List of practice Questions

A set of ‘n’ equal resistors, of value ‘R’ each, are connected in series to a battery of emf ‘E’ and internal resistance ‘R’. The current drawn is I. Now, the ‘n’ resistors are connected in parallel to the same battery. Then the current drawn from battery becomes 10 I. The value of ‘n’ is
A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is
The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is
A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s2 at a distance of 5 m from the mean position. The time period of oscillation is
The power radiated by a black body is P and it radiates maximum energy at wavelength, λ0 . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength \(\frac{3}{4}\lambda_0\), the power radiated by it becomes nP. The value of n is
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by \(\Delta l\) on applying a force F, how much force is needed to stretch the second wire by the same amount ?
A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to
A sample of 0.1 g of water at 100°C and normal pressure (1.013 × 105 Nm-2 ) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample, is
A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of – 0.004 cm, the correct diameter of the ball is
The CCCN code indicating the botanical drugs is:-
If A, B, C are the angles of $\Delta ABC$ then $\cot \, A. \cot \, B + \cot \, B. \cot \, C + \cot \, C. \cot \, A =$
If $f(x) = \begin{cases} x^2 + \alpha & \text{for } x \ge 0 \\[2ex] 2\sqrt{x^2 + 1} + \beta & \text{for} x < 0 \end{cases}$ is continuous at x = 0 and $f \left(\frac{1}{2} \right) = 2 $ then $\alpha^2+ \beta^2$ is
If $\log_{10} \left(\frac{x^{3} - y^{3} }{x^{3} + y^3} \right) = 2$ then $ \frac{dy}{dx} = $
If $y = \left(\tan^{-1} x\right)^{2}$ then $ \left(x^{2} + 1\right)^{2} \frac{d^{2}y}{dx^{2} } + 2x \left(x^{2} + 1 \right) \frac{dy}{dx} = $
A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) =
Letters in the word HULULULU are rearranged. The probability of all three L being together is
If $f : R - \{2\} \to R$ is a function defined by $f(x) = \frac{x^2 - 4}{x - 2}$ , then its range is
The sum of the first 10 terms of the series 9 + 99 + 999 + ?., is
The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
Which of the following pituitary hormone works indirectly?
Which of the following molecules represents the order of hybridisation sp2 , sp2 , sp, sp from left to right atoms ?
A man in a car at location $Q$ on a straight highway is moving with speed $v$. He decides to reach a point $P$ in a field at a distance d from the highway (point $M$) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance $RM$, so that the time taken to reach $P$ is minimum ?
If molar conductivity of \(Ca^{2+}\) and \(Cl^-\) ions are 119 and 71 Scm2 mol-1 respectivily, then the molar conductivity of \(CaCl_2\) at infinite dilution is
If 10 L of an ideal gas at a pressure of 5 atm expands isothermally and reversibly to a final volume of 100 L. the work done and heat absorbed in this process (in Lit-atm), respectively are
Hydrogen peroxide reacts with lead sulphide to produce lead sulphate. Identify the other product formed