List of practice Questions

\( \int 3^{-\log_3 x^2} dx = \)
For a CE transistor amplifier, the current amplification factor is 59 and the emitter current is 6.6 mA. Then the base current is
If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is not in the first quadrant, then \( 15 \sin 2\theta - 20 \cos 2\theta - 7 \tan 2\theta \) is:
A and B are mutually exclusive events of a random experiment and \( P(B^c) \ne 1 \), then \[ P(A | B^c) = ? \]
Let the equation \[ ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 \] represent a point circle (not at the origin). Then which one of the following conditions must hold?
If \[ \lim_{x \to 2} \frac{1 + \sqrt{1 + 4\log_2 x}}{2 + (2x + \sin^2 x + 2\cos x)(2x - 4)} = m, \] then \( m(m - 1) = \):
Total emf induced in a coil with \( N \) turns and changing magnetic flux \( \frac{d\phi_B}{dt} \) is:
Consider a gas phase reaction which occurs in a closed vessel. \[ 2A (g) \rightarrow 4B (c) + C (g) \] The concentration of B is found to be increased by \( 5 \times 10^{-3} \) mol L\(^{-1}\) in 10 seconds. The rate of disappearance of A (in mol L\(^{-1}\) s\(^{-1}\)) is
In \( \triangle ABC \), if \( (\sin A + \sin B)(\sin A - \sin B) = \sin C(\sin B + \sin C) \), then \( \angle A = \)
If the chord of contact of the point \( P(1, 1) \) with respect to the circle \( S = x^2 + y^2 + 4x + 6y - 3 = 0 \) meet the circle \( S = 0 \) at A and B, then the area of \( \triangle PAB \) is:
The greatest integer \( r \) such that \( 30^r \) divides \( 30! \) is:
If \( 2\sinh x = \cosh x \), then \( x = \)
If the velocity of a particle moving along a straight line with uniform acceleration, is given by \( V = \sqrt{196 - 16X} \, \text{m/s} \), then its acceleration is
Two particles of masses 1 g and 2 g move towards each other with velocities 10 m/s and 20 m/s respectively. The velocity of the centre of mass of the system of the two particles is
In the given reactions, 'X' and 'Y' respectively are: \[ \ce{C6H5CH2NH2 ⇔[X] C6H5CONH2 ⇒[Y] C6H5NH2} \]
If \[ \int \frac{\sin^2 \alpha - \sin^2 x}{\cos x - \cos \alpha} \, dx = f(x) + Ax + B, \, B \in \mathbb{R}, \text{ then} \] \[ \frac{\sin^2 \alpha - \sin^2 x}{\cos x - \cos \alpha} \, dx = f(x) + Ax + B, \, B \in \mathbb{R} \]
If \( q \) is electric charge, \( B \) is magnetic field, \( R \) is the dee radius and \( m \) is the mass of ions, the kinetic energy of the ions in cyclotron is given by:
Which of the following is not correct?
If A and B simultaneously toss one coin each every time, each 50 times, then the probability of not getting a tail on both the coins is:
If a Bernoulli trial is conducted n times, then which one of the following is not suitable to use Poisson distribution?
Let a focal chord \( 12x + 5y - 27 = 0 \) of the parabola \( y^2 = kx \) intersect the parabola at points \( P \) and \( P' \). If \( S \) is the focus of the parabola, then \( 9(SP + SP') \) = ?
If \( f(n) = n!(31-n)! \), where \( n \in \{ 0, 1, 2, \dots, 31 \} \), then the minimum value of \( f(n) \) is:
If \( C_j \) stands for \( \binom{n}{j} \), then: \[ \frac{C_1}{C_0} + 2 \times \frac{C_2}{C_1} + 3 \times \frac{C_3}{C_2} + ... + n \times \frac{C_n}{C_{n-1}} \]
If \( f(x) = \sqrt{x} + \sin x \), then all the points of the set \( \left( x, f(x) \right)/f'(x) = 0 \) lie on:
A block of steel of mass 2 kg slides down a rough inclined plane of inclination of \( \sin^{-1} \left( \frac{3}{5} \right) \) at a constant speed. The temperature of the block as it slides through 80 cm, assuming that the mechanical energy lost is used to increase the temperature of the block is nearly: