Day 180: NDA Maths

5 questions. Try each one first, then open its answer.

Question 1
Matrices & Determinants. Asked once: NDA 2 2019 (same type asked 4 times)
14 $A = \begin{pmatrix} 1 & -1 \\ -1 & 1 \end{pmatrix}$
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Question 2
Permutation & Combination. Asked once: NDA 1 2022 (same type asked 4 times)
16 $How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even positions?$
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Question 3
Probability. Asked once: NDA 2 2017 (same type asked 4 times)
101 $A committee of two persons is selected from two men and two women. The probability that the committee will have exactly one woman is$
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Question 4
Quadratic Equations. Asked once: NDA 2 2021 (same type asked 4 times)
45 $4x^{2}-(5k+1)x+5k=0$
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Question 5
Statistics. Asked once: NDA 2 2019 (same type asked 4 times)
116 $Mean of 100 observations is 50 and standard deviation is 10. If 5 is added to each observation, then what will be the new mean and new standard deviation respectively ?$
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Question 1