List of practice Questions

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to

Earthworms have no skeleton but during burrowing, the anterior end becomes turgid and acts as a hydraulic skeleton. It is due to

Amongst \( \text{Ni(CO)}_4 \), \( [\text{Ni(CN)}_4]^{2-} \), and \( [\text{NiCl}_4]^{2-} \), which is paramagnetic?

In which of the following octahedral complexes of Co (At no. 27), will the magnitude of \( \Delta_o \) be the highest?

Assertion (A): \( \text{Cu}^{2+} \) and \( \text{Cd}^{2+} \) are separated by first adding KCN solution and then passing H\(_2\)S gas. Reason (R): KCN reduces \( \text{Cu}^{2+} \) to \( \text{Cu}^+ \) and forms a complex with it.

The effective atomic number of cobalt in the complex \( [\text{Co(NH}_3)_6]^{3+} \) is:

The IUPAC name for the complex \( [\text{Co(NO}_3)_6\text{NH}_3]^{3+} \) is:

The freezing point of a solution composed of 10.0 g of KCl in 100 g of water is 4.5°C. Calculate the van't Hoff factor, \(i\), for this solution.

If \[ \mathbf{I} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \] then \( B \) is equal to:

Let \( R: \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = x^2 + 1 \), find \( f^{-1}(-5) \):

If \( X \) is a Poisson variate such that \( P(X = 1) = P(X = 2) \), then \( P(X = 4) \) is equal to:

The area enclosed by \( y = 3x - 5 \), \( y = 0 \), \( x = 3 \), and \( x = 5 \) is:

The order and degree of the differential equation \[ \left( 1 + 4 \frac{dy}{dx} \right)^{2/3} = 4 \frac{d^2 y}{dx^2} \] are respectively:

The solution of the differential equation \[ \frac{dy}{dx} = (4x + y + 1)^2 \] is:

The system of equations \[ 2x + y - 5 = 0, \quad x - 2y + 1 = 0, \quad 2x - 14y - a = 0 \] is consistent. Then, \( a \) is equal to:

A die is rolled twice and the sum of the numbers appearing on them is observed to be 7. What is the conditional probability that the number 2 has appeared at least once?

The locus of the mid-points of the focal chord of the parabola \( y^2 = 4ax \) is:

Find the value of \[ \sin 12^\circ \sin 48^\circ \sin 54^\circ \]

In an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio:

Let \( p \) and \( q \) be two statements. Then, \( p \vee q \) is false if:

In how many ways 6 letters can be posted in 5 different letter boxes?

If \( A \) and \( B \) are two sets such that \( A \times B \) consists of 6 elements, find \( B \times A \):

A line making angles 45° and 60° with the positive directions of the axes of \( x \) and \( y \) makes with the positive direction of \( z \)-axis, an angle of:

Which of the following is correct?

If \( \alpha, \beta, \gamma \) are the roots of \( x^3 + ax^2 + b = 0 \), then the value of \[ \frac{\alpha \beta}{\gamma}, \quad \frac{\beta \gamma}{\alpha}, \quad \frac{\gamma \alpha}{\beta} \]