Objective Questions On Class 11 Maths Chapter 8 Binomial Theorem

(1) The fourth term in the expansion (x - 2y)¹² is

[A] -1670 x⁹ * y³

[B] -7160 x⁹ * y³

[C] -1760 x⁹ * y³

[D] -1607 x⁹ * y³

Answer: -1760 x⁹ * y³

(2) The smallest positive integer for which the statement 3ⁿ⁺¹ < 4ⁿ is true for all

[A] 4

[B] 3

[C] 1

[D] 2

Answer: 4

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(3) If the sum of the coefficients in the expansion of (a + b)n is 4096, then the greatest coefficient in the expansion is

[A] 924

[B] 792

[C] 1594

[D] None of these

Answer: 924

(4) The greatest coefficient in the expansion of (1 + x)¹⁰ is

[A] 10!/(5!)

[B] 10!/(5!)²

[C] 10!/(5! * 4!)²

[D] 10!/(5! * 4!)

Answer: 10!/(5!)²

(5) The value of ∑(3^r * ⁿ_{C_r ) where 0 ≤ r ≤ 4}

[A] 2n

[B] 3n

[C] 4n

[D] 5n

Answer: 4n

(6) The general term of the expansion (a + b)ⁿ is

[A] T_r+1 = ⁿC_r * a^r * b^r

[B] T_r+1 = ⁿC_r * a^r * b^n-r

[C] T_r+1 = ⁿC_r * a^n-r * b^n-r

[D] T_r+1 = ⁿC_r * a^n-r * b^r

Answer: T_r+1 = ⁿC_r * a^n-r * b^r

(7) The value of 1/81ⁿ - (10/81ⁿ ) * ²ⁿC₁ + (10² /81ⁿ ) * ²ⁿC₂ - (10³ /81ⁿ ) * ²ⁿC₃ + ....... + 10²ⁿ /81ⁿ is

[A] 2

[B] 0

[C] 1/2

[D] 1

Answer: 1

(8) If n is positive integer, then (√3+1)²ⁿ−(√3−1)²ⁿ is

[A] an irrational number

[B] an odd positive integer

[C] none of these

[D] a rational number

Answer: an irrational number

(9) If the fourth term in the expansion (ax + 1/x)ⁿ is 5/2, then the value of x is

[A] 4

[B] 6

[C] 8

[D] 5

Answer: 6

(10) The sum of the coefficient of the polynomial (1 + x - 3x² )²¹⁴³ is

[A] -1

[B] 1

[C] 0

[D] None of these

Answer: -1

(11) Which one the following is the common factor of (47⁴³ + 43⁴³ ) and (47⁴⁷ + 43⁴⁷ )

[A] 47 - 43

[B] 47 + 43

[C] (47⁴³ + 43⁴³ )

[D] (47⁴⁷ + 43⁴⁷ )

Answer: 47 + 43

(12) If n is a positive integer, then (3 + √i)ⁿ+(3 -√i)ⁿ is

[A] a non real number

[B] a positive real number

[C] a real number

[D] none of these

Answer: a non real number

(13) The coefficient of y in the expansion of (y² + c/y)⁵ is

[A] 29c

[B] 10c

[C] 10c³

[D] 20c²

Answer: 10c³

(14) The number 111111…………..1 (91 times) is

[A] not an odd number

[B] none of these

[C] not a prime

[D] an even number

Answer: not a prime

(15) The remainder when (17)²⁰⁰ is divided by 18 is

[A] 0

[B] 1

[C] 2

[D] 17

Answer: 1

(16) The value of 1/81ⁿ - (10/81ⁿ ) * ²ⁿC₁ + (10² /81ⁿ ) * ²ⁿC₂ - (10³ /81ⁿ ) * ²ⁿC₃ + ....... + 10²ⁿ /81ⁿ is

[A] 2

[B] 0

[C] 1/2

[D] 1

Answer: 4

(17) The coefficient of a^-6 b⁴ in the expansion (1/a - 2b/3)¹⁰ is

[A] 1102/27

[B] 1120/72

[C] 1120/27

[D] 1120/37

Answer: 1120/27

(18) The term independent of x in (√x - 2/x)¹⁸ is

[A] ¹⁸C₄ * 2⁴

[B] ¹⁸C₅ * 2⁵

[C] ¹⁸C₆ * 2⁶

[D] None of these

Answer: ¹⁸C₆ * 2⁶

(19) The number (101)¹⁰⁰ - 1 is divisible by

[A] 100

[B] 1000

[C] 10000

[D] All the above

Answer: All the above

(20) The coefficient of a⁴ * b⁵ in the expansion of (a + b)⁹ is

[A] ⁹C₄

[B] ⁹C₃

[C] ⁸C₄

[D] ⁸C₃

Answer: ⁹C₄

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