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Recent questions tagged quantitative-aptitude
1
votes
1
answer
781
ISI2015-MMA-15
The number of real solutions of the equations $(9/10)^x = -3+x-x^2$ is $2$ $0$ $1$ none of the above
The number of real solutions of the equations $(9/10)^x = -3+x-x^2$ is$2$$0$$1$none of the above
Arjun
603
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
number-system
quadratic-equations
non-gate
+
–
2
votes
3
answers
782
ISI2015-MMA-16
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\: (\geq 2)$ and $n\: (\geq 1)$ respectively, satisfy $f(x^2+1)=f(x)g(x),$ for every $x \in \mathbb{R}$, then $f$ has exactly one real root $x_0$ such that $f’(x_0) \neq 0$ $f$ has exactly one real root $x_0$ such that $f’(x_0) = 0$ $f$ has $m$ distinct real roots $f$ has no real root
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\: (\geq 2)$ and $n\: (\geq 1)$ respectively, satisfy$$f(x^2+1)=f(x)g(x),$$for every $x \in \mathbb{R}$, then$f$ ha...
Arjun
958
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
quadratic-equations
functions
non-gate
+
–
2
votes
1
answer
783
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
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
Arjun
517
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
summation
+
–
2
votes
1
answer
784
ISI2015-MMA-18
The set of complex numbers $z$ satisfying the equation $(3+7i)z+(10-2i)\overline{z}+100=0$ represents, in the complex plane, a straight line a pair of intersecting straight lines a point a pair of distinct parallel straight lines
The set of complex numbers $z$ satisfying the equation $$(3+7i)z+(10-2i)\overline{z}+100=0$$ represents, in the complex plane,a straight linea pair of intersecting straig...
Arjun
1.2k
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
geometry
straight-lines
complex-number
non-gate
+
–
1
votes
2
answers
785
ISI2015-MMA-27
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 $0$ $1/32$ $15/32$ $10/32$
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$$1/32$$...
Arjun
622
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
trigonometry
non-gate
+
–
1
votes
1
answer
786
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 $\sqrt{125}$ $69/5$ $\sqrt{112}$ $\sqrt{864}/5$
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{11...
Arjun
620
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
geometry
median
non-gate
+
–
1
votes
1
answer
787
ISI2015-MMA-41
Let $k$ and $n$ be integers greater than $1$. Then $(kn)!$ is not necessarily divisible by $(n!)^k$ $(k!)^n$ $n! \cdot k! \cdot$ $2^{kn}$
Let $k$ and $n$ be integers greater than $1$. Then $(kn)!$ is not necessarily divisible by$(n!)^k$$(k!)^n$$n! \cdot k! \cdot$$2^{kn}$
Arjun
655
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
number-system
remainder-theorem
+
–
2
votes
4
answers
788
ISI2015-DCG-1
The sequence $\dfrac{1}{\log_3 2}, \: \dfrac{1}{\log_6 2}, \: \dfrac{1}{\log_{12} 2}, \: \dfrac{1}{\log_{24} 2} \dots $ is in Arithmetic progression (AP) Geometric progression ( GP) Harmonic progression (HP) None of these
The sequence $\dfrac{1}{\log_3 2}, \: \dfrac{1}{\log_6 2}, \: \dfrac{1}{\log_{12} 2}, \: \dfrac{1}{\log_{24} 2} \dots $ is inArithmetic progression (AP)Geometric progress...
gatecse
586
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
arithmetic-series
+
–
1
votes
4
answers
789
ISI2015-DCG-2
Let $S=\{6, 10, 7, 13, 5, 12, 8, 11, 9\}$ and $a=\underset{x \in S}{\Sigma} (x-9)^2$ & $b = \underset{x \in S}{\Sigma} (x-10)^2$. Then $a <b$ $a>b$ $a=b$ None of these
Let $S=\{6, 10, 7, 13, 5, 12, 8, 11, 9\}$ and $a=\underset{x \in S}{\Sigma} (x-9)^2$ & $b = \underset{x \in S}{\Sigma} (x-10)^2$. Then$a <b$$a>b$$a=b$None of these
gatecse
562
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
summation
+
–
0
votes
2
answers
790
ISI2015-DCG-4
If $\tan x=p+1$ and $\tan y=p-1$, then the value of $2 \cot (x-y)$ is $2p$ $p^2$ $(p+1)(p-1)$ $\frac{2p}{p^2-1}$
If $\tan x=p+1$ and $\tan y=p-1$, then the value of $2 \cot (x-y)$ is$2p$$p^2$$(p+1)(p-1)$$\frac{2p}{p^2-1}$
gatecse
826
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
trigonometry
+
–
1
votes
1
answer
791
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
The coefficient of $x^2$ in the product $(1+x)(1+2x)(1+3x) \dots (1+10x)$ is$1320$$1420$$1120$None of these
gatecse
403
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
number-system
coefficients
+
–
0
votes
1
answer
792
ISI2015-DCG-7
Let $x^2-2(4k-1)x+15k^2-2k-7>0$ for any real value of $x$. Then the integer value of $k$ is $2$ $4$ $3$ $1$
Let $x^2-2(4k-1)x+15k^2-2k-7>0$ for any real value of $x$. Then the integer value of $k$ is$2$$4$$3$$1$
gatecse
558
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
+
–
1
votes
2
answers
793
ISI2015-DCG-8
Let $S=\{0, 1, 2, \cdots 25\}$ and $T=\{n \in S: n^2+3n+2$ is divisible by $6\}$. Then the number of elements in the set $T$ is $16$ $17$ $18$ $10$
Let $S=\{0, 1, 2, \cdots 25\}$ and $T=\{n \in S: n^2+3n+2$ is divisible by $6\}$. Then the number of elements in the set $T$ is$16$$17$$18$$10$
gatecse
535
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
number-system
remainder-theorem
+
–
2
votes
1
answer
794
ISI2015-DCG-9
Let $a$ be the $81$ – digit number of which all the digits are equal to $1$. Then the number $a$ is, divisible by $9$ but not divisible by $27$ divisible by $27$ but not divisible by $81$ divisible by $81$ None of the above
Let $a$ be the $81$ – digit number of which all the digits are equal to $1$. Then the number $a$ is,divisible by $9$ but not divisible by $27$divisible by $27$ but not ...
gatecse
507
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
number-system
remainder-theorem
+
–
0
votes
1
answer
795
ISI2015-DCG-10
The $5000$th term of the sequence $1,2,2, 3,3,3,4,4,4,4, \cdots$ is $98$ $99$ $100$ $101$
The $5000$th term of the sequence $1,2,2, 3,3,3,4,4,4,4, \cdots$ is$98$$99$$100$$101$
gatecse
429
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
sequence-series
+
–
1
votes
1
answer
796
ISI2015-DCG-12
The highest power of $3$ contained in $1000!$ is $198$ $891$ $498$ $292$
The highest power of $3$ contained in $1000!$ is$198$$891$$498$$292$
gatecse
512
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
number-system
factors
+
–
0
votes
1
answer
797
ISI2015-DCG-13
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
For all the natural number $n \geq 3, \: n^2+1$ isdivisible by $3$not divisible by $3$divisible by $9$None of these
gatecse
363
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
number-system
+
–
0
votes
1
answer
798
ISI2015-DCG-14
For natural numbers $n$, the inequality $2^n >2n+1$ is valid when $n \geq 3$ $n < 3$ $n=3$ None of these
For natural numbers $n$, the inequality $2^n >2n+1$ is valid when$n \geq 3$$n < 3$$n=3$None of these
gatecse
361
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
number-system
+
–
0
votes
1
answer
799
ISI2015-DCG-15
The smallest integer $n$ for which $1+2+2^2+2^3+2^4+ \cdots +2^n$ exceeds $9999$, given that $\log_{10} 2=0.30103$, is $12$ $13$ $14$ None of these
The smallest integer $n$ for which $1+2+2^2+2^3+2^4+ \cdots +2^n$ exceeds $9999$, given that $\log_{10} 2=0.30103$, is$12$$13$$14$None of these
gatecse
376
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
summation
+
–
0
votes
2
answers
800
ISI2015-DCG-16
The shaded region in the following diagram represents the relation $y \leq x$ $\mid y \mid \leq \mid x \mid$ $y \leq \mid x \mid$ $\mid y \mid \leq x$
The shaded region in the following diagram represents the relation$y \leq x$$\mid y \mid \leq \mid x \mid$$y \leq \mid x \mid$$\mid y \mid \leq x$
gatecse
348
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
geometry
area
+
–
0
votes
1
answer
801
ISI2015-DCG-18
The value of $(1.1)^{10}$ correct to $4$ decimal places is $2.4512$ $1.9547$ $2.5937$ $1.4512$
The value of $(1.1)^{10}$ correct to $4$ decimal places is$2.4512$$1.9547$$2.5937$$1.4512$
gatecse
492
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
number-system
binomial-theorem
+
–
0
votes
1
answer
802
ISI2015-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 $n$
The expression $3^{2n+1} + 2^{n+2}$ is divisible by $7$ forall positive integer values of $n$all non-negative integer values of $n$only even integer values of $n$only odd...
gatecse
397
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
number-system
+
–
2
votes
2
answers
803
ISI2015-DCG-20
The total number of factors of $3528$ greater than $1$ but less than $3528$ is $35$ $36$ $34$ None of these
The total number of factors of $3528$ greater than $1$ but less than $3528$ is$35$$36$$34$None of these
gatecse
479
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
number-system
factors
+
–
1
votes
2
answers
804
ISI2015-DCG-23
The value of $\log _2 e – \log _4 e + \log _8 e – \log _{16} e + \log_{32} e – \cdots$ is $-1$ $0$ $1$ None of these
The value of $\log _2 e – \log _4 e + \log _8 e – \log _{16} e + \log_{32} e – \cdots$ is$-1$$0$$1$None of these
gatecse
464
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
logarithms
+
–
1
votes
1
answer
805
ISI2015-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 the above
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$$x^2-63x+2=...
gatecse
470
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
+
–
0
votes
1
answer
806
ISI2015-DCG-26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$$\frac{r+1}{b}=\frac{r}{ac}$$\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$$\lef...
gatecse
267
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
+
–
0
votes
1
answer
807
ISI2015-DCG-28
If one root of a quadratic equation $ax^2+bx+c=0$ be equal to the $n^{th}$ power of the other, then $(ac)^{\frac{n}{n+1}} +b=0$ $(ac)^{\frac{n+1}{n}} +b=0$ $(ac^{n})^{\frac{1}{n+1}} +(a^nc)^{\frac{1}{n+1}}+b=0$ $(ac^{\frac{1}{n+1}})^n +(a^{\frac{1}{n+1}}c)^{n+1}+b=0$
If one root of a quadratic equation $ax^2+bx+c=0$ be equal to the $n^{th}$ power of the other, then$(ac)^{\frac{n}{n+1}} +b=0$$(ac)^{\frac{n+1}{n}} +b=0$$(ac^{n})^{\frac{...
gatecse
272
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
+
–
3
votes
1
answer
808
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 $r^2-9pqr+q^3=0$ $27r^2-9pqr+3q^3=0$ $3r^3-27pqr-9q^3=0$ $27r^2-9pqr+2q^3=0$
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$$27r^2-9pqr+2q^3=0$
gatecse
463
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
cubic-equations
+
–
0
votes
1
answer
809
ISI2015-DCG-30
Let $p,q,r,s$ be real numbers such that $pr=2(q+s)$. Consider the equations $x^2+px+q=0$ and $x^2+rx+s=0$. Then at least one of the equations has real roots both these equations have real roots neither of these equations have real roots given data is not sufficient to arrive at any conclusion
Let $p,q,r,s$ be real numbers such that $pr=2(q+s)$. Consider the equations $x^2+px+q=0$ and $x^2+rx+s=0$. Thenat least one of the equations has real rootsboth these equa...
gatecse
387
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
quadratic-equations
roots
+
–
0
votes
1
answer
810
ISI2015-DCG-38
The length of the chord on the straight line $3x-4y+5=0$ intercepted by the circle passing through the points $(1,2), (3,-4)$ and $(5,6)$ is $12$ $14$ $16$ $18$
The length of the chord on the straight line $3x-4y+5=0$ intercepted by the circle passing through the points $(1,2), (3,-4)$ and $(5,6)$ is$12$$14$$16$$18$
gatecse
352
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
geometry
lines
circle
+
–
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