List of practice Questions

Area under the curve \(x^2 + y^2 = 169\) and below the line \(5x - y = 13\) is:

Evaluate: \(\lim\limits_{x→\frac \pi2^-}∫_{x^3}^{(\frac\pi2)^3} \frac {cos \ t^{\frac 13} dt}{(x-\frac \pi2)^2}\)

If \(∫_{-\frac \pi2}^{\frac \pi2} (\frac {x^2cos\ x}{1+π^x}+\frac {1+sin^2x}{1+e^{(sinx)^{2023}}})dx=\frac \pi4(π+α)-2\). Then the value of \(\alpha\) is equal to

If electric current passing through a conductor varies with time as \(I = 10 + A \;ẞt\), where \(I_o = 20 A\), \(B = \frac{3A}{S}\), then find charge flow through the conductor in first \(10\) sec is

Let a die rolled till 2 is obtained. The probability that 2 obtained on even numbered toss is equal to:

If \(f(x) =   \begin{cases}     2+2x  & ;x∈(-1,0)\\     1-\frac x3  & ;x∈[0,3)  \end{cases}\) and \(g(x) =   \begin{cases}     x  & ;x∈[0,1)\\     -x & ;x∈(-3,0)  \end{cases}\). Then range of \(fog(x)\) is

If \(\frac {dy}{dx} - \frac {(sin2x)}{(1+cos^2x)}y = \frac {sinx}{1+cos^2x }\)and \(y(0) =0\) then \(y(\frac \pi2)\) is ………..

Alkaline KMnO4 Oxidised iodide to a particular product (A). Determine the oxidation state of iodine in the compound (A).

Find product P of the following reaction-

A body of mass \(100\) kg traveled \(10\) m before coming to rest. If \(µ\) = \(0.4\), work done against friction is - (motion is happening in a horizontal surface, tak \(g\) = \(10\) \(m/s^2\))

A container contains 1g H₂ gas and 1g O₂ gas. What is the ratio of partial pressure of H₂ and O₂ (PH₂/PO₂)?

If a particle starting from rest having constant acceleration covers distance \(S1\) in first \((P -1)\) seconds & \(S2\) in first \(P\) seconds, then determine time for which displacement is \(S1 + S2\) :

A particle is executing simple harmonic motion along the \(x - axis\), with amplitude \(A\), about the origin. Then the ratio of Kinetic energy and total energy at \(x = \frac{A}{3}\) is

Consider the two statements (Assume density of water to be constant):
Statement 1: A capillary tube is first dipped in hot water and then dipped in cold water. The rise is higher in hot water.
Statement 2: Capillary tube is first dipped in cold water and then in hot water. The rise is higher in cold water.

De-Broglie wavelength of a proton and an electron is same. The ratio of kinetic energy of electron to that of proton is

A gas undergoes a cyclic process ABCA as shown. Find the work done by the gas from A→B→C.

If a biconvex lens of material of refractive index 1.5 has focal length 20 cm in air, then its focal length when it is submerged in a medium of refractive index 1.6 is

A capacitor having capacitance of 100uF is charged with a potential difference of 12 V is connected to an inductor of inductance 10 mH. Find the maximum current through the inductor.

If an object is having the same weight at the same distance above and below the surface of earth. Find its distance from the surface of earth.

A square loop of resistance \(16 \;Ω\) is connected with battery of \(9\) \(V\) and internal resistance of \(1\) \(Ω\). In steady state. Find energy stored in capacitor of capacity \(C = 4 µF\) as shown. (at steady state current divides symmetrically)

If \(|2A|^3 =21\) and \(\begin{bmatrix} 1 & 0 & 0 \\[0.3em] 0 & α & β \\[0.3em] 0 & β & α \end{bmatrix}\), then a is (if \(α,β∈I\))

Hydrolysis of protein gives which type of amino acids?

An electron is moving with the speed of \(1\) \(m/s\) at a distance of \(1\) \(m\), from a large sheet of charge with density \(σ\) \(C/m^2\). Find the maximum value of \(σ\) such that electron hits the sheet after \(1\) \(sec\). (mass of electron = \(9 × 10^{-31}\) kg, Permittivity of free space = \(9\times10^{12}\;C^2/Nm^2\)