List of practice Questions

A solution contains 4 g of NaOH and 16.2 g of water. The mole fraction solute and solvent are respectively

For a gas $\frac{R}{C_{v}} = 0.4$, where ?$R$? is the universal gas constant and ?$C_v$? is molar specific heat at constant volume. The gas is made up of molecules which are

A compound 'A'with molecular formula \({C_5H_{10}O}\)gives a positive \({2,4-DNP}\) test but a negative Tollen's test. On treatment with sodium hypochlorite, it gives \({CHCl_3}\) and compound 'B'. Compound 'B' is

Sphagnum is slowly carbonised, compressed and fossilised over thousands of years to produce a dark spongy mass called peat. Peat helps to keep soil porous and it also improves water holding capacity of the soil.

The number of surjective functions from $A$ to $B$ where $A = \{1, 2, 3, 4 \}$ and $B = \{a, b\}$ is

If the tangent to the function $y = f(x) $ at $(3,4)$ makes an angle of $\frac{3 \pi }{4}$ with the positive direction of x-axis in anticlockwise direction then $f ' (3)$ is

If $|\vec{a} | = 3, |\vec{b}| = 2, |\vec{c}| = 1$ then the value of $|\vec{a}. \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}| $ is (given that $\vec{a} + \vec{b} + \vec{c} = 0$)

The value of $ (1 + \omega - \omega^2)^7$ is

The equation of one of the common tangents to the parabola $y^2 = 8x$ and $x^2 + y^2 - 12x + 4 = 0$ is

What is the area of a loop of the curve $r = a \sin^3 \theta$ ?

A tetrahedron has vertices at $O (0, 0, 0), A (1, 2, 1) B (2, 1, 3) $ and $C (-1, 1, 2)$. Then the angle between the faces $OAB$ and $ABC$ will be

If $ A$ and $B$ are matrices and $B = ABA^{-1}$ then the value of $(A + B) (A - B)$ is

In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present.

If $e^x = y + \sqrt{ 1 + y^2}$ , then the value of y is

Let $z = 1 + ai$ be a complex number, $a > 0$, such that $z^3$ is a real number. Then the sum $1 + z + z^2 +..... + z^{11}$ is equal to :

If a curve $y = f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation, $y(1 + xy) dx = x \,dy$, then $f \left( - \frac{1}{2} \right)$ is equal to :

If all the words (with or without meaning) having five letters, formed using the letters of the word $SMALL$ and arranged as in a dictionary; then the position of the word $SMALL$ is:

If a variable line drawn through the intersection of the lines $\frac{x}{3} + \frac{y}{4} = 1$ and $\frac{x}{4} + \frac{y}{3} = 1$, meets the coordinate axes at $A$ and $B$, $(A \neq B)$, then the locus of the midpoint of $AB$ is :

Equation of the tangent to the circle, at the point $(1, -1)$, whose centre is the point of intersection of the straight lines $x - y = 1$and $+ y = 3$is :

An experiment succeeds twice as often as it fails. The probability of at least $5$ successes in the six trials of this experiment is :

The mean of $5$ observations is $5$ and their variance is $124$. If three of the observations are $1, 2$ and $6$ ; then the mean deviation from the mean of the data is :

Let $P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \}$ and $Q = \{\theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \}$ be two sets. Then :

The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x -60} = 1 $ is

$CO$ is a stronger ligand than $Cl^-$ because

The sulphur compound in which the sulphur atom has octet configuration in its valence shell among the following is