NDA II 2022 Mathematics Previous Year Paper (04-Sep-2022)

Question 1

How many four-digit natural numbers are there such that all of the digits are odd ?

Accepted Answer

625

Answer

400

Answer

196

Answer

120

Question 2

What is $\displaystyle\sum_{r=0}^n$ 2 r  C(n, r) equal to ?

Accepted Answer

3 n

Answer

2 n

Answer

2 2n

Answer

3 2n

Question 3

If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) are there in the list before the first word that starts with C ?

Accepted Answer

907200

Answer

302400

Answer

403600

Answer

1814400

Question 4

Consider the following statements :1. If f is the subset of Z &times; Z defined by f = {(xy, x &minus; y); x, y &isin; Z}, then f is a function from Z to Z.2. If f is the subset of N &times; N defined by f = {(xy, x + y); x, y &isin; N}, then f is a function from N to N.Which of the statements given above is/are correct?

Accepted Answer

Neither 1 nor 2

Answer

1 only

Answer

2 only

Answer

Both 1 and 2

Question 5

Consider the determinant&Delta; = $\left|\begin{array}{lll}\text{a}_{11} & \text{a}_{12} & \text{a}_{13} \ \text{a}_{21} & \text{a}_{22} & \text{a}_{23} \ \text{a}_{31} & \text{a}_{32} & \text{a}_{33}\end{array}\right|$If a 13  = yz, a 23  = zx, a 33  = xy and the minors of a 13 , a 23 , a 33  are respectively (z &minus; y), (z &minus; x), (y &minus; x) then what is the value of &Delta; ?

Accepted Answer

(z &minus; y) (z &minus; x) (y &minus; x)

Answer

(x &minus; y) (y &minus; z) (x &minus; z)

Answer

(x &minus; y) (z &minus; x) (y &minus; z) (x + y + z)

Answer

(xy + yz + zx) (x + y + z)

NDA II 2022 Mathematics Previous Year Paper (04-Sep-2022)

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