The solution for $$x$$ of the equation \int\limits_{\sqrt 2 }^x {{{dt} \over {t\sqrt {{t^2} - 1} }} = {\pi \over 2}} is

Let I = \int\limits_0^1 {{{\sin x} \over {\sqrt x }}dx} and J = \int\limits_0^1 {{{\cos x} \over {\sqrt x }}dx} . Then which one of the following is true?

If $$\left|z+4\right|\le 3$$, then the maximum value of $$\left|z+1\right|$$ is :

Consider a family of circles which are passing through the point $$(-1,1)$$ and are tangent to $$x$$-axis. If $$(h,k)$$ are the coordinate of the centre of the circles, then the set of values of $$k$$ is given by the interval :

Let $$f:R\to R$$ be a function defined by $$f(x)=\min \left\{x+1,\left|x\right|+1\right\}$$, then which of the following is true?

The function $$f:R/\left\{0\right\}\to R$$ given by f\left( x \right) = {1 \over x} - {2 \over {{e^{2x}} - 1}} can be made continuous at $$x$$ = 0 by defining $$f$$(0) as

If sin-1\left( {{x \over 5}} \right) + cosec-1\left( {{5 \over 4}} \right) = {\pi \over 2}, then the value of x is :

The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus $$A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\varphi$$. The number of ways to partition S is

If the difference between the roots of the equation $$x^2+ax+1=0$$ is less than $$\sqrt{5},$$ then the set of possible values of $$a$$ is

The normal to a curve at $$P(x,y)$$ meets the $$x$$-axis at $$G$$. If the distance of $$G$$ from the origin is twice the abscissa of $$P$$, then the curve is a :

For the Hyperbola {{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1 , which of the following remains constant when $$\alpha$$ varies$$=$$?

If a line makes an angle of $$\pi /4$$ with the positive directions of each of $$x$$-axis and $$y$$-axis, then the angle that the line makes with the positive direction of the $$z$$-axis is :

If $$(2,3,5)$$ is one end of a diameter of the sphere $$x^2+y^2+z^2-6x-12y-2z+20=0,$$ then the coordinates of the other end of the diameter are

Let $$L$$ be the line of intersection of the planes $$2x+3y+z=1$$ and $$x+3y+2z=2.$$ If $$L$$ makes an angle $$\alpha$$ with the positive $$x$$-axis, then cos $$\alpha$$ equals

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

The sum of series {1 \over {2!}} - {1 \over {3!}} + {1 \over {4!}} - ....... upto infinity is

In a geometric progression consisting of positive terms, each term equals the sum of the next two terns. Then the common ratio of its progression is equals

If $$p$$ and $$q$$ are positive real numbers such that $$p^2+q^2=1$$, then the maximum value of $$(p+q)$$ is

A value of $$c$$ for which conclusion of Mean Value Theorem holds for the function $$f\left(x\right)={\log }_{e}x$$ on the interval $$\left[1,3\right]$$ is

The function $$f\left(x\right)={\tan }^{-1}\left(\sin x+\cos x\right)$$ is an incresing function in