CSIR NET Maths previous year question papers

Multi-select · full marks only for the exact set · Sampling and Design of Experiments

1. A

   The design is incomplete

2. B

   The design is connected

3. C

   The design is balanced

4. D

   The design is orthogonal

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

1. A

   The first principal component based on $\sum$ explains exactly 90% of the total variability

2. B

   The second principal component based on $\sum$ explains exactly 10% of the total variability

3. C

   sup{$a^{T}\sum{}a : a \in \mathbb{R}^{2}$ and aᵀa = 1} = 3

4. D

   The first principal component based on $\sum$ is $(1/\sqrt{3})(X_{1} + \sqrt{2X_{2}})$

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

1. A

   q = 0.6

2. B

   E[Y] = 5.8

3. C

   Var(Y) = 3.04

4. D

   $Y = 0.4X_{1} +$ qX$_{2}$

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

1. A

   $(1/\sigma^{2}) Y^{T}X\beta$̂ has a central $\chi^{2}_{p+1}$ distribution

2. B

   $(1/\sigma^{2})(Y - X\beta$̂$)^{T}(Y - X\beta$̂) has a central $\chi^{2}_{n-p-1}$ distribution

3. C

   $X\beta$̂ and $(Y - X\beta$̂$)^{T}(Y - X\beta$̂) are independently distributed

4. D

   $(1/\sigma^{2}) \sum(Y_{i} -$ Ȳ$)^{2}$ has a central $\chi^{2}_{n-1}$ distribution