Recent questions tagged question-paper-2

If $a,b,c$ are non- Coplanar unit vector such that $a \times (b \times c) = \large\frac{b+c}{\sqrt 2}$, then the angle between a and b is

asked Mar 9, 2015 by meena.p

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Let z and w be two complex numbers such that $|z| \leq 1, |w| \leq 1$ and $|z+iw|$ = |z-i w}=2$ Then z equals

asked Mar 9, 2015 by meena.p

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The function $f(x) = \large\frac{\ln(\pi+x)}{\ln (e+x)}$ is

asked Mar 9, 2015 by meena.p

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If $f(x) = A \sin \bigg( \large\frac{\pi x}{2}\bigg)$$+B;f'\bigg(\large\frac{1}{2}\bigg)=$$\sqrt 2$ and $\int \limits_0^1 f(x)dx= \large\frac{2A}{\pi}$

asked Mar 6, 2015 by meena.p

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If $A,B$ and $C$ are three non- coplanar vectors then $(A+B+C).((A+B) \times (A+B) \times (A+C))$ equals

asked Mar 6, 2015 by meena.p

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If $p,q,r$ are positive and are in A.P the roots of quadratic equations $px^2+qx+r =0$ are all real for

asked Mar 6, 2015 by meena.p

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The value of $\int \limits_{\pi} ^{2 \pi} [ 2 \sin x]dx$ where [.] represents the greatest integer function , is

asked Mar 6, 2015 by meena.p

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Consider a circle with center lying on the focus of the parabola $ y^2=2px$ Such that it touches the directix of the parabola. Then a point of intersection of the circle and the parabola is

asked Mar 5, 2015 by meena.p

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Let $f(x) =(x+1)^2-1 , ( x \leq -1)$. Then the set $S= \{x : f(x) =f^{-1}(x)\}$ is

asked Mar 5, 2015 by meena.p

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The next term of the geometric progression $x,x^2+2,x^3-10$ is

asked Mar 5, 2015 by meena.p

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Let $u,v$ and $w$ be vectors such that $u+v+w$. If $|u|=3,|v|=4$ and $||w|=5$. Then the value of $ u.v+v.w+w.u $ is

asked Mar 5, 2015 by meena.p

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The slope of the tangent to a curve $y= f(x) $ at $(x,f(x))$ is $2x+1$. If curve passes through the point $(1,2)$ then the area of the region bounded by the curve the x-axis and the line $x=1$ is

asked Mar 5, 2015 by meena.p

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The minimum value of the expression $\sin \alpha +\sin \beta + \sin \gamma$ where $\alpha , \beta,\gamma$ real number satisfying $\alpha+\beta+\gamma=\pi$

asked Mar 5, 2015 by meena.p

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If P and Q are the roots of $x^2+px+q=0$ then

asked Mar 5, 2015 by meena.p

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The orthocenter of the triangle formed by the lines $xy =0$ and $x+y=1$ is

asked Mar 5, 2015 by meena.p

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Let $a,b,c$ be positive numbers. The following system of equations in $x,y$ and $z . \large\frac{x^2}{a^2} +\frac{y^2}{b^2} -\frac{z^2}{c^2} $$=1;\large\frac{x^2}{a^2} -\frac{y^2}{b^2} +\frac{z^2}{c^2} $$=1;\large\frac{-x^2}{a^2} +\frac{y^2}{b^2} + \frac{z^2}{c^2} $$=1$;

asked Mar 5, 2015 by meena.p

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Let z and w be two non-zero complex numbers such that $|z| =|w|$ and $Arg\; z+Arg\;W= \pi$ . Then Z equals

asked Mar 4, 2015 by meena.p

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The probability of India winning a test match against england is $\large\frac{1}{2}$ Assuming independent from match to match the probability that in a 5 match series india's second win occurs of the third test is

asked Mar 4, 2015 by meena.p

1 answer

Let $a = \overrightarrow{i} -\overrightarrow{j} ; b = \overrightarrow{j} -\overrightarrow{k}; c = \overrightarrow{k} -\overrightarrow{i}$ if $ \overrightarrow{d}$ is a unit vector such that $ \overrightarrow{a} -\overrightarrow{d} =0= [b,c,d]$ then d equals

asked Mar 4, 2015 by meena.p

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On the interval $[0,1]$ the function $x^{25} (1-x)^{75}$ takes the maximum values at the point

asked Mar 4, 2015 by meena.p

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Three of the six vertices of a regular hexagon are chosen at random . The probability that the triangle with these three vertices equilateral equals

asked Mar 4, 2015 by meena.p

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Let $f(x)$ be defined for all $x >0$ and be continued . Let $f(x)$ satisfy $f( \large\frac{x}{y} )=f(x)-f(y)$ for all x,y and f(e)=1$ Then

asked Mar 4, 2015 by meena.p

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Let $f(x)$ be defined for all $x >0$ and be continued . Let $f(x)$ satisfy $f( \large\frac{x}{y} )=f(x)-f(y)$ for all x,y and f(e)=1$ Then

asked Mar 4, 2015 by meena.p

1 answer

The radius of the circle passing through the foci of the ellipse $\large\frac{x^2}{16} +\frac{y^2}{9}$$=1$ and having its center at $(0,3)$ is

asked Mar 4, 2015 by meena.p

1 answer

Let $ n >1$ be a positive integer. Then the largest integer m such that $(n^m+1)$ divides $(1+n+n^2+...n^{127})$ is

asked Mar 4, 2015 by meena.p

1 answer

The radius of the circle passing through the foli of the ellipse $\large\frac{x^2}{16} +\frac{y^2}{9}$$=1$ and having its center at $(0,3)$ is

asked Mar 3, 2015 by meena.p

1 answer

Let $ n >1$ be a positive integer. Then the largest m such that $(n^m+1)$ divides $(1+n+n^2+.....n^{127})$ is

asked Mar 3, 2015 by meena.p

1 answer

In triangle ABC $\angle B = \large\frac{\pi}{3}$ and $\angle C = \large\frac{\pi}{4}$ Let d divide BC instantly in the ratio $1:3$ . Then $\large\frac{\sin \angle BAD}{\sin \angle CAD}$ equals

asked Mar 3, 2015 by meena.p

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The function $f(x) =[x] \cos \bigg[ \large\frac{2x-1}{2}\bigg]$$\pi$ Where $[.]$ denotes the greatest integer function, is discontinuous at

asked Mar 3, 2015 by meena.p

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If $ (\omega \neq 1)$ is a cube root of unity $(1+\omega)^7=\alpha+\beta \omega$ then $\alpha$ and $\beta$ are

asked Mar 3, 2015 by meena.p

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If $(w \neq 1)$ is a cube root of 1 then $\begin{bmatrix} 1 & 1+i+\omega^2 & \omega^2 \\ 1-i & -1 & \omega^2-1 \\ -1 & -i+\omega-1 & -1 \end{bmatrix}$ is a

asked Mar 3, 2015 by meena.p

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