List of practice Questions

The mass 'm' oscillates in simple harmonic motion with an amplitude 'A' as shown in the figure.
The amplitude of point \(P\) is

A wire of resistance 0.2 \( \Omega/{cm} \) is bent to form a square ABCD of side 10 cm. A similar wire is connected between the corners B and D. If 2 V battery is connected across A and C, the power dissipated is

The space between the plates of a parallel plate capacitor is halved and a dielectric medium of relative permittivity \( 10 \) is introduced between the plates. The ratio of the final and initial capacitances of the capacitor is:

Two simple harmonic motions are represented by \(y_1 = 5 \left[ \sin 2\pi t + \sqrt{3} \cos 2\pi t \right] \) and \(y_2 = 5 \sin \left[ 2\pi t + \frac{\pi}{4} \right] \). The ratio of their amplitudes is:

Let the set of all values of \( p \), for which \[ f(x) = (p^2 - 6p + 8)(\sin^2 2x - \cos^2 2x) + 2(2 - p)x + 7 \] does not have any critical point, be the interval \( (a, b) \). Then \( 16ab \) is equal to _____ .

Number of ways of arranging 5 officers in 4 rooms.

In the given circuit, find electric current drawn from battery :

\(3, 7, 1,......., 404\) and \(4, 7, 10,......, 403\). Find sum of common terms.

The value of integral \(∫_0^{\frac \pi4} \frac {xdx}{cos^42x+sin^42x}\).

What is the order of reducing character for \(AsH_3, NH_3, PH_3\) (group \(15\) hydrides)?

Which of the following compounds in 3d series does not show +3 oxidation state?

Which of the following sets of elements can be detected by Lassaigne's Test ?

\(L_1: γ^-=(i+2j+3k)+λ(i-j+k)\);
\(L_2: γ^-=(4i+5j+6k)+μ(i+j-k)\),
intersect \(L_1\) and \(L_2\) at P and Q respectively. If \((α, β, γ)\) is the mid point of the line segment PQ, then \(2(α, β, γ\)) is equal to

Five people are distributed in four identical rooms. A room can also contain zero people. Find the number of ways to distribute them.

A \(10\) \(mL\) hydrocarbon \((C_2H_4)\) on combustion give \(40\) \(mL\) \(CO_2\) and \(50\) \(mL\) \(H_20\). Calculate the value of \(x+y\)

Which of the following has the highest 3rd ionization energy?

Given: \(5f (x) 4f(\frac 1x) = x^2 - 4 \) & \(y = 9f(x) × x^2\) If y is strictly increasing, then find interval of \(x\).

Number of radial nodes present in 3p are

Let S = {1,2,3,..., 20}, R₁ = {(a, b): a divide b}, R₂ = {(a, b): a is integral multiple of b} and a, b ∈ S. n(R₁ - R₂) = ?

If \((t+1)dx=(2x+(t+1)^3)dt\) and \(x(0)=2\), then \(x(1) \)is equal to:

Which of the following have a trigonal bipyramidal shape?
\(PF_5, PBr_5, [PtCl_4], SF_6, BF_3, BrF_5, PCl_5, [Fe(CO)_5]\)

Which of the following is correct for adiabatic free expansion against vacuum?

Complementary stand of DNA ATGCTTCA is:

For a hypothetical economy, the government incurs an additional investment expenditure of Rs.5,000 crore. Assuming that the Marginal Propensity to Save (MPS) becomes half from its present level of 20 percent, estimate the change in income due to this fall in MPS.

A solution is prepared by dissolving 5 g of a non-volatile solute in 200 g of water. It has a vapor pressure of 31.84 mm Hg at 300 K. Calculate the molar mass of the solute.
(Vapor pressure of pure water at 300 K = 32 mm Hg)