List of practice Questions

Blue colour of the sky is due to
An ideal gas (X) present in a vessel of volume \( V \) exerted a pressure of 16.4 atm at 200 K. What is its concentration in mol \( L^{-1} \)? % Given Data Given \( R = 0.082 \, \text{L atm mol}^{-1} \text{K}^{-1} \)
The mean of 5 observations is 4.4 and their variance is 8.24. If three of those observations are 1, 2, and 6, then the other two observations are:
An inductor and a resistor are connected in series to an AC source. If the power factor of the circuit is 0.5, the ratio of the resistance of the resistor and the reactance of the inductor is:
Which of the following has more pK\(_a\) value?
A ray of light incident along a line meets another line $7x - y + 1 = 0$ at the point $(0,1)$ and is then reflected along the line $y + 2x = 1$. Then the equation of the line of inciden is
Sphalerite is the ore of metal \( M_1 \) and malachite is the ore of metal \( M_2 \). Atomic numbers of \( M_1 \) and \( M_2 \) are respectively
The correct order of reactivity of the following towards nucleophilic addition reactions is: \[ \text{I. CH}_3\text{COCH}_3,\quad \text{II. CH}_3\text{CH}_2\text{CHO},\quad \text{III. ClCH}_2\text{CHO} \]
The number of elements in the set $ S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \le 0 \text{ and } x^2 - 3x>0 \} $ is
In $ \triangle ABC $, if $ r $ is the inradius and $ r_1, r_2, r_3 $ are the ex-radii, then \[ \frac{1}{4} \left[ b^2 \sin 2C + c^2 \sin 2B \right] = \]
Among the following, Ampere’s circuital law is represented by:
If \( A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix} \) and \( B = \begin{bmatrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \end{bmatrix} \), then which one of the following is True?
If \( \frac{x^4 - 6x^3 + 9x^2 + 5x - 20}{x^2 - x - 2} = f(x) + \frac{a}{x + p} + \frac{b}{x + q} \), then \( 2(a + b) = \)
If \( \mathbf{a} = (2x + y)\mathbf{i} + 3\mathbf{j} + 9\mathbf{k} \) and \( \mathbf{b} = 2\mathbf{i} + \mathbf{j} - (x - y)\mathbf{k} \) are two collinear vectors, then \( x^3 + 27y^3 = \)
If \( y = x \log \left( \frac{1}{ax} \right) \), then \( x(1 + x) \frac{d^2 y}{dx^2} + x \frac{dy}{dx} - y = \)
If \( \lim_{x \to \infty} y(x) = \frac{\pi}{2} \), then the solution of \( x^3 \sin y \frac{dy}{dx} = 2 \) is \( \cos y = \)
For a positive real number \( \lambda \), if the vector \( \vec{a} = \lambda \vec{i} - 5\vec{j} + 6\vec{k} \) satisfies the equation \[ \left[ \vec{i} \times (\vec{a} \times \vec{i}) + \vec{j} \times (\vec{a} \times \vec{j}) + \vec{k} \times (\vec{a} \times \vec{k}) \right]^2 = 440, \] then \( \lambda = \)
One out of 9 ships is likely to sink when they are set on sail. When 6 ships are set on sail, the probability that exactly 3 of them will not arrive safely is:
If \( A + 2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix} \) and \( 2A - B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix} \), then \( \text{Tr}[A] - \text{Tr}[B] \) equals:
A truck of mass \( M \) and a car of mass \( \frac{M}{10} \) moving with the same momentum are brought to halt by the application of the same breaking force. The ratio of the distances travelled by the truck and car before they come to stop is:
A 50 g ice cube at -10°C is added to 200 g of water at 30°C. The final temperature of the mixture is: (Specific heat of water = 1 cal g\(^{-1}\)°C\(^{-1}\), latent heat of fusion of ice = 80 cal g\(^{-1}\), specific heat of ice = 0.5 cal g\(^{-1}\)°C\(^{-1}\))
In a hydrogen atom, an electron in an orbit with principal quantum number \( n \) jumps to the first excited state, emitting a photon of wavelength \( \lambda \). Then the value of \( n \) is:
The process which involves the treatment of the ore with a suitable reagent so as to make it soluble but not impurities is called
The time taken by a net force of 10 N to change the velocity by 4 m/s of a body of mass 10 kg is:
According to Newton's law of cooling, the temperature of a body is \( T \) at time \( t \) and the temperature of the surroundings is \( T_s \). The rate of change of temperature is given by \[ \frac{dT}{dt} = k(T_s - T) \] If the initial temperature at time \( t = 0 \) is \( T_0 \), then the temperature \( T \) is: