Which of the following molecular species has unpaired electrons(s)?

Identify the least stable ion amongst the following

Specify the coordination geometry around and hybridisation of N and B atoms in a 1 : 1 complex of BF3 and NH3

Identify the correct order of acidic strengths of CO2, CuO, CaO, H2O

If the nitrogen atom has electronic configuration 1s7, it would have energy lower than that of the normal ground state c

Rutherford's experiment, which established the nuclear model of the atom, used a beam of

How many moles of electron weigh one kilogram?

The point(s) in the curve $${y^3} + 3{x^2} = 12y$$ where the tangent is vertical, is (are)

Let $$\overrightarrow V = 2\overrightarrow i + \overrightarrow j - \overrightarrow k $$ and $$\overrightarrow W = \o

If $${\overrightarrow a }$$ and $${\overrightarrow b }$$ are two unit vectors such that $${\overrightarrow a + 2\overri

Let $$T>0$$ be a fixed real number . Suppose $$f$$ is a continuous function such that for all $$x \in R$$, $$f\left

Let $$T>0$$ be a fixed real number . Suppose $$f$$ is a continuous function such that for all $$x \in R$$, $$f\left

Let $$f\left( x \right) = \int\limits_1^x {\sqrt {2 - {t^2}} \,dt.} $$ Then the real roots of the equation $${x^2} - f

The integral $$\int\limits_{ - 1/2}^{1/2} {\left( {\left[ x \right] + \ell n\left( {{{1 + x} \over {1 - x}}} \right)} \r

The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is

For all complex numbers $${z_1},\,{z_2}$$ satisfying $$\left| {{z_1}} \right| = 12$$ and $$\left| {{z_2} - 3 - 4i} \righ

The length of a longest interval in which the function $$3\,\sin x - 4{\sin ^3}x$$ is increasing, is

Which of the following pieces of data does NOT uniquely determine an acute-angled triangle $$ABC$$ ($$R$$ being the radi

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $${y^2} = 4ax$$ is an

The equation of the common tangent to the curves $${y^2} = 8x$$ and $$xy = - 1$$ is

If $$a > 2b > 0$$ then the positive value of $$m$$ for which $$y = mx - b\sqrt {1 + {m^2}} $$ is a common tangent

If the tangent at the point P on the circle $${x^2} + {y^2} + 6x + 6y = 2$$ meets a straight line 5x - 2y + 6 = 0 at a

A straight line through the origin $$O$$ meets the parallel lines $$4x+2y=9$$ and $$2x+y+6=0$$ at points $$P$$ and $$Q$$

Let $$P = \left( { - 1,\,0} \right),\,Q = \left( {0,\,0} \right)$$ and $$R = \left( {3,\,3\sqrt 3 } \right)$$ be three p

Let $$0 < \alpha < {\pi \over 2}$$ be fixed angle. If $$P = \left( {\cos \theta ,\,\sin \theta } \right)$$ and $

Suppose $$a, b, c$$ are in A.P. and $${a^2},{b^2},{c^2}$$ are in G.P. If $$a < b < c$$ and $$a + b + c = {3 \over

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is

The sum $$\sum\limits_{i = 0}^m {\left( {\matrix{ {10} \cr i \cr } } \right)\left( {\matrix{ {20} \cr

The set of all real numbers x for which $${x^2} - \left| {x + 2} \right| + x > 0$$, is

If $${a_1},{a_2}.......,{a_n}$$ are positive real numbers whose product is a fixed number c, then the minimum value of $

The number of integral values of $$k$$ for which the equation $$7\cos x + 5\sin x = 2k + 1$$ has a solution is

An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The