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If the second term, in the expression [latex][sqrt[13]{a}+frac{a}{sqrt{a^{-1}}}]^{n}[/latex] is 14a^5/2, then the value of ⁿC₃ / ⁿC₂ is

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

If the expression in powers of x of the function 1 / [(1 – ax) (1 – bx)] is a₀ + a₁x + a₂x² + a₃x³ + ….. then the coefficient of xⁿ in the expansion is

1) [an - bn] / (b - a) 2) [an+1 - bn+1] / (a - b) 3) [bn+1 - an+1] / (b - a) 4) [bn - an] / (b - a) Solution: (2) [an+1 - bn+1] / (a - b)... View Article

The expression {x + (x³ – 1)^1/2}⁵ + {x – (x³ – 1)^1/2}⁵ is a polynomial of degree

1) 5 2) 6 3) 7 4) 8 Solution: (3) 7... View Article

For 2 ≤ r ≤ n, ⁿC_r + 2 ⁿC_r+1 + ⁿC_r+2 =

1) n+1Cr-1 2) 2 n+1Cr+1 3) 2 n+2Cr 4) n+2Cr+2 Solution: (4) n+2Cr+2 nCr + nCr+1 + nCr+1 + nCr+2 = n+1Cr+1 + n+1Cr+2 = n+2Cr+2... View Article

In the expansion of (2 – 3x³)²⁰, if the ratio of 10th term to 11th term is 45/22, then x is equal to

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

The coefficient of x⁵ in the expansion of (1 + x²)⁵ (1 + x)⁴ is

1) 30 2) 60 3) 40 4) None of the these Solution: (2) 60... View Article

The larger of 99⁵⁰ + 100⁵⁰ and 101⁵⁰ is

1) 9950 + 10050 2) Both are equal 3) 10150 4) None of these Solution: (3) 10150... View Article

In the expansion of (1 + x + x² + x³)⁶, the coefficient of x¹⁴ is

1) 130 2) 120 3) 128 4) 125 5) 115 Solution: (2) 120... View Article

The ninth term of the expansion (3x – 1 / 2x)⁸ is

1) 1 / (512 x9) 2) (- 1 / 512 x9) 3) (- 1 / 256x8) 4) (1 / 256 x8) Solution: (4) (1 / 256 x8)... View Article

The coefficient of t²⁴ in the expansion of (1 + t²)¹² (1 + t¹²) (1 + t²⁴) is

1) 12C6 + 2 2) 12C5 3) 12C6 4) 12C7 Solution: (1) 12C6 + 2... View Article

The coefficient of xⁿ in the expansion of (1 + x) (1 – x)ⁿ is

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

The coefficient of x²⁰ in the expansion of (1 + 3x + 3x² + x³)²⁰ is

1) 60C40 2) 30C20 3) 15C2 4) None of these Solution: (1) 60C40 Rewrite the given expression as [(1 + x)3]20 = (1 + x)60 The coefficient of... View Article

The coefficient of x^r in the expansion of (1 + x)^-2 is

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

If ɑ = [5 / (2! 3)] + [5 . 7] / [3! 3²] + [5 . 7 . 9] / [4! 3³] + ….. then ɑ² + 4ɑ =

1) 21 2) 23 3) 25 4) 27 Solution: (2) 23... View Article

The coefficient of xⁿ in expansion of (1 + 2x + 3x² + …)^1/2 is

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

In the expansion of [x – (1 / x)]⁶, the coefficient of x⁰ is

1) 20 2) - 20 3) 30 4) - 30 Solution: (2) - 20... View Article

The coefficient of x^-10 in [x² – (1 / x³)]¹⁰ is

1) – 252 2) 210 3) – (5!) 4) – 120 Solution: (2) 210... View Article

Indian Renewable Energy Development Agency (IREDA)

Established in 1987, the Indian Renewable Energy Development Agency Limited (IREDA) is a Mini Ratna (Category – I) Government of India Enterprise... View Article

Goods and Services Tax Council

Goods & Services Tax Council (GST Council) is a constitutional body for making recommendations to the Union and State Government on issues... View Article

Role of Regional Parties in India

The presence of a large number of regional parties is an important feature of the Indian Political System. They have come to play a vital role in... View Article