The charge accumulated on the capacitor connected in the following circuit is ______\mu\text{C}. (\text{Given } C = 150\text{ }\mu\text{F})
A train is moving with a speed of 12\text{ m s}^{-1} on rails which are 1.5\text{ m} apart. To negotiate a curve radius 400\text{ m}, the height by which the outer rail should be r
In a nuclear fission process, a high mass nuclide (A \approx 236) with binding energy 7.6\text{ MeV /Nucleon} dissociated into two middle mass nuclides (A \approx 118), having bind
Two bodies of mass 4\text{ g} and 25\text{ g} are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :
A body of mass 1000\text{ kg} is moving horizontally with a velocity 6\text{ m s}^{-1}. If 200\text{ kg} extra mass is added, the final velocity (in \text{m s}^{-1}) is:
The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gra
Given below are two statements : Statement (I) : Viscosity of gases is greater than that of liquids. Statement (II) : Surface tension of a liquid decreases due to the presence of i
0.08\text{ kg} air is heated at constant volume through 5^{\circ}\text{C}. The specific heat of air at constant volume is 0.17\text{ kcal kg}^{-1}\text{ }^{\circ}\text{C}^{-1} and
Which of the following cannot function as an oxidising agent?
The technique used for purification of steam volatile water immiscible substance is:
The final product A, formed in the following reaction sequence is: \text{Ph}-\text{CH}=\text{CH}_2 \xrightarrow[\text{(iv) } \text{Mg, ether, then } \text{HCHO}/\text{H}_3\text{O}^
If \alpha, \beta are the roots of the equation, x^2 - x - 1 = 0 and S_n = 2023\alpha^n + 2024\beta^n, then
The values of \alpha, for which \begin{vmatrix} 1 & \frac{3}{2} & \alpha + \frac{3}{2} \\ 1 & \frac{1}{3} & \alpha + \frac{1}{3} \\ 2\alpha + 3 & 3\alpha + 1 & 0 \end{vmatrix} = 0,
Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying \tan^{-1}(x) + \tan^{-1}(2x) = \frac{\pi}{4} is :
Let g(x) = 3f\left(\frac{x}{3}\right) + f(3 - x) and f''(x) > 0 for all x \in (0, 3). If g is decreasing in (0, \alpha) and increasing in (\alpha, 3), then 8\alpha is
The integral \int \frac{x^8 - x^2\,dx}{x^{12} + 3x^6 + 1 \tan^{-1}\left(x^3 + \frac{1}{x^3}\right)} is equal to :
The primary side of a transformer is connected to 230\text{ V},\ 50\text{ Hz} supply. The turn ratio of primary to secondary winding is 10 : 1. Load resistance connected to the sec
When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :
The reading of pressure metre attached with a closed pipe is 4.5 \times 10^4\text{ N m}^{-2}. On opening the valve, water starts flowing and the reading of pressure metre falls to
A closed organ pipe 150\text{ cm} long gives 7 beats per second with an open organ pipe of length 350\text{ cm}, both vibrating in fundamental mode. The velocity of sound is _____
Given below are two statements : Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials. Statement (II) : The limiting fo
The final product A formed in the following multistep reaction sequence is Styrene \xrightarrow{\text{(i) } \text{H}_2\text{O}.\text{H}^+} \xrightarrow{\text{(ii) } \text{CrO}_3} \
For the reaction \text{N}_2\text{O}_4\text{ (g)} \rightleftharpoons 2\,\text{NO}_2\text{ (g)}, \text{K}_p = 0.492\text{ atm} at 300\text{ K}. \text{K}_c for the reaction at same te
A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0.1\text{ m} high and 0.1\text{ m} wide. The minimum velocity u with which that ball just hits the
The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of 20\text{ cm} from its center is 1.5 \times 10^{-5}\text{ T m}. The magnetic moment
If the domain of the function f(x) = \cos^{-1}\left(\frac{2-|x|}{4}\right) + (\log_e(3 - x))^{-1} is [-\alpha, \beta) - \{\gamma\}, then \alpha + \beta + \gamma is equal to :
Let the latus rectum of the hyperbola \frac{x^2}{9} - \frac{y^2}{b^2} = 1 subtend an angle of \frac{\pi}{3} at the centre of the hyperbola. If b^2 is equal to \frac{l}{m}(1 + \sqrt
For \alpha, \beta \in \left[0, \frac{\pi}{2}\right] let 3\sin(\alpha + \beta) = 2\sin(\alpha - \beta) and a real number k be such that \tan\alpha = k\tan\beta. Then the value of k
A vector has magnitude same as that of \vec{A} = 3\hat{i} + 4\hat{j} and is parallel to \vec{B} = 4\hat{i} + 3\hat{j}. The x and y components of this vector in first quadrant are x
A block of ice at -10\text{ }^\circ\text{C} is slowly heated and converted to steam at 100\text{ }^\circ\text{C}. Which of the following curves represent the phenomenon qualitative