List of practice Questions

If \(\frac{dy}{dx}\) = y+7 and y(0) = 0, then the value of y(1) is?
The integral \(∫^∞_0  \frac{6}{(e^{3x} + 6e^{2x} + 11e{x} + 6)}dx\)
Find area bounded by the curves \(y\) = \(max\{sin x, cos x\}\) and \(x-axis\) between \(x = -  \pi  \)and \(x =   \pi\)
Plane P3 is passing through (1,1,1) and line of intersection of P1 and P2 where \(P_{1}: 2x - y + z = 5\) and \(P_{2}: x + 3y + 2z + 2 = 0\). Then distance of (1,1,10) from P3 is:
Incorrect statement about Borazine is:
The pair of lanthanides will exceptionally high 3rd ionisation enthalpy than neighbouring elements:
Which of the following shows an incorrect method of refining?
What happens when lyophilic sol is added to lyophobic sol. prevention from coagulation precipitation emulsion electrophoresis
If the height of the tower used for L.D.S is increased by 21% then percentage change in range is?
If a wire of resistance R is connected across Vo, then power is Po. The wire is cut into two equal parts and connected with Vo individually, then the sum of power dissipated is P1, then \(\frac{Po}{Pi}\) is \(\frac{1}{x}\). Find the value of x.
A particle is performing \(SHM\) having position \(x\) = \(A\; cos\; 30°\), and \(A\; = 40 \;cm\). If its kinetic energy at this position is \(200 \;J\), the value of force constant in \((kN/m)\) is?
For the 1st order reactions, the ratio of t50% to t87.5% will be:
An organic compound on combustion gives 0.22 g of CO2 and 0.126 g of H2O. If the percentage of C in given organic compound is 40%, the percentage of H will be?
Radius of the 2nd orbit of He+ is r0. Radius of the 4th orbit of Be3+ is xr0. Find x.
Let the number of matrices of order 3 x 3 are possible using the digits [0, 1, 2, 3, … , 10) is mn, then (m + n) is ___. (where m is a prime number)

The fractional part of the number \(\tfrac{4^{2022}}{15}\) is equal to:

 For \(x \in \mathbb{R}\), two real‐valued functions \(f(x)\) and \(g(x)\) are such that

To radiate EM signal of wavelength \( \lambda \) with high efficiency, the antennas should have a minimum size equal to:
A 10 μC charge is divided into two equal parts and kept at 1 cm distance. Find repulsion between charges?
A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of train B is 54 km/h, then the length of train B is:
A bi-convex lens of focal length 10 cm is cut perpendicularly to principal axis. 
Find Power (in D) of new lens.
Two bodies having the same linear momentum have a ratio of kinetic energy as 16:9. Find the ratio of masses of these bodies.
What is the center of gravity of a semi-circular disc of radius (R)?
Pressure for polytropic process P varies with volume V as P=av-3, find out the bulk modulus.

A particle is performing S.H.M whose distance from mean position varies as \(x = Asin(wt)\). Find the position of the particle from the mean position, where kinetic energy and potential energy is equal.