
generalaptitude
numericalability
0
votes
0
answers
30
Allen Career Institute:Aptitude
The vast majority of south Korean youngster's graduate from high school and of these, 82% go on to university. This is the highest rate in the OECD and for a country which had an adult literacy rate of just 22% in 1945, it is ... in both the years compared were almost same (4) The proportion of unemployed in recent times has increased exponentially compared to 1945
asked
Mar 22
in
Verbal Ability
by
srestha
Veteran
(
117k
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57
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generalaptitude
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