﻿ IIT - JEE Main Important Questions of Sequences and Series | Zigya

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# Sequences and Series

#### Multiple Choice Questions

1.

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

• 46th

• 59th

• 52nd

• 52nd

394 Views

2.

If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

• 8/5

• 4/3

• 1

• 1

272 Views

3.

If the sum of the first ten terms of the series, is 16/5 m, the m is equal to

• 102

• 101

• 100

• 100

347 Views

4.

The sum of first 9 terms of the series is

• 71

• 96

• 142

• 142

194 Views

5.

Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

• • • • 250 Views

6.

The sum of first 20  terms of the sequence 0.7,0.77,0.777...... is

• • • • 958 Views

7.

If x, y, z are in A.P. and tan−1 x, tan−1 y and tan−1 z are also in A.P., then

• x= y= z

• 2x =3y = 6z

• 6x = 3y= 2z

• 6x = 3y= 2z

207 Views

8.

Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000.
Statement 2: , for any natural number n.

• Statement 1 is false, statement 2 is true

• Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

178 Views

9.

If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150th term of this AP is

•  –150

• 150

• times its 50th term

• times its 50th term

263 Views

10.

Let x1, x2, ......, xn be n observations, and let be their arithmetic mean and σ2 be their variance.
Statement 1: Variance of 2x1, 2x2, ......, 2xn is 4 σ2.
Statement 2: Arithmetic mean of 2x1, 2x2, ......, 2xn is 4 .

• Statement 1 is false, statement 2 is true

• Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

213 Views