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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

1 answer

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

1 answer

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

1 answer

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

1 answer

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

1 answer

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

1 answer

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

asked Mar 5, 2015 by meena.p

1 answer

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

1 answer

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

1 answer

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

1 answer

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

asked Mar 5, 2015 by meena.p

1 answer

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

asked Mar 5, 2015 by meena.p

1 answer

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

1 answer

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

1 answer

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

1 answer

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

1 answer

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

1 answer

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

0 answers

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

1 answer

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

1 answer

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

1 answer

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

1 answer

If the expansion of $(x+\large\frac{\alpha}{x})^n$ and $(x+\large\frac{\beta}{x^2})$ in power of x have one term independently of x, the n is divisible by

asked Mar 3, 2015 by meena.p

1 answer

The area of the region bounded by $y= |x-1|$ and $y=1$ is

asked Mar 3, 2015 by meena.p

1 answer

Let $E$ be the ellipse $\large\frac{x^2}{9} +\frac{y^2}{4}$ $=1$ and C be the circle $x^2+y^2=9$ . Let P and Q be the points $(1,2)$ and $(2,1)$ respectively Then

asked Mar 3, 2015 by meena.p

1 answer

Let $\alpha, \beta, \gamma$ be distinct real numbers points with position vector $\alpha\overrightarrow{i}+\beta \overrightarrow {i} + \gamma \overrightarrow {k},\beta\overrightarrow{i}+\beta \overrightarrow {i} + \gamma \overrightarrow {k},r\overrightarrow{j}+\alpha \overrightarrow {j} + \beta\overrightarrow {k}$ ,

asked Mar 3, 2015 by meena.p

1 answer

The circle $x^2+y^2-10x+16 =0$ and $x^2+y^2=r^2$ intersect each other in two distinct points if

asked Mar 3, 2015 by meena.p

1 answer

Which one of the following curves cuts the parabola $y^2=4ax$ at right angles ?

asked Mar 3, 2015 by meena.p

1 answer

The equations to a pair of opposite sides of parallelogram are $x^2-5x+6=0$ and $y^2-6y+5=0$ . The equations to its diagonals are

asked Mar 3, 2015 by meena.p

1 answer

For a real number $x,[x]$ denotes the integral part of x the value of $\bigg[ \large\frac{1}{2}\bigg]+\bigg[\large\frac{1}{2}+\frac{2}{100}\bigg] +.....+ \bigg[ \large\frac{1}{2}+\frac{99}{100}\bigg]$ is

asked Mar 2, 2015 by meena.p

1 answer

The locus of a variable point whose distance from $(-2,0)$ is $\large\frac{2}{3}$ times its distance from the line $x = \large\frac{-9}{2}$ is

asked Mar 2, 2015 by meena.p

1 answer

Let $2 \sin ^2 x + 3 \sin x -2 >0$ and $x^2-x-2 < 0$ (x is measured in radians). Then x lies in the interval

asked Mar 2, 2015 by meena.p

0 answers

Let $2 \sin ^2 x + 3 \sin x -2 >0$ and $x^2-x-2 < 0$ (x is measured in radians). Then x lies in the interval

asked Mar 2, 2015 by meena.p

1 answer

If we consider only the principal values of the inverse trigonometric function Then the value of $\tan \bigg[\cos ^{-1} \large\frac{1}{5 \sqrt 2} -$ $\sin ^{-1} \large\frac{4}{\sqrt{17}}\bigg]$ is

asked Mar 2, 2015 by meena.p

1 answer

An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tossed needed is

asked Mar 2, 2015 by meena.p

1 answer

If the length of the sides of triangle are $3,5,7$ then the largest angle of the triangle is

asked Mar 2, 2015 by meena.p

1 answer

If $y =(\sin x)^{\tan x}$ then $\large\frac{dy}{dx}$ is equal to

asked Mar 2, 2015 by meena.p

1 answer

Let n be a positive integer such that $\sin \large\frac{\pi}{2n}$ $+\cos \large\frac{\pi}{2n} =\frac{\sqrt n }{2}$ Then,

asked Mar 2, 2015 by meena.p

1 answer

If $y =4x-5$ is tangent to the curve $y^2=px^3+q$ at $(2,3)$ then

asked Mar 2, 2015 by meena.p

1 answer

Let A,B,C be three mutually independent event. Consider the two statements $S_1$ , and $S_2;S_1:A$ and $B \cap C$ are independent . $S_1:A$ and $B \cap C$ are independent . Then

asked Feb 28, 2015 by meena.p

1 answer

Let $0 < x > \large\frac{\pi}{4}$ .Then $(\sec 2x- \tan 2x)$ equal

asked Feb 28, 2015 by meena.p

1 answer

Let p and q be the position vectors of P and Q respectively, with respect to O and $|P|=P,|q|=q$ The points R and S divide POQ internally and externally in the ratio $2:3$ respectively. If OR and OS are perpendicular then

asked Feb 28, 2015 by meena.p

1 answer

The equation $2x^2+3y^2 -8x+18y +35=k$ represents

asked Feb 27, 2015 by meena.p

1 answer

The equation $2x^2+3y^2-8x+18y+35=k$ represents

asked Feb 27, 2015 by meena.p

1 answer

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