Worksheets Class 11 Mathematics Principle of Mathematical Induction

Students should refer to Worksheets Class 11 Mathematics Principle of Mathematical Induction Chapter 4 provided below with important questions and answers. These important questions with solutions for Chapter 4 Principle of Mathematical Induction have been prepared by expert teachers for Class 11 Mathematics based on the expected pattern of questions in the class 11 exams. We have provided Worksheets for Class 11 Mathematics for all chapters on our website. You should carefully learn all the important examinations questions provided below as they will help you to get better marks in your class tests and exams.

Principle of Mathematical Induction Worksheets Class 11 Mathematics

Question. If the 4th term in the expansion of (px+x-1)m is 2.5 for all x∈R then:         
(a) p = 5 / 2,m = 3
(b) p = 1/2, m= 6
(c) p = -1/2, m= 6
(d) None of these

Question. The coefficient of x32 in the expansion of (x⁴−1/x3)¹⁵ is         
(a) ¹⁵C₅
(b) ¹⁵C₆
(c) ¹⁵C₄
(d) ¹⁵C₇

Question. Let R (5√5 + 11) ²ⁿ⁺¹ and f = R − [R] where [.] denotes the greatest integer function. The value of R.f is:         
(a) 4²ⁿ⁺¹
(b) 42n
(c) 4^2n–1
(d) 4^-2n

Question. If in the expansion of (1 + x)m (1 − x)n , the coefficient of x and x² are 3 and – 6 respectively, then m is:         
(a) 6
(b) 9
(c) 12
(d) 24

Question. If T₂/T₃ in the expansion of (a + b)n and T₃/T₄ in the expansion of 3 (a+b) are equal, then n = ?        
(a) 3
(b) 4
(c) 5
(d) 6

Question. The term independent of x in the expansion of (1+x)ⁿ (1+1/x)ⁿ is:         
(a) C₀² +2C₁² +…..+(n+1)C_n²
(b) (C₀ + C₁+…….+C_n)²
(c) C₀² +2C₁² +…..+C_n²
(d) None of these

Question. 

Question. The sum to (n +1) terms of the following series C₀/2+C₁/3+C₂/4 +C₃/5 +…..is         
(a) 1/n+1
(b) 1/n+2
(c) 1/(n+1)
(d) None of these

Question. The coefficient of xn in the expansion of (1 + x) (1 – x)ⁿ is:         
(a) 1 (-1)ⁿ⁻¹
(b) (1)ⁿ(1-n)
(c) (-1)^n-1(n-1)²
(d) (n −1)

Question. 6th term in expansion of (2x²–1/3x²)10 is:         
(a) 4580/17
(b) –896/27
(c) 5580/17
(d) None of these

Question. If n is an integer greater than 1, then a−nC₁(a-1)+ⁿC₂(a-2) +………+ (-1)ⁿ(a-n)=?     
(a) a
(b)0
(c)a²
(d)2ⁿ

Question. If the sum of the coefficients in the expansion of (α²x² − 2αx +1)⁵¹ vanishes, then the value of α is:         
(a) 2
(b) –1
(c) 1
(d) – 2

Question. If the coefficients of rth term and (r + 4)th term are equal in the expansion of (1+ x)²⁰ , then the value of r will be:         
(a) 7
(b) 8
(c) 9
(d) 10

Question. If the expansion of (y²+C/y) the coefficient of y will be:         
(a) 20c
(b)10c
(c) 10c³
(d) 20c²

Question.

(a) 2n/n+1
(b) 2ⁿ–1/n+1
(c) 2ⁿ⁺¹–1/n+1
(d) None of these

Question. In the expansion of (x/2−3/x²)10 the coefficient of x4 is:         
(a) 405/256
(b) 504/259
(c) 450/263
(d) None of these

Question. The term independent of x in the expansion of

(a) 3/2
(b) 5/4
(c) 5/2
(d) 2/3

Question. The coefficient of 7 x in the expansion of (x²/2−2/x)¹⁰ is:         
(a) – 56
(b) 56
(c) – 14
(d) 14

Question. If coefficients of 2nd, 3rd and 4th terms in the binomial expansion of (1 + x)ⁿ are in (a)P., then n² − 9ⁿ is equal to:         
(a) – 7
(b) 7
(c) 14
(d) – 14

Question. The number of integral terms in the expansion of  (√3 +³√5)²⁵⁶ is:         
(a) 32
(b) 33
(c) 34
(d) 35

Question. The coefficient of x³⁹ in the expansion of (x⁴−1/x³)¹⁵ is:         
(a) – 455
(b) – 105
(c) 105
(d) 455

Question. Coefficient of xr in the expansion of (1–2x)^-1/2 ?

Question. If x is so small that its two and higher power can be neglected and (1–2x)^–1/2 (1–4x)^–5/2 =1+ kx then k = ?         
(a) 1
(b) –2
(c) 10
(d) 11

Question. The smallest positive integer n, for which n!(n+1/2)n hold is:             
(a) 1
(b) 2
(c) 3
(d) 4

Question. The fourth term in the expansion of (1–2x)^3/2 will be:       

Question. The expansion of 1/(4x–3x)1/2 binomial theorem will be valid, if:         
a. x <1
b. | x |< 1
c. -2/√3 < x < 2/√3 
d. None of these

Question. The value of c₀2 + 3c12 + ⁵c22 + …. to (n +1 terms (given that Cr ≡ ⁿCr) is:         

Question. The number of distinct terms in the expansion of (x + 2y − 3z + 5w− u)u is:       
a. n+1
b. ⁿ⁺⁴C₄
c. ⁿ⁺⁴C_n
d. (n+1)(n+2)(n+3)(n+4)/24   

Question. Let 2 S(k) = 1+ 3+ 5 +…+ (2k −1) = 3+ k . Then which of the following is true:         
(a) Principle of mathematical induction can be used to prove the formula
(b) S(k)⇒ S(k + 1)
(c) S(k)⇒/ S(k +1)
(d) S(1) is correct

Question. The expression

 is a polynomial of degree:   
a. ⁹C₂
b. ⁷C₈
c. 7
d. ⁸C₁

Question. The coefficient of the middle term in the expansion of (1+x)²ⁿ is:     
a. ²ⁿC_n
b. 1.3.5..(2n-1).2n/n!
c. 2⋅6…(4n − 2)
d. none of the above

Question. The approximate value of (7.995)^1/3 correct to four decimal places is:         
a.1.9995
b.1.9996
c.1.9990
d.1.9991

Question.

is equal to:       
a. x
b. (1+x)^1/3
c. (1−x)^1/3
d. (1+x)^-1/3

Question. The last digit of 3³⁴ⁿ + 1,n∈N is:       
a. ⁴C₃
b. ⁸C₇
c. 8
d. 4

Paragraph

If m, n, r are positive integers and if r <m, r < n then

Question. The value of  nC₀ + nC_n+nC_1.nC_n-1+…….+ ⁿC_{n .}ⁿC₀ is:       
a. ²ⁿC_n-1
b. ²ⁿC_n
c. ²ⁿC_n+1
d. ²ⁿC₂

Question. The value of r for which ³⁰Cr . ²⁰Cr + ³⁰Cr-1 . ²⁰C1+….+³⁰C0 . ²⁰Cr is maximum, is:       
a. 10
b. 15
c. 20
d. 25

Question. The value of r(0 ≤ r ≤ 30)for which ²⁰Cr + ¹⁰C_r-1 . ²⁰C₀ + ²⁰C_r-1 . ¹⁰C₁ + ………..+ ²⁰C₀ . ¹⁰C_r is minimum, is:         
a. 0
b. 1
c. 5
d. 15

Question. If Sn =   nC₀ + ⁿC₁+ⁿC_1.nC2 +……..+ ⁿC_n-1 .ⁿC_n and if S_n+1/S_n = 15/4. then n equals:     
a. 2, 4
b. 4, 6
c. 6, 8
d. 8, 10

Question. If (1+x)n = C₀+C₁x+C₂x²+…..+C_nxⁿ and n is odd, then the value of C₀²–C₁² = C₂² –C₃² +…….+ (-1)ⁿC_n² is :       
a. 0
b. ²ⁿC_n
c. c. (–1)ⁿ²ⁿC_n-1
d. d. 3²ⁿC_n-2 d

Assertion and Reason
Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:
a. If both assertion and reason are true and the reason is the correct explanation of the assertion.
b. If both assertion and reason are true but reason is not the correct explanation of the assertion.
c. If assertion is true but reason is false.
d. If the assertion and reason both are false.
e. If assertion is false but reason is true.

Question. Assertion: Greatest term in the expansion of (√3+√2)⁵⁰ is (50  20) 3¹⁴2¹¹     
Reason: Greatest term in the expansion (1+x)ⁿ ,x > 0 of is the rth term if (n+1)x/x+1 is not an integer and [(n+1)x/x+1 ] where [y] denotes the greatest integer ≤y.

Question. Let (1+x)n = C₀ + C₁x+C₂x²+….C_nxⁿ

Question. Assertion: The coefficient of the term of independent of x in the expansion of

 Reason: The coefficient of xr in the expansion of (1+x)n is (n r).

Question. Assertion: For any positive integers m, n (with n ≥ m), 

Reason: Coefficient of xr in the expansion of (1+x)ⁿ is (n r).

Question. Let (1+x)ⁿ = C₀ +C₁x+C₂x²+….+C_nxⁿ.         
Assertion: 5C₀²+7C₁²₊₉C₂²+…

Reason: C₀²+C₁²+…+C_n²=²ⁿC_n

Match the Column

Question. Observe the following columns:

a. A→1, B→2→5, C→3-4
b. A→1, B→3-5, C→2-4
c. A→2, B→4-5, C→3-1
d. A→2, B→1-4, C→3-5

Question. Observe the following columns:  

a. A→2-3, B→1-3-5, C→4
b. A→1-3, B→2-3-4, C→5
c. A→1-3, B→2-3-4, C→5
d. A→4-3, B→1-3-5, C→2

Question. Observe the following columns: 

 

Question. The coefficient of x50 in the polynomials after parenthesis have been removed and like terms have been collected in the expansion.       
(1+ x)1000 + x(1+ x)999 + x2(1+ x)998 is λ/μv! then the value of λ + 2μ+3v must be (v > μ ) ?

Question. If (1+x)ⁿ = C0+C₁x+C₂x²+…….+C_nxⁿ and

Question. If