List of practice Questions

A patient underwent surgery for the varicose vein. He now complains of sensory loss over the medial aspect of the leg and foot. Which of the following nerves is most likely to be injured?

The de-Broglie wavelength of an electron moving with a velocity $ \frac{c}{3} $ (where $ c = 3 \times 10^8 \, {m/s} $) is equal to the wavelength of a photon. The ratio of the kinetic energies of the electron and the photon is:

Time taken by light to travel in two different materials A and B of refractive indices μ_Aand μ_B of same thickness is t₁ and t₂ respectively. If t₂ – t₁ = 5 × 10^–10 s and the ratio of μA to μB is 1 : 2. Then, the thickness of material, in meter is: (Given v_A and v_B are velocities of light in A and B materials, respectively.)

Fill in the blank with the most appropriate word/group of words to make the sentence meaningfully complete.
Mohan tries his best to keep___the reputation of his family.

Which one of the following statements in relation to the hydrogen atom is correct?

If
$\lim_{{x \to 1}} \frac{{\sin(3x^2 - 4x + 1) - x^2 + 1}}{{2x^3 - 7x^2 + ax + b}} = -2$
, then the value of (a – b) is equal to_______.

The reduction potential $\left(E^0, in\ V\right)$ of $MnO _4^{-}( aq ) / Mn ( s )$ is$\left[ Given : E_{\left( MnO _4^-( aq ) / MnO _2( s )\right)}^0=1.68 V ; E_{\left( MnO _2( s )/ Mn ^{2+}( aq )\right)}^0=1.21 V ; E_{\left( Mn ^2( aq ) / Mn ( s )\right)}^0=-1.03 V \right]$

Let $\beta$ be a real number. Consider the matrix
$A=\begin{pmatrix}\beta & 0 & 1 \\2 & 1 & -2 \\3 & 1 & -2\end{pmatrix}$
If $A^7-(\beta-1) A^6-\beta A^5$ is a singular matrix, then the value of $9 \beta$ is __.

The base of a right pyramid is a square and the length of the side of the square is 32 cm, and the height of the pyramid is 12 cm. Then what is the total surface area of the square pyramid?

A gaseous mixture of two substances A and B, under a total pressure of 0.8 atm is in equilibrium with an ideal liquid solution. The mole fraction of substance A is 0.5 in the vapour phase and 0.2 in the liquid phase. The vapour pressure of pure liquid A is ______ atm. (Nearest integer)

If
$\sum\limits_{k=1}^{31}$ $(^{31}C_k) (^{31}C_{k-1})$ $-\sum\limits_{k=1}^{30}$ $(^{30}C_k) (^{30}C_{k-1})$ $= \frac{α (60!)} {(30!) (31!)}$
where $α ∈ R$, then the value of 16α is equal to

A proton moves with a velocity of 5 x 10⁶ j m/s, through the uniform electric field E = 4 x 10⁶ (2i + 0.2j + 0.1k) Vm^-1and the uniform magnetic field B = 0.2( i + 0.2 j + k) T. The approximate net force acting on the proton is

Two identical positive charges Q each are fixed at a distance of 2a apart from each other. Another point charge q₀ with mass m is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q₀ executes SHM. The time period of oscillation of charge q₀ will be

In the following circuit $C_1=12 \mu F, C_2=C_3=4 \mu F$ and $C_4=C_5=2 \mu F$.The Charge stored in $C_3$ is ___$\mu C$

150 g of acetic acid was contaminated with 10.2 g ascorbic acid (C₆H₈O₆) to lower down its freezing point by (x × 10^–1)°C. The value of x is ______. (Nearest integer)

(Given : K_f = 3.9 K kg mol^–1; molar mass of ascorbic acid = 176 g mol^–1)

Two bodies of masses m₁ = 5 kg and m₂ = 3 kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass m₁ will be
[Take g = 10 ms^–2]

Two bodies of masses m1 = 5 kg and m2 = 3 kg are connected by a light

Identify the correct sequence of current assets in company's Balance sheet?
A. Bills Receivables
B. Cash & cash equivalents
C. Short term loans & advances
D. Inventories
E. Current investments
Choose the correct answer from the options given below:

2.5 g of protein containing only glycine (C₂H₅NO₂) is dissolved in water to make 500 mL of solution. The osmotic pressure of this solution at 300 K is found to be 5.03 × 10^–3 bar. The total number of glycine units present in the protein is _______.
(Given : R = 0.083 L bar K^–1 mol^–1)

If $ \frac{d}{dx} \left( \frac{x^2+1}{(x^2+5)(x^2+9)} \right) = \frac{2x(x^2+1)}{(x^2+5)(x^2+9)} \left[ \frac{1}{f(x)} - \frac{1}{g(x)} - \frac{1}{h(x)} \right] $, then $ 2h(x)-f(x)-g(x) = $

$ \int \frac{dx}{(1+\sqrt{x})^{2022}} = $

If $ \int \frac{\sin(x-\pi/4)}{2+\sin 2x} dx = -\frac{1}{\sqrt{2}} \tan^{-1}(f(x)) + C $, then $f(x) = $

$ \int_{a-1}^{a} \frac{e^x(a-x)}{(x-a+1)^2} dx = $

For $n \in N$, If $ I_n = \int \frac{\sin nx}{\sin x} dx = \frac{2}{n-1}\sin((n-1)x) + I_{n-2} $ and $ \int_0^{\pi} \frac{\sin nx}{\sin x} dx = \frac{k\pi}{2} $ then k =

If a and b are respectively the order and degree of a differential equation $ y^2(y'')^2 + 3x(y')^{1/3} + x^2y^2 = \sin x $, then