The elevation in boiling point of a solution of 13.44 g of CuCl2 in 1kg of water using the following information will be

Which species has the maximum number of lone pair of electrons on the central atom?

The number of radial nodes of 3s and 2p orbitals are respectively

$$\int\limits_{ - 2}^0 {\left\{ {{x^3} + 3{x^2} + 3x + 3 + \left( {x + 1} \right)\cos \left( {x + 1} \right)} \right\}\,

If $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$ are three non-zero, non-coplanar vectors and $$\ov

A variable plane at a distance of the one unit from the origin cuts the coordinates axes at $$A,$$ $$B$$ and $$C.$$ If t

A six faced fair dice is thrown until $$1$$ comes, then the probability that $$1$$ comes in even no. of trials is

The differential equation $${{dy} \over {dx}} = {{\sqrt {1 - {y^2}} } \over y}$$ determines a family of circles with

The solution of primitive integral equation $$\left( {{x^2} + {y^2}} \right)dy = xy$$ $$dx$$ is $$y=y(x),$$ If $$y(1)=1$

For the primitive integral equation $$ydx + {y^2}dy = x\,dy;$$ $$x \in R,\,\,y > 0,y = y\left( x \right),\,y\left( 1

If $$y=y(x)$$ and it follows the relation $$x\cos \,y + y\,cos\,x = \pi $$ then $$y''(0)=$$

The area bounded by the parabola $$y = {\left( {x + 1} \right)^2}$$ and $$y = {\left( {x - 1} \right)^2}$$ and the line

$$a,\,b,\,c$$ are integers, not all simultaneously equal and $$\omega $$ is cube root of unity $$\left( {\omega \ne 1}

If $$\int\limits_{\sin x}^1 {{t^2}f\left( t \right)dt = 1 - \sin x,} $$ then f$$\left( {{1 \over {\sqrt 3 }}} \right)$$

If $$P(x)$$ is a polynomial of degree less than or equal to $$2$$ and $$S$$ is the set of all such polynomials so that

In a triangle $$ABC$$, $$a,b,c$$ are the lengths of its sides and $$A,B,C$$ are the angles of triangle $$ABC$$. The corr

If $$f(x)$$ is a twice differentiable function and given that $$f\left( 1 \right) = 1;f\left( 2 \right) = 4,f\left( 3 \r

Tangent to the curve $$y = {x^2} + 6$$ at a point $$(1, 7)$$ touches the circle $${x^2} + {y^2} + 16x + 12y + c = 0$$ at

The minimum area of triangle formed by the tangent to the $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and

A circle is given by $${x^2}\, + \,{(y\, - \,1\,)^2}\, = \,1$$, another circle C touches it externally and also the x-a

In the quadratic equation $$\,\,a{x^2} + bx + c = 0,$$ $$\Delta $$ $$ = {b^2} - 4ac$$ and $$\alpha + \beta ,\,{\alpha ^

If the LCM of p, q is $${r^2}\,{r^4}\,{s^2}$$, where r, s, t are prime numbers and p, q are the positive integers then n

A rectangle with sides of lenght (2m - 1) and (2n - 1) units is divided into squares of unit lenght by drawing parallel

The value of $$$\left( {\matrix{ {30} \cr 0 \cr } } \right)\left( {\matrix{ {30} \cr {10} \cr }

$$\cos \left( {\alpha - \beta } \right) = 1$$ and $$\,\cos \left( {\alpha + \beta } \right) = 1/e$$ where $$\alpha ,\,

A simple pendulum has time period T1. The point of suspension is now moved upward according to the relation y = Kt2, (K

Which of the following set have different dimensions?