List of practice Questions

\(\frac{dy}{dx}\) + \(\frac{5}{x(1+x^5)}\)y = \(\frac{(1+x^5)^2}{x^7}\) If y(1) = 2, then the value of y(2) is:

Let mean and variance of the data 1, 2, 4, 5, x, y are 5 and 10 then the mean deviation about mean is?

Equation of progressive wave is \(y = A\text{ sin}(160t-0.5x)\). Let the speed of the wave be 10x then, find x.

If \(y = max \{ {\sqrt{x}, x^2-4, x^3+2}\}\), then the number of solution(s) of y=1 is/are____?

Force acting on a particle moving along the x - axis is given by F = (2 + 3x)i. The work done by this force from x = 0 to x = 4 m is

If half life of a radio-active nuclide A is equal to average life of another radio-active nuclide B. Find the ratio of decay constant of A to that of B.

Variation of magnetic field through a coil of area 4 m² is shown in figure. What is the EMF induced in the coil (in mV)?

The characteristics of two coil is given below. If the magnetic moment of both coil A and B are equal then choose the correct relation,

Coil A	Coil B
Radius r_A=10 cm	r_B=20 cm
Number of turns N_A	N_B
Current I_A	I_B

If light is passing through a medium of critical angle 45°, then the wave speed will be

In a moving coil galvanometer if the number of turns increases by 25%, then change in voltage sensitivity is?

The variation of impedance (Z) with angular frequency (w) for two electrical elements is shown in the graph given. If XL,Xc, and R are inductive reactance, capacitive reactance and resistance respectively, then

Find the current flowing in 3Ω resistor in the given circuit

Find the spin magnetic moment ratio for complexes \([Cr(Cn)_{6}]^{-3}\) & \([Cr(H_{2}O)_{6}]^{+3}\)

25% of 250g sugar solution & 40% of 500g sugar solution are mixed then find out the mass percentage in the solution.

In a container at a constant temperature , arrange the RMS velocity of the following: Ne, Cl₂ , UF₆

Correct order of first ionization energy of Li, Be, C, B, N, O, F

Which of the following can be represented as a meridional isomer?

Find the number of atoms per unit cell if edge length is 300pm, density = 3 g/cm³ , molecular mass = 40 g(nearest integer)

Identify the correct statement about the compound GaAIC₁₄

If \(x+y+z=17\) and x, y, z are non-negative integers, then find the number of integral solutions is

5 boys with allotted roll numbers and seat numbers are seated in such a way that no one sits on the allotted seat. The number of such seating arrangements is?

Let \( S = \{ M = [a_{ij}], a_{ij} \in \{0, 1, 2\}, 1 \leq i, j \leq 2 \} \) be a sample space and \( A = \{ M \in S : M \text{ is invertible} \} \) be an event. Then \( P(A) \) is equal to:

Suppose a situation in which two planets orbits around the sun in the same orbit. If the mass of plant 1 is twice the mass of planet 2, then what do they have same?

pH of 1 litre of HCL solution is 1. How much water (in litres) is added to make pH=2?

Match the terms in Column-I with their description in Column-II and choose the correct option:

	Column 1(Type of hydride)		Column II
A.	Electron	1.	MgH₂
B.	Electron precise	2.	HF
C.	Electron rich	3.	CH₄
D.	Saline Hydride	4.	B₂H₆