List of practice Questions

If $A(1, 1, 1), B(0, λ, 0), C(λ + 1, 0, 1), D(2, -2, 2)$ are co-planer then $\sum (\lambda_i + 2)^2$ is equal to

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

A train is moving with a speed of $10 m/s$ towards a platform and blows a horn with frequency $400 Hz$. Find the frequency heard by a passenger standing on the platform. Take speed of sound = $310 m/s$.

If $sin^{-1}x=2\,tan^{-1}x$ , then the number of integral values of x is equal to:

Shortest distance between lines $\frac{(x-5)}{4}$=$\frac{(y-3)}{6}$=$\frac{(z-2)}{4}$ and $\frac{(x-3)}{7}=\frac{(y-2)}{5}=\frac{(z-9)}{6}$ is ?

In which of the following cities photochemical smog is minimum?

Two circles having radius $r_1$ and $r_2$ touch both the coordinate axes. Line $x+y=2$ makes intercept 2 on both the circles. The value of $r_{1}^{2} + r_{2}^{2} - r_{1}r_{2}$ is:

Let $y = y(x), y > 0,$ be a solution curve of the differential equation $(1 +x^2)dy = y(x−y)dx.$ If $y(0) = 1$ and $y(2√2) = β$, then

The absolute difference of the coefficients of $x^{10}$ and $x^7$ in the expansion of $\left(2x^2 + \frac{1}{2x}\right)^{11}$ is equal to:

Which compound is added to cement to increase its setting time?

If (21)18 + 20·(21)17 + (20)2 · (21)16 + ……….. (20)18 = k (2119 – 2019) then k =

Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?

The depression in freezing point observed for a formic acid solution of concentration $05\, mL\, L ^{-1}$ is $00405^{\circ} C$ Density of formic acid is $105 \, g \, mL ^{-1}$ The Van't Hoff factor of the formic acid solution is nearly : (Given for water $k _{ f }=186 \, K \, kg \, mol ^{-1}$ )

According to MO theory, the molecule which contain only π-Bonds between the atoms is

If the n terms a₁,a₂........a_n are in A.P. with increment r, then the difference between the mean of their squares and square of their mean is

Find the effective resistance between points A and B. Each resistance is equal to R.

What is the percentage drop in the production of Ludo from 1992 to 1994?

The bond dissociation energies of $ X_2, Y_2, $ and $ XY $ are in the ratio of 1:0.5:1. If $ \Delta H $ for the formation of $ XY $ is -200 kJ mol$^{-1}$, what is the bond dissociation energy of $ X_2 $?

Suppose a line parallel to $ax+by=0$ (where $b≠0$)intersects$ 5x-y+4=0$ and $3x+4y-4=0$ ,respectively at P and Q. If the midpoint of PQ is $(1,5)$,then the value of $\dfrac{a}{b}$ is

An element X has a body-centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm$^{-3}$. The number of atoms present in 300g of the element X is:
Given: Avogadro Constant, $ N_A = 6.0 \times 10^{23} $ mol$^{-1} $.

The rate constants of a reaction at 200 K and 300 K are 0.02 s^-1 and 0.04 s^-1. Ea for this reaction will be:

A uniform magnetic field b exists in a region. An electron of charge q and mass m moving with velocity v enters the region in a direction perpendicular to the magnetic field. Considering Bohr angular momentum quantization, which of the following statement(s) is/are true?

A Carnot engine takes $ 3 \times 10^6 $ cal of heat from a reservoir at $ 627^\circ C $, and gives it to a sink at $ 27^\circ C $. The work done by the engine is:

A particle of mass m is projected at velocity at a velocity u, making an angle θ with the horizontal(x-axis). If the angle of projection θ is varied keeping all other parameters same, then magnitude of angular momentum(L) at its maximum height about the point of projection varies with θ as,

A biased die is rolled such that the probability of getting k dots,1≤k≤6, on the upper face of the die is proportional to k. Then the probability that five dots appear on the upper face of the die is