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Rwandan Genocide

The Rwandan Genocide of 1994 was one of the worst genocides in human history. What led to this massacre of about a million people in the tiny... View Article

World Health Assembly – WHA

74th Session of World Health Assembly - WHA took place virtually from May 24th to June 1st 2021. Dr Harsh Vardhan, Union Minister for Health and... View Article

01 Jun 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 1st Jun 2021. Important news and views to boost... View Article

Bureau of Police Research and Development (BPR&D)

Established on August 28, 1970, the Bureau of Police Research and Development had replaced the Police Research and Advisory Council (1966) with... View Article

Banni Grassland Reserve

The Banni Grassland Reserve, (also known as Banni Grasslands) is a region consisting of an arid grassland system. They are located near the... View Article

The coefficient of x³ y⁴ z⁵ in the expansion of (xy + yz + xz)⁶ is

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

In the expansion of (1 + 3x + 2x²)⁶ is , the coefficient of x¹¹ is

1) 144 2) 288 3) 216 4) 576 5) 3 . 211 Solution: (4) 576... View Article

The number of terms in the expansion of (a + b + c)¹⁰ is

1) 11 2) 21 3) 55 4) 66 Solution: (4) 66... View Article

If a_k is the coefficient of x^k in the expansion of (1 + x + x²) for k = 0, 1, 2, … 2n then the value of ∑_k=1²ⁿ ka_k is

1) - a0 2) 3n 3) n . 3n+1 4) n . 3n Solution: (2) 3n... View Article

If (1 + 2x + 3x²)¹⁰ = a₀ + a₁ x + a₂x² + …+ a₂₀ x²⁰, then a₁ equals

1) 10 2) 20 3) 210 4) None of these Solution: (2) 20... View Article

²⁰C₄ + 2 . ²⁰C₃ + ²⁰C₂ – ²²C₁₈ is equal to

1) 0 2) 1242 3) 7315 4) 6345 Solution: (1) 0... View Article

If n is an integer greater than 1, then a – ⁿC₁ (a – 1) + ⁿC₂ (a – 2) + …+ (- 1)ⁿ (a – n) is equal to

1) a 2) 0 3) a2 4) 2n Solution: (2) 0... View Article

The sum of the coefficients in the expansion of (1 + x – 3x²)³¹⁴⁸ is

1) 8 2) 7 3) 1 4) - 1 Solution: (3) 1 Put x = 1 in the given expansion, the sum of the coefficients in that expansion. (1 + 1 -... View Article

If C₁, C₂, C₃ are the usual binomial coefficients and S = C₁ + 2C₂ + 3C₃ + …+ nC_n, then S equals

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

If the coefficient of rth, (r + 1)th and (r + 2)th term in the binomial expansion of (1 + y)^m are in AP, then m and r satisfy the equation

1) m2 – m(4r – 1) + 4r2 + 2 = 0 2) m2 - m(4r–1) + 4r2 – 2 = 0 3) m2 – m (4r + 1) + 4r2 - 2 = 0 4) m2 – n(4r – 1) + 4r2 – 2 = 0 Solution: (3)... View Article