CSIR NET Maths previous year question papers

Multi-select · full marks only for the exact set · Estimation

1. A

   n⁻$^{1} \sum_{i=1}^{n}$ $X_{i}$

2. B

   n⁻$^{1} \sum_{i=1}^{2n}$ $X_{i}$

3. C

   n⁻$^{1} \sum_{i=1}^{n}$ $X_{2i}$₋$_{1}$

4. D

   n⁻$^{1}(\sum_{i=1}^{n}$ $X_{i} + W)$

Multi-select · full marks only for the exact set · Integration

1. A

   $\int$₋$_{1}^{1} f(x)x^{n}$ dx = 0 for all n ≥ 0.

2. B

   $\int$₋$_{1}^{1} f(x)p(x)$ dx = 0 for all real polynomials p(x).

3. C

   $\int$₋$_{1}^{1} f(x)x^{n}$ dx = 0 for all n ≥ 0 odd.

4. D

   $\int$₋$_{1}^{1} f(x)x^{n}$ dx = 0 for all n ≥ 0 even.

Multi-select · full marks only for the exact set · Lebesgue Measure and Integration

1. A

   $A_{n}$ is finite for every integer n ≥ 1.

2. B

   $A_{n}$ is finite for some integer n ≥ 1.

3. C

   $A_{n}$ is infinite for some integer n ≥ 1.

4. D

   $A_{n}$ is countable (finite or infinite) for every integer n ≥ 1.

Multi-select · full marks only for the exact set · Classical Mechanics

1. A

   $a^{2} + b^{2} = 2$

2. B

   a − b = 2

3. C

   a + b = 2

4. D

   a = 1, b = 1

Multi-select · full marks only for the exact set · Linear Models and Multivariate

1. A

   $(1/\sum{}n_{i}) \sum_{i}\sum_{j} Y_{ij}$ is an unbiased estimator of $\mu$

2. B

   $2\mu + \alpha_{1} + \alpha_{2}$ is an estimable linear parametric function

3. C

   $\mu + \alpha_{1} + \alpha_{2}$ is an estimable linear parametric function

4. D

   $(1/n_{2}) \sum_{j} (Y_{2j} -$ Ȳ$_{2})$ is an unbiased estimator of $\alpha_{2}$

Multi-select · full marks only for the exact set · Linear Models and Multivariate

1. A

   If $X_{1}$ and $Y_{1}$ are independent, then $S_\rho = 0$

2. B

   $S_\rho = (6/\pi) \sin$⁻$^{1}(\rho/2)$

3. C

   If $S_\rho = 0$, then $X_{1}$ and $Y_{1}$ are independent

4. D

   If $X_{1}$ and $Y_{1}$ are independent, then $S_\rho = 1/2$