List of practice Questions

Let $S_1 = {(x, y) ∈ R^2 ∶ x + y ≥ 1, x + y ≤ 2, y ≥ x^2, x, y ≥ 0}$ and $S_2 = {(x, y) ∈ R^2 ∶ x + y ≥ 1, x + y ≤ 2, y ≤ x^2, x, y ≥ 0}.$ Then, which of the following is CORRECT ?

Suppose nominal GDP equals 1,000 units and money supply equals 250 units. Based on the quantity theory of money, the velocity of money equals

Which of the following measures was NOT initiated by the Government of India as a part of economic reforms in 1991?

Suppose a random variable 𝑋 follows an exponential distribution with mean 50. Then, the value of the conditional probability $ P(X > 70 | X > 60)$ is

Which of the following was announced in the Union Budget 2023-24 to enhance the skills of lakhs of youth in the next 3 years?

Consider a closed economy with consumption function $ C = 2 + 0.5𝑌$, where 𝑌 is income. The government expenditure is 3 and investment function is $ I = 4 − 0.5r $ , where r is interest rate. Then, the slope of the IS curve will be

Consider a production function of the form:
$ Y = 𝑎 log L + (1 − 𝑎) log K , 𝑎 ∈ (0, 1), 𝑎 ≠ 0.5 $
where, Y is output, L is labour, and K is capital. Then, the absolute value of elasticity of substitution is

Let 𝑥 and 𝑦 be two consumption bundles, assumed to be non-negative and perfectly divisible. Further, the assumptions of completeness, transitivity, reflexivity, non-satiation, continuity, and strict convexity are satisfied. Then, which of the following statements is NOT CORRECT?

Which one of the following is a non-parametric test?

Mobility of ions Li⁺ , Na⁺ , K⁺ , Ag⁺ in water at 298 K follows the order

If \( F_1(Q, q) = Qq \) is the generating function of a canonical transformation from \((p, q)\) to \((P, Q)\), then which one of the following relations is correct?

A landfill sample was analyzed by dilution and plating techniques for viable bacterial count. When one gram of the landfill sample was diluted \(1 \times 10^{-4}\) (w/v), it yielded 400 CFU. The viable bacterial count (in millions, rounded off to the nearest integer) in one gram of the landfill sample is ___.

Adsorption of acetone from aqueous solution on activated carbon can be represented by the Langmuir equation: \[ \frac{q}{C} = \frac{1}{0.146} + \frac{0.190}{C} \] where \( q \) is the adsorbate loading mol/kg, and \( C \) is solute concentration in aqueous solution mol/m³. The maximum adsorbate loading in kg acetone/kg carbon is