Mathematics Crash Course NDA & NA EE>Chapter 9 - Sequence and Series>Exercise 1>Q 9

EASY

NDA & NA EE

IMPORTANT

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If $\frac{3 + 5 + 7 + \dots + n}{5 + 8 + 11 + \dots + 10 terms} = 7$ , then the value of $n$ is

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Important Questions on Sequence and Series

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 9 - Sequence and Series>Exercise 1>Q 10

Which term of the sequence

20, 19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \dots

is the first negative term?

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 9 - Sequence and Series>Exercise 1>Q 11

If

p

times the

p^{th}

term of an A.P. is

q

times the

q^{th}

term, then what is the

{(p + q)}^{th}

term equal to?

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 9 - Sequence and Series>Exercise 1>Q 12

Let $a, b$ and $c$ be in an A.P. Consider the following statements

$I$ . $\frac{1}{a b}, \frac{1}{c a}$ and $\frac{1}{b c}$ are in an A.P.

$II$ . $\frac{1}{\sqrt{b} + \sqrt{c}}, \frac{1}{\sqrt{c} + \sqrt{a}}$ and $\frac{1}{\sqrt{a} + \sqrt{b}}$ are in A.P.

Which of the above statement(s) is / are correct?

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 9 - Sequence and Series>Exercise 1>Q 13

The sum of the first five terms and the sum of the first ten terms of an

AP

are same. Which one of the following is the correct statement?

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 9 - Sequence and Series>Exercise 1>Q 14

If the

n t h

term of an

AP

is

\frac{3 + n}{4}

, then the sum of first

105

terms is

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 9 - Sequence and Series>Exercise 1>Q 15

If

e^{(\cos^{2} x + \cos^{4} x + \cos^{6} x + . . . . \infty) \log_{e} 2}

satisfies the equation

t^{2} - 9 t + 8 = 0

, then the value of

\frac{2 \sin x}{\sin x + \sqrt{3} \cos x}

, where

0 < x < \frac{π}{2}

, is equal to

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 9 - Sequence and Series>Exercise 1>Q 16

If

a, b, c

are positive integers forming an increasing

G . P .

,

b - a

is a perfect cube and

\log_{6} a + \log_{6} b + \log_{6} c = 6

, then

a + b + c

is

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 9 - Sequence and Series>Exercise 1>Q 17

If

a, b, c

form a

G . P .

with common ratio

r

such that

0 < r < 1

, and if

a, \frac{3 b}{2}, - 4 c

form an

A . P .

, then

r

is equal to -