List of practice Questions

A current of $5\,A$ is flowing at $220 \,V$ in the primary coil of a transformer. If the voltage produced in the secondary coil is $2200\, V$ and $50\%$ of power is lost, then the current in the secondary will be

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is $90^\circ$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

A roller coaster is designed such that riders experience ''weightlessness'' as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is

If g (x) is a polynomial satisfying g (x) g(y) = g(x) + g(y) + g(xy) - 2 for all real x and y and g (2) = 5 then $\underset{\text{x $\rightarrow$ 3}}{{Lt }}$ g(x)is

An aqueous solution of 6.3 g of oxalic acid dihydrate is made upto 250 mL. The volume of $ \text{0}\text{.1}\,\text{N}\,\text{NaOH} $ required to completely neutralize 10 mL of this solution is

If $ X $ is the total number of collisions which a gasmolecule register with others per unit time under particular conditions, then the collision frequency of the gas containing N molecules per unit volume is

The wavelength of the radiation emitted, when in a hydrogen atom electron falls from infinity to stationary state one, would be (Rydberg constant $ =1.097\times {{10}^{7}}\,{{m}^{-1}} $ )

AgCl dissolves in a solution of NH₃, but not in water because

Which of the following is hexadentate ligand?

A coordinate bond is a dative covalent bond. Which of the below is true?

Which of the following complex has zero magnetic moment (spin only)?

If \( A(\theta) = \left[ \begin{matrix} 1 & -\tan \theta \\ \end{matrix} \right] \) and \( AB = 1 \), then \[ (\cos \theta)B \] is equal to

If the probability density function of a random variable \( X \) is \( f(x) = \frac{x}{2} \) for \( 0 \leq x \leq 2 \), then \[ P(X>1.5 \mid X>1) \] is equal to

If \( x = -5 \) is a root of the equation \[ \begin{vmatrix} 2x+1 & 4 & 8 \\ 2 & 2x & 2 \\ 7 & 6 & 2x \end{vmatrix} = 0 \] then the other roots are

If the rank of the matrix \[ \begin{pmatrix} -1 & 2 & 5 \\ 2 & -4 & -4 \\ 1 & -2 & a + 1 \end{pmatrix} \] is 1, then the value of \( a \) is

A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even}or {even, odd} is

If \( P(A) = \frac{1}{2}, P(B) = \frac{5}{12} \) and \( P(B/A) = \frac{1}{15} \), then \[ P(A \cup B) \] is equal to

If \( x \sin \left( \frac{y}{x} \right) \, dy = \sin \left( \frac{y}{x} \right) - x \, dx \) and \( y(1) = \frac{\pi}{2} \), then the value of \( \cos \left( \frac{y}{x} \right) \) is

The function \( f(x) = x^2 e^{-x} \), \( x>0 \). Then the maximum value of \( f(x) \) is

The value of \( \int_0^\infty \frac{dx}{(a^2 + x^2)^7} \) is equal to

The product of all values of \( \cos(\alpha) + i \sin(\alpha) )^{3/5} \) is equal to

The imaginary part of \( \frac{(1+i)^2}{i(2i-1)} \) is

If \( H \) is the harmonic mean between \( P \) and \( Q \), then the value of \[ \frac{H}{P} + \frac{H}{Q} \] is

If \( \vec{a} \) and \( \vec{b} \) are two unit vectors, then the vector \[ (\vec{a} + \vec{b}) \times (\vec{a} \times \vec{b}) \] is parallel to the vector