Center for Development Studies (CDS) - Entrance Solutions (2019)

Answer Key


  1. $\boxed{B} \ 4$ 
  2. $\boxed{A} \ \frac{5}{14}$
  3. $\boxed{A} \ \frac{27}{35}$
  4. $\boxed{B} \ 63$
  5. $\boxed{C} \ \frac{1}{8}$
  6. $\boxed{A}$ The probability of correctly rejecting the null hypothesis.
  7. $\boxed{B} \ 4\%$ probability that average marks are equal.
  8. $\boxed{B} \ a^2\sigma_{x}+b^2\sigma_{y}$.
  9. $\boxed{A}$ A $\chi^{2}$ distribution with mean $n$ and variance $2n$.
  10. $\boxed{A} \ Z^2 \succ F[1,n]$.
  11. $\boxed{C}$ Coefficient of Variation.
  12. $\boxed{C}$ with mean $\mu$ and variance $\frac{\sigma^{2}}{n}$.
  13. $\boxed{A}$ The mean of the sampling distribution is $\theta$.
  14. $\boxed{A}$ Its sampling distribution has the least variance.
  15. $\boxed{B}$ $\frac{1}{108}$
  16. $\boxed{B}$ $\frac{29}{72}$
  17. $\boxed{C}$ $\frac{25}{69}$
  18. $\boxed{B}$  Maximum allowable probability of type $I$ error.
  19. $\boxed{C}$ $\beta_{xy}=\beta_{yx}=0$
  20. $\boxed{C}$ Biased and inconsistent.
  21. $\boxed{C}$ $L_{B}<L_{A}$ and $K_{A}<K_{B}$ . Since, $Q_{B}$ have higher $A$ or the Total Factor Productivity compared to $Q_{A}$ ceteris paribus.
  22. $\boxed{C}$ He prefers black tea over lemon tea. Since it is given that, $Coffee \succ Black \ tea$,  $Black \ tea \sim Green \ tea$ and $Lemon \ tea \succ Green \ tea$. This implies, the only false statement is $Black \ tea \succ Lemon \ tea$
  23. $\boxed{A}$ $(tx_{1}+(1-t)x_{2},ty_{1}+(1-t)y_{2})\succcurlyeq (x_{1},y_{2})$ 
  24. $\boxed{C}$ $f(B)-f(C)<0$
  25. $\boxed{A}$ $U=5x_{1}+5x_{2}$ represents a straight line with slope 1 or it represents the indifference curve of perfect substitutes.
  26. $\boxed{C}$ Figure C represents the Engel curve derived from homothetic preferences
  27. $\boxed{A}$ AC continuously falls as output rises since $AC=\frac{TC}{q}=\frac{q(VC)+FC}{q}=VC+\frac{FC}{q}$
  28. $\boxed{C}$ Greater than one, but less than 2.
  29. $\boxed{A}$ Increase
  30. $\boxed{C}$ Figure C represents the IC of strict complementarity.
  31. $\boxed{C}$ Consumer prefernces have changed in favour of A.
  32. $\boxed{B}$ Producing same output with more inputs.
  33. $\boxed{B}$ Variable cost
  34. $\boxed{B}$ Decrease
  35. $\boxed{B}$ Figure B represents the IC of Ramu.
  36. $\boxed{B}$ $MR=MC$
  37. $\boxed{D}$ Total utlity
  38. $\boxed{D}$ Limiting production
  39. $\boxed{A}$ Increased barrier to entry
  40. $\boxed{D}$ None of these
  41. $\boxed{B}$ No
  42. $\boxed{B}$ $8.5$
  43. $\boxed{A}$ True
  44. $\boxed{A}$ 25
  45. $\boxed{A}$ True
  46. $\boxed{D}$ Figure D represents the Saving-Income relationship.
  47. $\boxed{B}$$3\%$
  48. $\boxed{B}$ The stability criteria of the model.
  49. $\boxed{A}$ Fully on permanent income.
  50. $\boxed{A}$ To finance old age consumption
  51. $\boxed{B}$ The change in the GDP.
  52. $\boxed{D}$ Remains unchanged under 100-percent reserve banking but decrease under fractional -reserve banking
  53. $\boxed{B}$ Always
  54. $\boxed{C}$ Equilibrium output will increase but private consumption will not change.
  55. $\boxed{C}$ Two
  56. $\boxed{D}$ All of the above
  57. $\boxed{A}$ MPC will be lower and interst sensitivity of  the investment will be lower. 
  58. $\boxed{C}$ For a special case, we can get a vertical LM curve.
  59. $\boxed{B}$ Average Propensity to Consume (APC) falls as income rises.
  60. $\boxed{D}$ Greater than one.
  61. $\boxed{D}$ The rate of technological progress.
  62. $\boxed{D}$ The persistence of fiscal shock and elasticity of labour supply.
  63. $\boxed{A}$ Interest rate is low and savings rate is high.
  64. $\boxed{B}$ Only fiscal policy is effective.
  65. $\boxed{B}$ Accelerator principle
  66. $\boxed{C}$ Inflation is a monetary phenomenon.
  67. $\boxed{C}$ Real variables can be analysed without analyzing their nominal counterparts.
  68. $\boxed{A}$ $Y=1000$ ,$i=5\%$
  69. $\boxed{C}$ Though money is neutral in long run but not in short run, governments cannot exploit because agents are rational.
  70. $\boxed{C}$ basically arising from interaction between workers choice of labour and liesure and productivity shocks.
  71. $\boxed{C}$ $e^{3x}(3x+1)$
  72. $\boxed{A} \ d=\frac{1}{4}$
  73. $\boxed{C}$ $tx+(1-t)y \in X \  \ \ \forall x,y \in X$ and $\forall t \in (0,1)$
  74. $\boxed{A}$ $+1$
  75. $\boxed{C}$ $f(\lambda x+(1- \lambda )y) \geq \lambda f(x)+(1- \lambda)f(y) \ \ \  \forall x,y \in S$ and $ \lambda \in (0,1)$
  76. $\boxed{B}$ $e$
  77. $\boxed{A}$ $(A \cap C) \cup (B \cap C)$
  78. $\boxed{C}$ $\frac{1-r^{n+1}}{1-r}$
  79. $\boxed{A}$ Figure A represents the fucntion.
  80. $\boxed{D}$ $\frac{4}{3}$
  81. $\boxed{C}$ It's maximal rank is $n$.
  82. $\boxed{B}$$B^{-1}A^{-1}$
  83. $\boxed{D}$ $4$
  84. $\boxed{D}$ $a=1$ ,$b=0$
  85. $\boxed{C}$ Limit does not exist
  86. $\boxed{B}$ $(-3, \inf)$
  87. $\boxed{C}$ $36^o$
  88. $\boxed{B}$ A relation
  89. $\boxed{B}$ $m \times n \times p$
  90. $\boxed{A}$ $135$
  91. $\boxed{D}$ $17 \%$
  92. $\boxed{A}$ $4+/-2$
  93. $\boxed{C}$ Fiscal deficit
  94. $\boxed{D}$ Software and non-factor service
  95. $\boxed{C}$ Private Corporate Sector
  96. $\boxed{A}$ $0.70 \%$
  97. $\boxed{D}$ China
  98. $\boxed{D}$ India
  99. $\boxed{B}$ Rice
  100. $\boxed{A}$ Household sector

Detailed Solutions


1. Given,
$$Expected \ Value \ of \ x, \ E(x)=2 \ \\ Variance \ of \ x, \ V(x)=1$$
We know,
$$E(x)=NP=2 \\ \implies P=\frac{2}{N} \ ...(1)$$ $$V(x)=NP(1-P) \ ...(2)$$
Substitute $(1)$ in $(2)$,
$$N \times \frac{2}{N} (1-\frac{2}{N})=1 \\ \implies 2N-4=N \\ \boxed{\therefore N=4}$$


2. Given,
$$Number \ of \ black \ balls, \ \ n(B)=5 \\ Number \ of \ red \ balls, \ \ n(R)=3 \\ Total \ number \ of \ balls, \ \ n(T)=5+3=8 \\$$ $$\implies Pr(Both \ balls \ being \ black) \\ = \frac{n(B)}{n(T)} \times \frac{n(B-1)}{n(T-1)} \\ = \frac{5}{8} \times \frac{4}{7} \\ \boxed{\therefore Pr(BB)=\frac{5}{14}}$$

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