Which one of the following is the strongest base?

An equal volume of a reducing agent is titrated separately with 1M KMnO4 in acid neutral and alkaline media. The volume

The correct set of quantum numbers for the unpaired electron of chlorine atom is

The correct ground state electronic configuration of chromium atom is

Which one of the following is the smallest in size?

Sodium sulphate is soluble in water whereas barium sulphate is sparingly soluble because

The molecule which has zero dipole moment is:

The molecule which has pyramidal shape is

The compound in which $$\mathop C\limits^* $$ uses its sp3 hybrid orbitals for bond formation is

Which of the following is paramagnetic?

Eight gram each of oxygen and hydrogen at 27oC will have the total kinetic energy in the ratio of _______.

The electrolysis of molten sodium hydride liberates ____ gas at the _____

Write down the balanced equation for the reaction when: Potassium ferricyanide reacts with hydrogen peroxide in basic so

n-Butane is produced by the monobromination of ethane followed by the Wurtz reaction. Calculate the volume of ethane at

The vapour pressure of a dilute aqueous solution of glucose (C6H12O6) is 750 mm of mercury at 373 K. Calculate (i) molal

If the probability for $$A$$ to fail in an examination is $$0.2$$ and that for $$B$$ is $$0.3$$, then the probability th

If $$E$$ and $$F$$ are independent events such that $$0 < P\left( E \right) < 1$$ and $$0 < P\left( F \right) &

Suppose the probability for A to win a game against B is $$0.4.$$ If $$A$$ has an option of playing either a "best of $$

For any three vectors $${\overrightarrow a ,\,\overrightarrow b ,}$$ and $${\overrightarrow c ,}$$ $$\left( {\overright

If vectors $$\overrightarrow A ,\overrightarrow B ,\overrightarrow C $$ are coplanar, show that $$$\left| {\matrix{

In a triangle $$OAB,E$$ is the midpoint of $$BO$$ and $$D$$ is a point on $$AB$$ such that $$AD:DB=2:1.$$ If $$OD$$ and

A pair of fair dice is rolled together till a sum of either $$5$$ or $$7$$ is obtained. Then the probability that $$5$$

The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle $${x^2} + {y^2} = 4\

If $$a,\,b,\,c,$$ are the numbers between 0 and 1 such that the ponts $${z_1} = a + i,{z_2} = 1 + bi$$ and $${z_3} = 0$$

The equation $${x^{3/4{{\left( {{{\log }_2}\,\,x} \right)}^2} + {{\log }_2}\,\,x - 5/4}} = \sqrt 2 $$ has

If x and y are positive real numbers and m, n are any positive integers, then $${{{x^n}\,{y^m}} \over {(1 + {x^{2n}})\,(

If $$\alpha $$ and $$\beta $$ are the roots of $${x^2}$$+ px + q = 0 and $${\alpha ^4},{\beta ^4}$$ are the roots of $$\

Let a, b, c be real numbers, $$a \ne 0$$. If $$\alpha \,$$ is a root of $${a^2}{x^2} + bx + c = 0$$. $$\beta \,$$ is the

A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The tota

Using mathematical induction, prove that $${}^m{C_0}{}^n{C_k} + {}^m{C_1}{}^n{C_{k - 1}}\,\,\, + .....{}^m{C_k}{}^n{C_0}

Prove that $${C_0} - {2^2}{C_1} + {3^2}{C_2}\,\, - \,..... + {\left( { - 1} \right)^n}{\left( {n + 1} \right)^2}{C_n}

Let $$ABC$$ be a triangle with $$AB = AC$$. If $$D$$ is the midpoint of $$BC, E$$ is the foot of the perpendicular drawn

The line x + 3y = 0 is a diameter of the circle $${x^2} + {y^2} - 6x + 2y = 0\,$$.

The general solutions of $$\,\sin x - 3\sin 2x + \sin 3x = \cos x - 3\cos 2x + \cos 3x$$ is

If the two circles $${(x - 1)^2} + {(y - 3)^2} = {r^2}$$ and $${x^2} + {y^2} - 8x + 2y + 8 = 0$$ intersect in two distin

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle of area 154 sq. units. Then the equation of this circle

If $$\left( {{m_i},{1 \over {{m_i}}}} \right),\,{m_i}\, > \,0,\,i\, = 1,\,2,\,3,\,4$$ are four distinct points on a c

If $$x = \sec \theta - \cos \theta $$ and $$y = {\sec ^n}\theta - {\cos ^n}\theta $$, then show that $$\left( {{x^2}

$$ABC$$ is a triangular park with $$AB=AC=100$$ $$m$$. A television tower stands at the midpoint of $$BC$$. The angles o

The greater of the two angles $$A = 2{\tan ^{ - 1}}\left( {2\sqrt 2 - 1} \right)$$ and $$B = 3{\sin ^{ - 1}}\left( {1/3

Find all maxima and minima of the function $$$y = x{\left( {x - 1} \right)^2},0 \le x \le 2$$$ Also determine the area

Evaluate $$\int {\left( {\sqrt {\tan x} + \sqrt {\cot x} } \right)dx} $$

The value of $$\int\limits_{ - 2}^2 {\left| {1 - {x^2}} \right|dx} $$ is ...............

If $$f$$ and $$g$$ are continuous function on $$\left[ {0,a} \right]$$ satisfying $$f\left( x \right) = f\left( {a - x}