The set of points where f\left( x \right) = {x \over {1 + \left| x \right|}} is differentiable is

The number of values of $$x$$ in the interval $$\left[0,3\pi \right]$$ satisfying the equation $$2{\sin }^{2}x+5\sin x-3=0$$ is

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is

If $$x$$ is real, the maximum value of {{3{x^2} + 9x + 17} \over {3{x^2} + 9x + 7}} is

If the roots of the quadratic equation $$x^2+px+q=0$$ are $$\tan 30^{\circ }$$ and $$\tan 15^{\circ }$$, respectively, then the value of $$2+q-p$$ is

All the values of $$m$$ for which both roots of the equation $$x^2-2mx+m^2-1=0$$ are greater than $$-2$$ but less then 4, lie in the interval

The image of the point $$(-1,3,4)$$ in the plane $$x-2y=0$$ is :

The two lines $$x=ay+b,z=cy+d;$$ and $$x=a^{\prime }y+b^{\prime },$$ $$z=c^{\prime }y+d^{\prime }$$ are perpendicular to each other if :

Suppose a population A has 100 observations 101, 102,........, 200, and another population B has 100 observations 151, 152,......., 250. If VA and VB represent the variances of the two populations, respectively, then {{{V_A}} \over {{V_B}}} is

If $$a_1,a_2,....a_n$$ are in H.P., then the expression $$a_1{a}_2+a_2{a}_3+....+a_{n-1}{a}_n$$ is equal to

Let $$a_1$$, $$a_2$$, $$a_3$$.....be terms on A.P. If {{{a_1} + {a_2} + .....{a_p}} \over {{a_1} + {a_2} + .....{a_q}}} = {{{p^2}} \over {{q^2}}},\,p \ne q,\,then\,{{{a_6}} \over {{a_{21}}}}\, equals

The function f\left( x \right) = {x \over 2} + {2 \over x} has a local minimum at

Angle between the tangents to the curve $$y=x^2-5x+6$$ at the points $$(2,0)$$ and $$(3,0)$$ is

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is

The refractive index of a glass is $$1.520$$ for red light and $$1.525$$ for blue light. Let $$D_1$$ and $$D_2$$ be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then,

A thermocouple is made from two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is kept cold, then, an electric current will

An electric bulb is rated $$220$$ volt - $$100$$ watt. The power consumed by it when operated on $$110$$ volt will be

In a Wheatstone's bridge, three resistance $$P,Q$$ and $$R$$ connected in the three arms and the fourth arm is formed by two resistances $$S_1$$ and $$S_2$$ connected in parallel. The condition for the bridge to be balanced will be

The resistance of bulb filmanet is $$100\Omega$$ at a temperature of $$100^{\circ }C.$$ If its temperature coefficient of resistance be $$0.005$$ per $${}^{\circ }C$$, its resistance will become $$200\Omega$$ at a temperature of

The current $$\mathrm{I}$$ drawn from the $$5$$ volt source will be