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Social Media – New Rules & implications: RSTV – Big Picture

Rajya Sabha TV programs and discussions are very insightful and informative from a UPSC perspective. In this article, we provide a gist of the... View Article

27 May 2021: UPSC Exam Comprehensive News Analysis

CNA 27 May 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY AND GOVERNANCE 1. WhatsApp approaches Delhi HC to... View Article

Operation Trident

Operation Trident was an offensive operation carried out by the Indian Navy on 4–5 December 1971 against the Pakistani port city of Karachi.... View Article

The coefficients of x in the expansion of (1 + x) (1 + 2x) (1 + 3x)…(1 + 100x) is

1) 5050 2) 10100 3) 5151 4) 4950 5) 1100 Solution: (1) 5050 The coefficients in the expansion of (1 + x) (1 + 2x) (1 + 3x) …. (1 + 100x) is... View Article

The two consecutive terms in the expansion of (3 + 2x)⁷⁴ whose coefficients are equal, are

1) 11, 12 2) 7, 8 3) 30, 31 4) None of the above Solution: (3) 30, 31... View Article

If (1 + 2x + x²)² = ∑_k=0¹⁵ a_kx^k, then ∑_k=0⁷ a_2k =

1) 128 2) 256 3) 512 4) 1024 Solution: (3) 512... View Article

If x^2r occurs [x + (2 / x²)]ⁿ, then n – 2r must be of the form

1) 3k – 1 2) 3k 3) 3k + 1 4) 3k + 2 Solution: (2) 3k... View Article

If the coefficient of x² and x³ in the expansion of (3 + ax)⁹ is the same, then the value of a is

1) 3/7 2) 7/3 3) 7/9 4) 9/7 Solution: (4) 9/7... View Article

If in the expansion of (1 + x)^m (1 – x)ⁿ, the coefficients of x and x² are 3 and – 6 respectively, then m is

1) 6 2) 9 3) 12 4) 24 Solution: (3) 12... View Article

Let [x] denotes the greatest integer less than or equal of x. If x = (√3 + 1)⁵, then [x] is equal to

1) 75 2) 50 3) 76 4) 51 5) 152 Solution: (5) 152... View Article

The total number of terms in the expansion of (x + y)¹⁰⁰ + (x – y)¹⁰⁰ after simplification is

1) 51 2) 202 3) 100 4) 50 Solution: (1) 51 If x and y are real numbers, then for all n belongs to N,... View Article

Sum of infinite series 1 + (2 / 3) (1 / 2) + (2 / 3) (5 / 6) (1 / 2²) + …… ∞ is

1) 21/3 2) 41/3 3) 81/3 4) 21/5 Solution: (2) 41/3... View Article

7⁹ + 9⁷ is divided by

1) 128 2) 24 3) 64 4) 72 Solution: (3) 64... View Article

The remainder left out when 8²ⁿ – (62)²ⁿ⁺¹ is divided by 9, is

1) 0 2) 2 3) 7 4) 8 Solution: (2) 2... View Article

If in the expansion of (a – 2b)ⁿ, the same of 5th and 6th terms is zero, then the value of a/b is

1) (n – 4)/ 5 2) 2(n – 4)/5 3) 5/(n – 4) 4) 5/2(n – 4) Solution: (2) 2(n – 4)/5... View Article

The coefficient of pⁿqⁿ in the expansion of [(1 + p) (1 + q) (p + q)]ⁿ is

1) ∑k=0n [C (n, k)]2 2) ∑k=0n [C (n, k + 2)]2 3) ∑k=0n [C (n, k + 3)]2 4) ∑k=0n [C (n, k)]3 Solution: (4) ∑k=0n [C (n, k)]3 Using principle... View Article

5th term from the end in the expansion of [(x³ / 2) – (2 / x²)]¹² is

1) - 7920 x- 4 2) 7920 x4 3) 7920 x- 4 4) - 7920 x4 Solution: (3) 7920 x- 4 5th term from the end = (12 – 5 + 2)th term from the beginning =... View Article

In the expansion of (x³ – 1 / x²)ⁿ, n ∈ N, if the sum of the coefficients of x⁵ and x¹⁰ is 0, then n is equal to

1) 25 2) 20 3) 15 4) None of these Solution: (3) 15... View Article

If A and B are coefficients of xⁿ in the expansion of (1 + x)²ⁿ and (1 + x)^{2n – 1} respectively, then A/B is equal

1) 4 2) 2 3) 9 4) 6 Solution: (2) 2... View Article

If (1 + ax)ⁿ = 1 + 6x + (27 / 2) x² + aⁿxⁿ, then the values of a and n are respectively

1) 2 , 3 2) 3 , 2 3) 3/2 , 4 4) 1 , 6 5) 3/2 , 6 Solution: (3) 3/2 , 4... View Article