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Recent questions tagged quantitative-aptitude

1 votes
1 answer
811
ISI2015-DCG-39
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b)$, $B(0,0)$ and $C(a,0)$ are mutually perpendicular if $b=\sqrt{2}a$ $b=\pm \sqrt{2}b$ $b= – \sqrt{2}a$ $b=a$
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b)$, $B(0,0)$ and $C(a,0)$ are mutually perpendicular if$b=\sqrt{2}a$$b=\pm \sqrt{2}b$$b= – \sqrt{2}a$$b=a$...
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0 votes
0 answers
812
ISI2015-DCG-40
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) represent a circle a parabola an ellipse a hyperbola
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) representa circlea ...
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0 votes
1 answer
814
ISI2015-DCG-59
If in a $\Delta ABC$, $\angle B = \frac{2 \pi}{3}$, then $\cos A + \cos C$ lies in $[\:- \sqrt{3}, \sqrt{3}\:]$ $(\: – \sqrt{3}, \sqrt{3}\:]$ $(\:\frac{3}{2}, \sqrt{3}\:)$ $(\:\frac{3}{2}, \sqrt{3}\:]$
If in a $\Delta ABC$, $\angle B = \frac{2 \pi}{3}$, then $\cos A + \cos C$ lies in$[\:- \sqrt{3}, \sqrt{3}\:]$$(\: – \sqrt{3}, \sqrt{3}\:]$$(\:\frac{3}{2}, \sqrt{3}\:)$...
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0 votes
0 answers
815
ISI2015-DCG-60
Which of the following relations is true for the following figure? $b^2 = c(c+a)$ $c^2 = a(a+b)$ $a^2=b(b+c)$ All of these
Which of the following relations is true for the following figure?$b^2 = c(c+a)$$c^2 = a(a+b)$$a^2=b(b+c)$All of these
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1 votes
1 answer
816
ISI2015-DCG-61
The value of $\sin^6 \frac{\pi}{81} + \cos^6 \frac{\pi}{81}-1+3 \sin ^2 \frac{\pi}{81} \cos^2 \frac{\pi}{81}$ is $\tan ^6 \frac{\pi}{81}$ $0$ $-1$ None of these
The value of $\sin^6 \frac{\pi}{81} + \cos^6 \frac{\pi}{81}-1+3 \sin ^2 \frac{\pi}{81} \cos^2 \frac{\pi}{81}$ is$\tan ^6 \frac{\pi}{81}$$0$$-1$None of these
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0 votes
0 answers
817
ISI2015-DCG-62
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is $1$ $2$ $3$ more than $3$
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is$1$$2$$3$more than $3$
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1 votes
1 answer
818
ISI2015-DCG-63
If $\sin^{-1} \frac{1}{\sqrt{5}}$ and $\cos ^{-1} \frac{3}{\sqrt{10}}$ lie in $\bigg[0, \dfrac{\pi}{2}\bigg]$, their sum is equal to $\frac{\pi}{6}$ $\frac{\pi}{3}$ $ \sin^ {-1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$
If $\sin^{-1} \frac{1}{\sqrt{5}}$ and $\cos ^{-1} \frac{3}{\sqrt{10}}$ lie in $\bigg[0, \dfrac{\pi}{2}\bigg]$, their sum is equal to$\frac{\pi}{6}$$\frac{\pi}{3}$$ \sin^ ...
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0 votes
2 answers
819
ISI2015-DCG-64
If $\cos 2 \theta = \sqrt{2}(\cos \theta – \sin \theta)$ then $\tan \theta$ equals $1$ $1$ or $-1$ $\frac{1}{\sqrt{2}}, – \frac{1}{\sqrt{2}}$ or $1$ None of these
If $\cos 2 \theta = \sqrt{2}(\cos \theta – \sin \theta)$ then $\tan \theta$ equals$1$$1$ or $-1$$\frac{1}{\sqrt{2}}, – \frac{1}{\sqrt{2}}$ or $1$None of these
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2 votes
1 answer
820
ISI2015-DCG-65
The value of $\sin ^2 5^{\circ} + \sin ^2 10^{\circ} + \sin ^2 15^{\circ} + \dots + \sin^2 90^{\circ}$ is $8$ $9$ $9.5$ None of these
The value of $\sin ^2 5^{\circ} + \sin ^2 10^{\circ} + \sin ^2 15^{\circ} + \dots + \sin^2 90^{\circ}$ is$8$$9$$9.5$None of these
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0 votes
1 answer
821
ISI2015-DCG-66
If $\sin(\sin^{-1} \frac{2}{5} + \cos ^{-1} x) =1$, then $x$ equals $1$ $\frac{2}{5}$ $\frac{3}{5}$ None of these
If $\sin(\sin^{-1} \frac{2}{5} + \cos ^{-1} x) =1$, then $x$ equals$1$$\frac{2}{5}$$\frac{3}{5}$None of these
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4 votes
1 answer
822
ISI2016-DCG-1
The sequence $\dfrac{1}{\log_{3} 2},\dfrac{1}{\log_{6} 2},\dfrac{1}{\log_{12} 2},\dfrac{1}{\log_{24} 2}\cdots$ is in Arithmetic progression (AP) Geometric progression (GP) Harmonic progression (HP) None of these
The sequence $\dfrac{1}{\log_{3} 2},\dfrac{1}{\log_{6} 2},\dfrac{1}{\log_{12} 2},\dfrac{1}{\log_{24} 2}\cdots$ is inArithmetic progression (AP)Geometric progression (GP)H...
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1 votes
2 answers
823
ISI2016-DCG-2
Let $S=\{6,10,7,13,5,12,8,11,9\},$ and $a=\sum_{x\in S}(x-9)^{2}\:\&\: b=\sum_{x\in S}(x-10)^{2}.$ Then $a<b$ $a>b$ $a=b$ None of these
Let $S=\{6,10,7,13,5,12,8,11,9\},$ and $a=\sum_{x\in S}(x-9)^{2}\:\&\: b=\sum_{x\in S}(x-10)^{2}.$ Then$a<b$$a>b$$a=b$None of these
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1 votes
1 answer
824
ISI2016-DCG-6
The coefficient of $x^{2}$ in the product $(1+x)(1+2x)(1+3x)\cdots (1+10x)$ is $1320$ $1420$ $1120$ None of these
The coefficient of $x^{2}$ in the product $(1+x)(1+2x)(1+3x)\cdots (1+10x)$ is$1320$$1420$$1120$None of these
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0 votes
1 answer
825
ISI2016-DCG-7
Let $x^{2}-2(4k-1)x+15k^{2}-2k-7>0$ for any real value of $x$. Then the integer value of $k$ is $2$ $4$ $3$ $1$
Let $x^{2}-2(4k-1)x+15k^{2}-2k-7>0$ for any real value of $x$. Then the integer value of $k$ is$2$$4$$3$$1$
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1 votes
1 answer
826
ISI2016-DCG-8
Let $S=\{0,1,2,\cdots,25\}$ and $T=\{n\in S\: : \: n^{2}+3n+2\: \text{is divisible by}\: 6\}$. Then the number of elements in the set $T$ is $16$ $17$ $18$ $10$
Let $S=\{0,1,2,\cdots,25\}$ and $T=\{n\in S\: : \: n^{2}+3n+2\: \text{is divisible by}\: 6\}$. Then the number of elements in the set $T$ is$16$$17$$18$$10$
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1 votes
1 answer
827
ISI2016-DCG-9
The $5000$th term of the sequence $1,2,2,3,3,3,4,4,4,4,\cdots$ is $98$ $99$ $100$ $101$
The $5000$th term of the sequence $1,2,2,3,3,3,4,4,4,4,\cdots$ is$98$$99$$100$$101$
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0 votes
1 answer
828
ISI2016-DCG-10
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 di...
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1 votes
1 answer
829
ISI2016-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$$292$
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0 votes
1 answer
830
ISI2016-DCG-13
For all the natural number $n\geq 3,\: n^{2}+1$ is divisible by $3$ not divisible by $3$ divisible by $9$ None of these
For all the natural number $n\geq 3,\: n^{2}+1$ isdivisible by $3$not divisible by $3$divisible by $9$None of these
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0 votes
1 answer
831
ISI2016-DCG-14
For natural numbers $n,$ the inequality $2^{n}>2n+1$ is valid when $n\geq 3$ $n<3$ $n=3$ None of these
For natural numbers $n,$ the inequality $2^{n}>2n+1$ is valid when$n\geq 3$$n<3$$n=3$None of these
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0 votes
1 answer
832
ISI2016-DCG-17
The smallest integer $n$ for which $1+2+2^{2}+2^{3}+2^{4}+\cdots+2^{n}$ exceeds $9999$, given that $\log_{10}2=0.30103$, is $12$ $13$ $14$ None of these
The smallest integer $n$ for which $1+2+2^{2}+2^{3}+2^{4}+\cdots+2^{n}$ exceeds $9999$, given that $\log_{10}2=0.30103$, is$12$$13$$14$None of these
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0 votes
0 answers
833
ISI2016-DCG-18
The value of $(1.1)^{10}$ correct to $4$ decimal places is $2.4512$ $1.9547$ $2.5937$ $1.4512$
The value of $(1.1)^{10}$ correct to $4$ decimal places is$2.4512$$1.9547$$2.5937$$1.4512$
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1 votes
2 answers
834
ISI2016-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 i...
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1 votes
1 answer
835
ISI2016-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
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1 votes
1 answer
836
ISI2016-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
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1 votes
1 answer
837
ISI2016-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 these
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$$x^{2}-63...
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1 votes
2 answers
838
ISI2016-DCG-26
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$ $\frac{r+1}{b}=\frac{r}{ac}$ $\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$ $\left(\frac{r}{b}\right)^{2}=\frac{r+1}{ac}$
If $r$ be the ratio of the roots of the equation $ax^{2}+bx+c=0,$ then $\frac{r}{b}=\frac{r+1}{ac}$$\frac{r+1}{b}=\frac{r}{ac}$$\frac{(r+1)^{2}}{r}=\frac{b^{2}}{ac}$$\lef...
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1 votes
0 answers
840
ISI2016-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}-...
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