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28 May 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 28th May 2021. Important news and views to boost... View Article

Making Medical Education Affordable: 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

National Project on Aquifer Management (NAQUIM)

The National Project on Aquifer Management (NAQUIM) is an initiative of the Ministry of Jal Shakti, GOI for the mapping and management of all the... View Article

Gist of EPW May Week 4, 2021

The Economic and Political Weekly (EPW) is an important source of study material for IAS, especially for the current affairs segment. In this... View Article

28 May 2021: UPSC Exam Comprehensive News Analysis

CNA 28 May 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related INTERNATIONAL RELATIONS 1. U.S.-China engagement era has... View Article

Gist of EPW May Week 3, 2021

The Economic and Political Weekly (EPW) is an important source of study material for IAS, especially for the current affairs segment. In this... View Article

27 May 2021: PIB Summary & Analysis

May 27th, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. National Digital Health Mission 2. Ayush Ministry 1. National Digital Health... View Article

The 13th term in the expansion of [x² + (2 / x)]ⁿ is independent of x. Then the sum of the divisors of n is

1) 36 2) 37 3) 38 4) 39 Solution: (4) 39... View Article

In the binomial expansion of (a – b)ⁿ, n ≥ 5, the sum of the 5th and 6th terms is 0. Then a / b =

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

Middle term in the expansion [x² + (1 / x²) + 2]ⁿ is

1) n!/(n!)2 2) (2n)!/(n!)2 3) (2n - n)!/n! 4) (2n)!/n! Solution: (2) (2n)!/(n!)2... View Article

If the term from x in the expansion of [√x – (k / x²)]¹⁰ is 405, then the value of k is

1) ± 1 2) ± 3 3) ± 4 4) ± 2 Solution: (2) ± 3... View Article

If (1 + x)¹⁵ = a₀ + a₁x +…+ a₁₅ x¹⁵, then ∑_r=1¹⁵ r (a_r / a_r – 1) is

1) 110 2) 115 3) 120 4) 135 Solution: (3) 120... View Article

If x = then √x – (1 / √x) =

1) 0.2 2) 4.8 3) 1.02 4) 5.2 Solution: (4) 5.2... View Article

If |x| < 1 / 2, then the coefficient of x^r in the expansion of [1 + 2x] / [1 – 2x]² is

1) r2r 2) (2r - 1)2r 3) r22r+1 4) (2r + 1)2r Solution: (4) (2r + 1)2r... View Article

The coefficient of x² in the binomial expansion of [(1 / 3) x^1/2 + (x^-¼)]¹⁰ is

1) 70/243 2) 60/423 3) 50/13 4) None of these Solution: (1) 70/243... View Article

If in the expansion of (1 + x)²¹, the coefficients of x^r and x^r+1 are equal, then r is equal to

1) 9 2) 10 3) 11 4) 12 Solution: (2) 10 Given the coefficients of xr and xr+1are equal, 21Cr = 21Cr+1 If nC5 = nCk then s + k = n or s = k... View Article

For all integers n ≥ 1, which of the following is divisible by 9?

1) 8n + 1 2) 4n – 3n – 1 3) 32n + 3n + 1 4) 10n + 1 Solution: (2) 4n – 3n – 1... View Article

The digit at the unit place in the number 19²⁰⁰⁵ + 11²⁰⁰⁵ – 9²⁰⁰⁵ is

1) 2 2) 1 3) 0 4) 8 5) 9 Solution: (2) 1... View Article

Coefficient of x¹⁹ in the polynomial (x – 1) (x – 2)…(x – 20) is equal to

1) 210 2) –210 3) 20! 4) None of these Solution: (2) –210... View Article

The coefficient of x¹⁰⁰ in the expression of ∑_j=0²⁰⁰ (1 + x)^j is

1) 200C100 2) 201C102 3) 200C101 4) 201C100 Solution: (2) 201C102... View Article