List of practice Questions

Two masses of 1 gram and 4 gram are moving with equal kinetic energy. The ratio of the magnitudes of their momenta is

If the frequency of incident radiation is kept constant and the experiment is repeated by using incident light of different intensities, then stopping potential (\( V_s \))

If \( A(0, 4, 0) \), \( B(0, 0, 3) \), and \( C(0, 4, 3) \) are the vertices of \( \Delta ABC \), then its incenter is:

The probability distribution of a discrete r.v. \( X \) is: \[ \begin{array}{c|ccccc} X = x & 0 & 1 & 2 & 3 & 4 \\ P(X = x) & k & 2k & 4k & 2k & k \\ \end{array} \] Then, the value of \( P(X \leq 2) \) is:

The equation of the line passing through the points \( (3, 4, -7) \) and \( (6, -1, 1) \) is:

If \( \frac{x}{x-y} = \log \left( \frac{a}{x-y} \right) \), then \( \frac{dy}{dx} = \)

Evaluate the integral: \[ \int_{-1}^{1} \left[ \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right] dx \]

The co-ordinates of the foot of the perpendicular from the point \( (0, 2, 3) \) on the line
\[ \frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3} \]

The approximate value of \( \log_{10}99 \) is (Given \( \log_{10}e = 0.4343 \))

The maximum value of \(Z = 10x + 25y\) subject to \[ 0 \le x \le 3,\; 0 \le y \le 3,\; x + y \le 5,\; x \ge 0,\; y \ge 0 \] is

Evaluate the integral: \[ \int \frac{\sin x}{\sin\left(x-\frac{\pi}{4}\right)}\,dx \]

If \((\sim p \wedge q)\rightarrow r\) is false, then the truth values of \(p,q,r\) respectively are

The value of \(x\) such that the matrix \[ \begin{bmatrix} x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 & 5 \end{bmatrix} \] is not invertible is

What is the approximate ratio of roasted ore, coke, and lime stone respectively in the charge to be added into the blast furnace for extraction of iron?

Relation between \( \Delta H \) and \( \Delta U \) for the reaction \[ \text{2SO}_3 (g) \rightarrow \text{2SO}_2 (g) + \text{O}_2 (g) \] is

Evaluate the integral: \[ \int \left[ \log(1+\cos x) - x \tan\left(\frac{x}{2}\right) \right] dx \]

If the population grows at the rate of 5% per year, the time taken for the population to become double is (Given \( \log 2 = 0.6912 \))

The reaction \( \text{N}_2\text{O}_5 \rightarrow 2\text{NO}_2 + \text{O}_2 \) is first order in \( \text{N}_2\text{O}_5 \), having rate constant \( 6 \times 10^{-4} \, \text{L}^{-1} \, \text{s}^{-1} \). What is the value of rate of reaction when concentration of \( \text{N}_2\text{O}_5 \) is 1.25 mol L\(^{-1}\)?

Which of the following properties is of thermoplastic polymer?

The molecular mass of an organic monobasic acid is 129 and the value of \( n \) is 2, what is empirical formula mass of compound?

What is the value of \( K_f \) if 30 g urea (molar mass 60) dissolved in 0.5 dm³ of water decreases freezing point by 0.15°C?

An aqueous solution of sodium nitrite on boiling with \( \alpha \)-chlorosodium propionate gives

What is the molality of a solution containing 300 mg of urea (molar mass 60) dissolved in 30 g of water?

Which of the following elements exhibits oxidation states other than +3?

The IUPAC name of isobutyl bromide is