The radius of which of the following orbit is same as that of the first Bohr's orbit of hydrogen atom?

The pair of compounds having metals in their highest oxidation state is

According to molecular orbital theory which of the following statement about the magnetic character and bond order is co

A sodium salt on treatment with MgCl3 gives white precipitate only on heating. The anion of the sodium salt is

The area enclosed between the curves $$y = a{x^2}$$ and $$x = a{y^2}\left( {a > 0} \right)$$ is $$1$$ sq. unit, then

If $$f(x)$$ is differentiable and $$\int\limits_0^{{t^2}} {xf\left( x \right)dx = {2 \over 5}{t^5},} $$ then $$f\left( {

If $$y=y(x)$$ and $${{2 + \sin x} \over {y + 1}}\left( {{{dy} \over {dx}}} \right) = - \cos x,y\left( 0 \right) = 1,$$

If three distinct numbers are chosen randomly from the first $$100$$ natural numbers, then the probability that all thre

If $$\overrightarrow a = \left( {\widehat i + \widehat j + \widehat k} \right),\overrightarrow a .\overrightarrow b =

If the lines $${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over 4}$$ and $$\,{{x - 3} \over 1} = {{y - k} \over 2}

The unit vector which is orthogonal to the vector $$3\overrightarrow i + 2\overrightarrow j + 6\overrightarrow k $$ an

The value of the integral $$\int\limits_0^1 {\sqrt {{{1 - x} \over {1 + x}}} dx} $$ is

If $$\omega $$ $$\left( { \ne 1} \right)$$ be a cube root of unity and $${\left( {1 + {\omega ^2}} \right)^n} = {\left(

If $$f\left( x \right) = {x^a}\log x$$ and $$f\left( 0 \right) = 0,$$ then the value of $$\alpha $$ for which Rolle's th

If $$f\left( x \right) = {x^3} + b{x^2} + cx + d$$ and $$0 < {b^2} < c,$$ then in $$\left( { - \infty ,\infty } \r

The value of $$x$$ for which $$sin\left( {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right) = \cos \left( {{{\tan }^{ - 1}

The sides of a triangle are in the ratio $$1:\sqrt 3 :2$$, then the angles of the triangle are in the ratio

If $$y$$ is a function of $$x$$ and log $$(x+y)-2xy=0$$, then the value of $$y'(0)$$ is equal to

If the line $$62x + \sqrt 6 y = 2$$ touches the hyperbola $${x^2} - 2{y^2} = 4$$, then the point of contact is

If tangents are drawn to the ellipse $${x^2} + 2{y^2} = 2,$$ then the locus of the mid-point of the intercept made by th

The angle between the tangents drawn from the point $$(1, 4)$$ to the parabola $${y^2} = 4x$$ is

If one of the diameters of the circle $${x^2} + {y^2} - 2x - 6y + 6 = 0$$ is a chord to the circle with centre (2, 1), t

Area of the triangle formed by the line $$x + y = 3$$ and angle bisectors of the pair of straight line $${x^2} - {y^2}

An infinite G.P. has first term '$$x$$' and sum '$$5$$', then $$x$$ belongs to

If $${}^{n - 1}{C_r} = \left( {{k^2} - 3} \right)\,{}^n{C_{r + 1,}}$$ then $$k \in $$

For all $$'x',{x^2} + 2ax + 10 - 3a > 0,$$ then the interval in which '$$a$$' lies is

If one root is square of the other root of the equation $${x^2} + px + q = 0$$, then the realation between $$p$$ and $$q

Given both $$\theta $$ and $$\phi $$ are acute angles and $$\sin \,\theta = {1 \over 2},\,$$ $$\cos \,\phi = {1 \over

Pressure depends on distance as, $$P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)$$, w

A wire of length $$l = 6 \pm 0.06$$ cm and $$r = 0.5 \pm 0.005$$ cm and mass $$m = 0.3 \pm 0.003$$ gm. Maximum percentag

A body starts from rest at time t = 0, the acceleration time graph is shown in the figure. The maximum velocity attained

A particle starts sliding down a frictionless inclined plane. If Sn is the distance traveled by it from time t = n - 1 s

A particle is acted by a force F = kx, where k is a +ve constant. Its potential energy at x = 0 is zero. Which curve cor