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Mathematics Exam  >  Mathematics Tests  >  Topic-wise Tests & Solved Examples for Mathematics  >  Test: Binomial Theorem - 4 - Mathematics MCQ

Test: Binomial Theorem - 4 - Mathematics MCQ


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Test: Binomial Theorem - 4

Test: Binomial Theorem - 4 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Test: Binomial Theorem - 4 questions and answers have been prepared according to the Mathematics exam syllabus.The Test: Binomial Theorem - 4 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Binomial Theorem - 4 below.
Solutions of Test: Binomial Theorem - 4 questions in English are available as part of our Topic-wise Tests & Solved Examples for Mathematics for Mathematics & Test: Binomial Theorem - 4 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 - 4 | 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 - 4 - Question 1
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Coefficient of x5 in the expansion of 

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= Coefficient of x25 in (1 + x)30

Test: Binomial Theorem - 4 - Question 2
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The coefficients of 9th, 10th and 11th terms in the expansion of (1 + x)n are in A.P. then n =

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(n - 2r)2 = n + 2

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Test: Binomial Theorem - 4 - Question 3
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Coefficient of x4 in (1 + x – 2x2)6 is

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Factorise and expand

Test: Binomial Theorem - 4 - Question 4
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Test: Binomial Theorem - 4 - Question 5
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Test: Binomial Theorem - 4 - Question 6
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The sum of the coefficient of even powers of x in the expansion (1 - x + x2 - x3)5 is
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Test: Binomial Theorem - 4 - Question 7
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The number of terms in the expansion of [a + 4b)3 + (a + 4b)3]2 are
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Test: Binomial Theorem - 4 - Question 8
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then a1 - 2a2 + 3a3 - ... - 2na2n = ....
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Differentiate above and put x = -1

Test: Binomial Theorem - 4 - Question 9
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The sum of the binomial coefficients of the 3rd, 4th terms from the beginning and from the end of (a + x)n is 440 then n =
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Test: Binomial Theorem - 4 - Question 10
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Let  f = R - [R], then Rf = 
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Test: Binomial Theorem - 4 - Question 11
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If  = I + F when I is  odd and 0 < F < 1, then (I + F) (I - F) =
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Test: Binomial Theorem - 4 - Question 12
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The expansion [x + (x3 - 1)1/2]5 + [x + (x3 - 1)1/2]5 is a polynomial of degree
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Expand using the formula 

Test: Binomial Theorem - 4 - Question 13
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If t0, t1, t2, ............tn are the consecutive terms in the expansion (x + a)n then (t0 - t2 + t4 - t6 +...)2 + (t1 - t3 + t5....)2 = 
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Expand (x + ai)n and (x – ai)n then multiply.

Test: Binomial Theorem - 4 - Question 14
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Coefficient of x50 in (1 + x)1000 + 2x(1 + x)999 + 3x(1 + x)998 + .....is
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Take (1 + x)1000 as common, after simplification it becomes (1 + x)1000 coefficient of x50 is 1002C50

Test: Binomial Theorem - 4 - Question 15
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The coefficient of x9 in (x + 2) (x + 4) (x + 8).....(x + 1024) is
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2 + 4 + 8 + …..1024

Test: Binomial Theorem - 4 - Question 16
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The coefficient of xn in the polynomial (x + nC0) (x + 3.nC1) (x + 5.n C2)...  [x + (2n + 1).nCn] is
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Coefficient of

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If x = (2 + √3)n, n ∈ N and f = x - [x], then 
Test: Binomial Theorem - 4 - Question 18
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If 22006 - 2006 divided by 7, the remainder is
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22006 = 4(8)668 = 4 (7 +1)668  leaves remainder 4
2006 = 7 x 268 + 4 leaves remainder
∴ 22006 - 2006 leaves remainder 0.

Test: Binomial Theorem - 4 - Question 19
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The number of rational terms in the expansion of 
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Use multinomial theorem.
General term of given expansion is

Test: Binomial Theorem - 4 - Question 20
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The coefficient of the term independent of x in the expansion of 
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We

for this term to be independent of x. we must have

So, the required coefficient is
10C4(-1)4 = 210

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