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# Sequences and Series

#### Multiple Choice Questions

1.

If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in

• G.P.

• A.P.

• Arithmetic − Geometric Progression

• H.P.

B.

A.P. 322 Views

2.

If a1, a2, a3 , ....,an , .... are in G.P., then the value of the determinant is

• 0

• -2

• 1

• 2

A.

0

262 Views

3.

Suppose four distinct positive numbers a1, a2, a3, a4 are in G.P. Let b1 = a1, b2 = b1 + a2, b3 = b2 + a3 and b4 = b3 + a4.
Statement-I: The numbers b1, b2, b3, b4are neither in A.P. nor in G.P. Statement-II: The numbers b1, b2, b3, b4 are in H.P.

• Both statement-I and statement-II are true but statement-II is not the correct explanation of statement-I

• Both statement-I and statement-II are true, and statement-II is correct explanation of Statement-I

• Statement-I is true but statement-II is false.

• Statement-I is false but statement-II is true

C.

Statement-I is true but statement-II is false.

a1 = 1
a2 = 2
a3 = 4
a4 = 8

So, b1 = 1
b2 = 1 + 2 = 3
b3 = 3 + 4 = 7
b4 = 7 + 8 = 15
The numbers b1, b2, b3 , b4 are not in G.P. and A.P. Statement-I is correct but Statement-II wrong.

233 Views

4.

The sum of series • • • • B.  120 Views

5.

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

• x2 + 18x +16 = 0

• x2-18x-16 = 0

• x2+18x-16 =0

• x2-18x +16 =0

D.

x2-18x +16 =0

Let α and β be two numbers whose arithmetic mean is 9 and geometric mean is 4.
∴ α + β = 18 ........... (i)
and αβ =16 ........... (ii)
∴ Required equation is x2 - (α + β)x + (αβ) = 0 ⇒ x2 - 18x + 16 = 0 [using equation (i) and equation (ii)]

211 Views

6.

Let T be the rth term of an A.P. whose first term is a and the common difference is d. If for r some positive integers m, n, m ≠ n, Tm = 1/n  and Tn = 1/m, then a-b equals

• 0

• 1

• 1/mn

• A.

0 254 Views

7.

If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

• 601

• 600

• 602

• 603

A.

601

Alphabetical order is A, C, H, I, N, S
No. of words starting with A – 5!
No. of words starting with C – 5!
No. of words starting with H – 5!
No. of words starting with I – 5!
No. of words starting with N – 5!
SACHIN – 1 601.

174 Views

8.

The sum of the first n terms of the series when n is even. When n is odd the sum is

• • • • B. 19. The sum of n terms of given series = if n is even.
Let n is odd i.e. n = 2m + 1
Then, S2m+1 = S2m + (2m + 1)th term 178 Views

9.

If where a, b, c are in A.P. and |a| < 1, |b|<1, |c|< 1, then x, y, z are in

• G.P.

• A.P.

• Arithmetic − Geometric Progression

• H.P.

D.

H.P. 117 Views

10.

If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the binomial expansion of (1 + y)m are in A.P., then m and r satisfy the equation

• m2 – m(4r – 1) + 4r2 – 2 = 0

• m2 – m(4r+1) + 4r2 + 2 = 0

• m2 – m(4r + 1) + 4r2 – 2 = 0

• m2 – m(4r – 1) + 4r2 + 2 = 0

C.

m2 – m(4r + 1) + 4r2 – 2 = 0 197 Views