Mathematics (NDA/NA SOLVED PAPER 2022-II) (01 to 50)

Total Questions: 50

21. If d is the common difference of A, and D is the common difference of B, then which one of the following is always correct?

Let P be the sum of first n positive terms of an increasing arithmetic progression A. Let Q be the sum of first n positive terms of another increasing arithmetic progression B.
Let P : Q = (5n+4): (9n+6)

Correct Answer: (c) 7D > 12d
Solution:(c)

22. What is the value of q if the coefficients of x³ and x⁶ are equal?

Consider the binomial expansion of (p + qx)⁹ :

Correct Answer: (a) p
Solution:

23. What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x)?

Consider the binomial expansion of (p + qx)⁹ :

Correct Answer: (b) p/q
Solution:

24. Under what condition the coefficients of x² and x⁴ are equal?

Consider the binomial expansion of (p + qx)⁹ :

Correct Answer: (b) p² : q = 7 : 2
Solution:Coefficient of x² = coefficient of x⁴
⁹C₂ p⁷ q² = ⁹C₄ p⁵ q⁴ .
9.8/2.1 p² = 9.8.7.6/ 4.3.2.1 q²
p²/q² = 7/2

25. How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed?

Consider the word 'QUESTION' :

Correct Answer: (d) 864
Solution:Number of words contains two vowels and two consonants
= ⁴C₂ . ⁴C₂ × 4!
= 6 . 6 . 24 = 864

26. How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?

Consider the word 'QUESTION' :

Correct Answer: (c) 1152
Solution:C V C V C V / C V or VC VC VC VC
Number of 8 letter words such that vowels and consonants occupy alternate positions.
= 2 × 4! 4! = 2 × 24 × 24 = 1152

27. How many 8-letter words with or without meaning, can be formed so that all consonants are together?

Consider the word 'QUESTION' :

Correct Answer: (b) 2880
Solution:Number 8 letter words such that all consonants are together
= 4! 5! = 2880

28. What is the value of a₁₁ C₁₁ + a₁₂ C₁₂ + a₁₃ C₁₃

Correct Answer: (c) Δ
Solution:We know that
a₁₁ C₁₁ + a₁₂ C₁₂ + a₁₃ C₁₃= Δ

29. What is the value of a₂₁ C₁₁ + a₂₂ C₁₂ + a₂₃ C₁₃?

Correct Answer: (a) 0
Solution:We know that
a₂₁ C₁₁+ a₂₂ C₁₂ + a₂₃ C₁₃ = O

30. Find the value?

Correct Answer: (d) - Δ
Solution: