Let S(k) = 1 + 3 + 5 + ...+ (2k -= 3 + k 2 . Then which of the following is true.

Principle of mathematical induction can be used to prove the formula

JEE Questions for Maths Binomial Theorem And Mathematical Lnduction Quiz 8

Maths-Binomial Theorem and Mathematical lnduction-11816.png

0%
0%
2)
0%
0%
None of these

Maths-Binomial Theorem and Mathematical lnduction-11821.png

0%
(2,12)
0%
(-2,12)
0%
(2,-12)
0%
None of these

Maths-Binomial Theorem and Mathematical lnduction-11823.png

0%
0%
2)
0%
0%

Maths-Binomial Theorem and Mathematical lnduction-11829.png

0%
4n
0%
4n – 3
0%
4n + 1
0%
None of these

Maths-Binomial Theorem and Mathematical lnduction-11831.png

0%
x > 1
0%
|x| > 1
0%
x < 1
0%
|x| < 1

Maths-Binomial Theorem and Mathematical lnduction-11833.png

0%
8
0%
32
0%
50
0%
None of these

If |x| > 1, then (1 + x)^-2

0%
0%
2)
0%
0%

Maths-Binomial Theorem and Mathematical lnduction-11840.png

0%
0%
2)
0%
0%
None of these

The first four terms in the expansion of (1 - x)^3/2 will be when |x| < 1

0%
0%
2)
0%
0%
None of the above

Maths-Binomial Theorem and Mathematical lnduction-11849.png

0%
5
0%
6
0%
7
0%
8

Maths-Binomial Theorem and Mathematical lnduction-11851.png

0%
n(n – 1)
0%
n(n + 1)
0%
n2
0%
(n + 1)2

Coefficient of x^r in the expansion of (1 – 2x)^–1/2 is

0%
0%
2)
0%
0%

The coefficient of xⁿ, where n is any positive integer, in the expansion of (1 + 2x + 3x² + ... ∞)^1/2 is

0%
1
0%
2)
0%
2n + 1
0%
n + 1

The coefficient of xⁿ in the expansion of (1 – 9x + 20x²)^–1 is

0%
5n – 4n
0%
5n + 1 – 4n + 1
0%
5n – 1 – 4n – 1
0%
None of these

Maths-Binomial Theorem and Mathematical lnduction-11861.png

0%
0%
2)
0%
0%
None of these

If x is positive , the first negative term in the expansion of (1 + x)^27/5 is

0%
7th term
0%
5th term
0%
8th term
0%
6th term

Maths-Binomial Theorem and Mathematical lnduction-11867.png

0%
0
0%
1/2
0%
-1/2
0%
1

Maths-Binomial Theorem and Mathematical lnduction-11869.png

0%
0%
2)
0%
0%

Maths-Binomial Theorem and Mathematical lnduction-11875.png

0%
21
0%
23
0%
25
0%
27

Maths-Binomial Theorem and Mathematical lnduction-11877.png

0%
3
0%
4
0%
5
0%
6

Maths-Binomial Theorem and Mathematical lnduction-11879.png

0%
0%
2)
0%
0%
None of these

Maths-Binomial Theorem and Mathematical lnduction-11884.png

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b0 = 1, b1 = 3
0%
b0 = 0, b1 = n
0%
b0 = –1, b1 = n
0%
b0 = 0, b1 = n2 – 3n + 3

Maths-Binomial Theorem and Mathematical lnduction-11886.png

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0%
2)
0%
0%

Maths-Binomial Theorem and Mathematical lnduction-11892.png

0%
0%
2)
0%
0%

Maths-Binomial Theorem and Mathematical lnduction-11898.png

0%
0%
2)
0%
0%
None of these

Maths-Binomial Theorem and Mathematical lnduction-11903.png

0%
0%
2)
0%
0%

The interval in which x must lie so that the numerically greatest term in the expansion of (1 – x)²¹ has the numerically greatest coefficient is

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0%
2)
0%
0%

Maths-Binomial Theorem and Mathematical lnduction-11914.png

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4
0%
3
0%
2
0%
1
0%
Both 3 and 4

Maths-Binomial Theorem and Mathematical lnduction-11916.png

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0%
2)
0%
0%

The coefficient of the middle term in the binomial expansion in powers of x of (1 + αx)⁴ and of (1 - αx)⁶ is the same if α equals

0%
0%
2)
0%
0%

If for positive integers r > 1, n > 2 the coefficient of the (3r)^th and (r + 2)^th powers of x in the expansion of (1 + x)²ⁿ are equal , then

0%
n = 2r
0%
n = 3r
0%
n = 2r + 1
0%
None of these

If the coefficient of the second, third and fourth terms in the expansion of (1 + x)ⁿ are in A.P., then n is equal to

0%
7
0%
2
0%
6
0%
None of these

Maths-Binomial Theorem and Mathematical lnduction-11929.png

0%
0%
2)
0%
0%

Maths-Binomial Theorem and Mathematical lnduction-11935.png

0%
0%
2)
0%
0%
None of these

Maths-Binomial Theorem and Mathematical lnduction-11940.png

0%
1
0%
2
0%
3
0%
4

Let S(k) = 1 + 3 + 5 + ...+ (2k -= 3 + k². Then which of the following is true.

0%
Principle of mathematical induction can be used to prove the formula
0%
S(k) ⇒ S(k + 1)
0%
S(k) ⇏ S(k + 1)
0%
S(is correct

Maths-Binomial Theorem and Mathematical lnduction-11943.png

0%
1/256
0%
1/562
0%
1/265
0%
-1/256

Maths-Binomial Theorem and Mathematical lnduction-11945.png

0%
2
0%
1
0%
3
0%
5

Maths-Binomial Theorem and Mathematical lnduction-11946.png

0%
18
0%
16
0%
12
0%
-10

If the coefficients of r^th term and (r + 4)^th th term are equal in the expansion of (1 + x)²⁰, then the value of r will be

0%
7
0%
8
0%
9
0%
10

Maths-Binomial Theorem and Mathematical lnduction-11947.png

0%
0%
2)
0%
0%
None of the above

Maths-Binomial Theorem and Mathematical lnduction-11951.png

0%
1/3
0%
-1/3
0%
2/3
0%
3/2

Maths-Binomial Theorem and Mathematical lnduction-11952.png

0%
7
0%
8
0%
9
0%
10

Maths-Binomial Theorem and Mathematical lnduction-11953.png

0%
9
0%
10
0%
8
0%
6

The first 3 terms in the expansion of (1+ ax)ⁿ (n ≠are 1,6x and 16x² . Then , the value of a and n are respectively.

0%
2 and 9
0%
3 and 2
0%
2/3 and 9
0%
3/2 and 6

Maths-Binomial Theorem and Mathematical lnduction-11954.png

0%
0%
2)
0%
0%

If A and B are the coefficients of xⁿ in the expansions of (1 + x)²ⁿ and (1 + x)^2n-1 respectively, then

0%
A = B
0%
A = 2B
0%
2A = B
0%
None of the above

If p and q be positive, then the coefficients of x^p and x^q in the expansion of (1 + x)^p+q will be

0%
Equal
0%
Equal in magnitude but opposite in sign
0%
Reciprocal to each other
0%
None of these

Maths-Binomial Theorem and Mathematical lnduction-11959.png

0%
0%
2)
0%
0%
None of these

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

0%
12C6 + 2
0%
12C5
0%
12C6
0%
12C7

JEE Questions for Maths Binomial Theorem And Mathematical Lnduction Quiz 8 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Binomial Theorem And Mathematical Lnduction Quiz 8 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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