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Mathematics Exam  >  Mathematics Tests  >  Topic-wise Tests & Solved Examples for Mathematics  >  Test: Binomial Theorem - 5 - Mathematics MCQ

Test: Binomial Theorem - 5 - Mathematics MCQ


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Test: Binomial Theorem - 5

Test: Binomial Theorem - 5 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Test: Binomial Theorem - 5 questions and answers have been prepared according to the Mathematics exam syllabus.The Test: Binomial Theorem - 5 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Binomial Theorem - 5 below.
Solutions of Test: Binomial Theorem - 5 questions in English are available as part of our Topic-wise Tests & Solved Examples for Mathematics for Mathematics & Test: Binomial Theorem - 5 solutions in Hindi for Topic-wise Tests & Solved Examples for Mathematics course. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free. Attempt Test: Binomial Theorem - 5 | 20 questions in 60 minutes | Mock test for Mathematics preparation | Free important questions MCQ to study Topic-wise Tests & Solved Examples for Mathematics for Mathematics Exam | Download free PDF with solutions
Test: Binomial Theorem - 5 - Question 1
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The coefficient of x12 in the expansion of (1 + 2x2- x3)8 is

Test: Binomial Theorem - 5 - Question 2
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Test: Binomial Theorem - 5 - Question 3
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The value of 

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Test: Binomial Theorem - 5 - Question 4
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Coefficient of x11 in the expansion of (1 + x2)4 (1 + x3)7 (1 + x4)12 is
Test: Binomial Theorem - 5 - Question 5
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The number of irrational terms in the expansion of (21/5 + 31/10)55 is
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(21/5 + 31/10)55 Total terms = 55 + 1 = 56 

Here  r = 0, 10, 20, 30, 40, 50
Number of  rational terms = 6;  
Number of irrational terms = 56 - 6 = 50

Test: Binomial Theorem - 5 - Question 6
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In the expansion of the coefficient of x-10 will be 
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Given expansion is 
∴ General term 
Since, we have to find coefficient of x-10
∴ -12 + 2r = -10  ⇒ r = 1
Now, then coefficient of x -10 is 12C1(a)11(b)1 = 12a11b

Test: Binomial Theorem - 5 - Question 7
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The middle term in the expansion of (1 – 2x + x2)n is 
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Here 2n is even integer, therefore,  term will be the middle term.

Test: Binomial Theorem - 5 - Question 8
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Replacing x by -x, 
Subtracting and putting 

Test: Binomial Theorem - 5 - Question 9
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(103)86 - (86)103 is divisible by 
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Given expression

Test: Binomial Theorem - 5 - Question 10
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The number of dissimilar terms in the expansion of (a + b + c)2n+1 – (a + b – c)2n+1 is 
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Given expansion 

Number of dissimilar term = (2n + 1) + (2n -1) + ....(2n - 3) + .... + 5 + 3 + 1

Test: Binomial Theorem - 5 - Question 11
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The fourth and fifth term of a sequence {tn}n≥1 are 4 and 5 respectively and the nth term is given as tn = 2tn-1 - tn-2, n > 3 (n ∈ N). Then the sum to first 2009 terms is 
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Thus {an} is a constant sequence  
a5 = t5 − t4 = 1  
Now a4 = t4 − t3 ⇒ 1 = 4 − t3 ⇒ t3 = 3
Similarly t2 = 2 , t1 = 1
Thus {tn} is an A.P with r = 1 and common difference 1 

Test: Binomial Theorem - 5 - Question 12
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 where tr denotes the rth term of a series, then 
Test: Binomial Theorem - 5 - Question 13
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 where a, b, c are in AP and | a | < 1, | b | < 1, | c | < 1, then x, y, z are in 
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Test: Binomial Theorem - 5 - Question 14
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Test: Binomial Theorem - 5 - Question 15
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Sum to 20 terms of the series 1.32 + 2.52 + 3.72 + ... is  
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We have, tn = [nth term of 1, 2, 3, ... ] × [nth term of 3, 5, 7, ... ]2

Test: Binomial Theorem - 5 - Question 16
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Sum up to 16 terms of the series 
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Test: Binomial Theorem - 5 - Question 17
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The value of n terms is equal to  
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Test: Binomial Theorem - 5 - Question 18
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The sum of the series  upto n terms 
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Test: Binomial Theorem - 5 - Question 19
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Test: Binomial Theorem - 5 - Question 20
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