# Progressions Test 4

Total Questions:50 Total Time: 75 Min

Remaining:

## Questions 1 of 50

Question:If the $${9^{th}}$$term of an A.P. is 35 and $${19^{th}}$$ is 75, then its $${20^{th}}$$ terms will be

78

79

80

81

## Questions 2 of 50

Question:The $${9^{th}}$$ term of the series $$27 + 9 + 5\frac{2}{5} + 3\frac{6}{7} + ........$$ will be

$$1\frac{{10}}{{17}}$$

$$\frac{{10}}{{17}}$$

$$\frac{{16}}{{27}}$$

$$\frac{{17}}{{27}}$$

## Questions 3 of 50

Question:The sum of the series $$\frac{1}{2} + \frac{1}{3} + \frac{1}{6} + ........$$to 9 terms is

$$- \frac{5}{6}$$

$$- \frac{1}{2}$$

1

$$- \frac{3}{2}$$

## Questions 4 of 50

Question:The interior angles of a polygon are in A.P. If the smallest angle be $${120^o}$$and the common difference be 5o, then the number of sides is

8

10

9

6

## Questions 5 of 50

Question:If the first term of an A.P. be 10, last term is 50 and the sum of all the terms is 300, then the number of terms are

5

8

10

15

## Questions 6 of 50

Question:The maximum sum of the series $$20 + 19\frac{1}{3} + 18\frac{2}{3} + .........$$ is

310

300

320

None of these

## Questions 7 of 50

Question:If $${a_1},\,{a_2},....,{a_{n + 1}}$$are in A.P., then $$\frac{1}{{{a_1}{a_2}}} + \frac{1}{{{a_2}{a_3}}} + ..... + \frac{1}{{{a_n}{a_{n + 1}}}}$$ is

$$\frac{{n - 1}}{{{a_1}{a_{n + 1}}}}$$

$$\frac{1}{{{a_1}{a_{n + 1}}}}$$

$$\frac{{n + 1}}{{{a_1}{a_{n + 1}}}}$$

$$\frac{n}{{{a_1}{a_{n + 1}}}}$$

## Questions 8 of 50

Question:If the sum of the first $$n$$terms of a series be $$5{n^2} + 2n$$, then its second term is

7

17

24

42

## Questions 9 of 50

Question:If $$A$$ be an arithmetic mean between two numbers and $$S$$ be the sum of $$n$$ arithmetic means between the same numbers, then

$$S = n\,A$$

$$A = n\,S$$

$$A = S$$

None of these

## Questions 10 of 50

Question:The arithmetic mean of first n natural number

$$\frac{{n - 1}}{2}$$

$$\frac{{n + 1}}{2}$$

$$\frac{n}{2}$$

$$n$$

## Questions 11 of 50

Question:The difference between an integer and its cube is divisible by

4

6

9

None of these

## Questions 12 of 50

Question:If $$a,\,b,\,c$$ are in A.P., then $$(a + 2b - c)$$$$(2b + c - a)$$$$(c + a - b)$$ equals

$$\frac{1}{2}abc$$

abc

2 abc

4 abc

## Questions 13 of 50

Question:If the third term of a G.P. is 4 then the product of its first 5 terms is

$${4^3}$$

$${4^4}$$

$${4^5}$$

None of these

## Questions 14 of 50

Question:If the $${5^{th}}$$ term of a G.P. is $$\frac{1}{3}$$ and $${9^{th}}$$ term is $$\frac{{16}}{{243}}$$, then the $${4^{th}}$$ term will be

$$\frac{3}{4}$$

$$\frac{1}{2}$$

$$\frac{1}{3}$$

$$\frac{2}{5}$$

## Questions 15 of 50

Question:If the sum of three terms of G.P. is 19 and product is 216, then the common ratio of the series is [Roorkee 1972]

$$- \frac{3}{2}$$

$$\frac{3}{2}$$

2

3

## Questions 16 of 50

Question:The sum of the series $$6 + 66 + 666 + ..........$$upto $$n$$ terms is

$$({10^{n - 1}} - 9n + 10)/81$$

$$2({10^{n + 1}} - 9n - 10)/27$$

$$2({10^n} - 9n - 10)/27$$

None of these

## Questions 17 of 50

Question:The sum of a G.P. with common ratio 3 is 364, and last term is 243, then the number of terms is

6

5

4

10

## Questions 18 of 50

Question:If $$n$$ geometric means be inserted between $$a$$ and $$b$$then the $${n^{th}}$$ geometric mean will be

$$a\,{\left( {\frac{b}{a}} \right)^{\frac{n}{{n - 1}}}}$$

$$a\,{\left( {\frac{b}{a}} \right)^{\frac{{n - 1}}{n}}}$$

$$a\,{\left( {\frac{b}{a}} \right)^{\frac{n}{{n + 1}}}}$$

$$a\,{\left( {\frac{b}{a}} \right)^{\frac{1}{n}}}$$

## Questions 19 of 50

Question:The sum can be found of a infinite G.P. whose common ratio is $$r$$

For all values of $$r$$

For only positive value of $$r$$

Only for $$0 < r < 1$$

Only for $$- 1 < r < 1(r \ne 0)$$

## Questions 20 of 50

Question:If $$A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + .......\infty$$, then the value of r will be

$$A{(1 - A)^z}$$

$${\left( {\frac{{A - 1}}{A}} \right)^{1/z}}$$

$${\left( {\frac{1}{A} - 1} \right)^{1/z}}$$

$$A{(1 - A)^{1/z}}$$

## Questions 21 of 50

Question:If $$y = x + {x^2} + {x^3} + .......\,\infty ,\,{\rm{then}}\,\,x =$$

$$\frac{y}{{1 + y}}$$

$$\frac{{1 - y}}{y}$$

$$\frac{y}{{1 - y}}$$

None of these

## Questions 22 of 50

Question:If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3, then its first term and common ratio are

3/2, 1/2

1, ½

3/2, 2

None of these

## Questions 23 of 50

Question:If $${a_1},\;{a_2},\;{a_3},...............,\;{a_n}$$ are in H.P., then $${a_1}{a_2} + {a_2}{a_3} +$$ $$.......... + {a_{n - 1}}{a_n}$$ will be equal to

$${a_1}{a_n}$$

$$n{a_1}{a_n}$$

$$(n - 1){a_1}{a_n}$$

None of these

## Questions 24 of 50

Question:If $$x,\;y,\;z$$ are in H.P., then the value of expression $$\log (x + z) + \log (x - 2y + z)$$ will be

$$\log (x - z)$$

$$2\log (x - z)$$

$$3\log (x - z)$$

$$4\log (x - z)$$

## Questions 25 of 50

Question:If $$\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}}$$ be the harmonic mean between $$a$$ and $$b$$, then the value of $$n$$ is

1

$$- 1$$

0

2

## Questions 26 of 50

Question:If the harmonic mean between $$a$$ and $$b$$ be $$H$$, then $$\frac{{H + a}}{{H - a}} + \frac{{H + b}}{{H - b}} =$$

4

2

1

$$a + b$$

## Questions 27 of 50

Question:If $$\frac{1}{{b - a}} + \frac{1}{{b - c}} = \frac{1}{a} + \frac{1}{c}$$, then $$a,\;b,\;c$$ are in

A.P.

G.P.

H.P.

In G.P. and H.P. both

## Questions 28 of 50

Question:If $$a$$ and $$b$$ are two different positive real numbers, then which of the following relations is true

$$2\sqrt {ab} > (a + b)$$

$$2\sqrt {ab} < (a + b)$$

$$2\sqrt {ab} = (a + b)$$

None of these

## Questions 29 of 50

Question:If $$a,\;b,\;c$$ are in A.P., then $${3^a},\;{3^b},\;{3^c}$$ shall be in

A.P.

G.P.

H.P.

None of these

## Questions 30 of 50

Question:If the $${(m + 1)^{th}},\;{(n + 1)^{th}}$$ and $${(r + 1)^{th}}$$ terms of an A.P. are in G.P. and $$m,\;n,\;r$$ are in H.P., then the value of the ratio of the common difference to the first term of the A.P. is

$$- \frac{2}{n}$$

$$\frac{2}{n}$$

$$- \frac{n}{2}$$

$$\frac{n}{2}$$

## Questions 31 of 50

Question:An A.P., a G.P. and a H.P. have the same first and last terms and the same odd number of terms. The middle terms of the three series are in

A.P.

G.P.

H.P.

None of these

## Questions 32 of 50

Question:If $$,a,\;b,\,c$$ be in G.P. and $$a + x,\;b + x,\;c + x$$ in H.P., then the value of $$x$$ is ($$a,\;b,\;c$$ are distinct numbers)

$$c$$

$$b$$

$$a$$

None of these

## Questions 33 of 50

Question:If the ratio of H.M. and G.M. between two numbers $$a$$ and $$b$$ is $$4:5$$, then the ratio of the two numbers will be

$$1:2$$

$$2:1$$

$$4:1$$

$$1:4$$

3 and 4 are correct

## Questions 34 of 50

Question:If the A.M., G.M. and H.M. between two positive numbers $$a$$ and $$b$$ are equal, then

$$a = b$$

$$ab = 1$$

$$a > b$$

$$a < b$$

## Questions 35 of 50

Question:If $$a,\;b,\;c$$ are in A.P., then $${10^{ax + 10}},\;{10^{bx + 10}},\;{10^{cx + 10}}$$ will be in

A.P.

G.P. only when $$x > 0$$

G.P. for all values of $$x$$

G.P. for $$x < 0$$

## Questions 36 of 50

Question:The common difference of an A.P. whose first term is unity and whose second, tenth and thirty fourth terms are in G.P., is

$$\frac{1}{5}$$

$$\frac{1}{3}$$

$$\frac{1}{6}$$

$$\frac{1}{9}$$

## Questions 37 of 50

Question:Let the positive numbers a, b, c, d be in A.P., then abc, abd acd, bcd are

Not in A.P./G.P./H.P.

In A.P.

In G.P.

In H.P.

## Questions 38 of 50

Question:If in the equation $$a{x^2} + bx + c = 0,$$ the sum of roots is equal to sum of square of their reciprocals, then $$\frac{c}{a},\frac{a}{b},\frac{b}{c}$$ are in

A.P.

G.P.

H.P.

None of these

## Questions 39 of 50

Question:The harmonic mean between two numbers is $$14\frac{2}{5}$$and the geometric mean 24 . The greater number them is

72

54

36

None of these

## Questions 40 of 50

Question:When $$\frac{1}{a} + \frac{1}{c} + \frac{1}{{a - b}} + \frac{1}{{c - d}} = 0$$ and $$b \ne a \ne c$$, then $$a,\;b,\;c$$ are

In H.P.

In G.P.

In A.P.

None of these

## Questions 41 of 50

Question:If $${a^2},\,{b^2},\,{c^2}$$ be in A.P., then $$\frac{a}{{b + c}},\,\frac{b}{{c + a}},\,\frac{c}{{a + b}}$$ will be in

A.P.

G.P.

H.P.

None of these

## Questions 42 of 50

Question:The sum of the first $$n$$ terms of the series $$\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{{15}}{{16}} + .........$$ is

$${2^n} - n - 1$$

$$1 - {2^{ - n}}$$

$$n + {2^{ - n}} - 1$$

$${2^n} - 1$$

## Questions 43 of 50

Question:The sum of $$1 + \frac{2}{5} + \frac{3}{{{5^2}}} + \frac{4}{{{5^3}}} + ...........$$upto $$n$$ terms is

$$\frac{{25}}{{16}} - \frac{{4n + 5}}{{16 \times {5^{n - 1}}}}$$

$$\frac{3}{4} - \frac{{2n + 5}}{{16 \times {5^{n + 1}}}}$$

$$\frac{3}{7} - \frac{{3n + 5}}{{16 \times {5^{n - 1}}}}$$

$$\frac{1}{2} - \frac{{5n + 1}}{{3 \times {5^{n + 2}}}}$$

## Questions 44 of 50

Question:$${2^{1/4}}{.4^{1/8}}{.8^{1/16}}{.16^{1/32}}..........$$is equal to

1

2

$$\frac{3}{2}$$

$$\frac{5}{2}$$

## Questions 45 of 50

Question:The sum of the series $${1^2}.2 + {2^2}.3 + {3^2}.4 + ........$$ to n terms is

$$\frac{{{n^3}{{(n + 1)}^3}(2n + 1)}}{{24}}$$

$$\frac{{n(n + 1)(3{n^2} + 7n + 2)}}{{12}}$$

$$\frac{{n(n + 1)}}{6}[n(n + 1) + (2n + 1)]$$

$$\frac{{n(n + 1)}}{{12}}[6n(n + 1) + 2(2n + 1)]$$

## Questions 46 of 50

Question:The sum of the series $$1.2.3 + 2.3.4 + 3.4.5 + .......$$ to n terms is

$$n(n + 1)(n + 2)$$

$$(n + 1)(n + 2)(n + 3)$$

$$\frac{1}{4}n(n + 1)(n + 2)(n + 3)$$

$$\frac{1}{4}(n + 1)(n + 2)(n + 3)$$

## Questions 47 of 50

Question:The sum of $${1^3} + {2^3} + {3^3} + {4^3} + ..... + {15^3}$$,is [MP PET 2003]

22000

10,000

14,400

15,000

## Questions 48 of 50

Question:The sum to $$n$$ terms of the infinite series $${1.3^2} + {2.5^2} + {3.7^2} + ..........\infty$$ is

$$\frac{n}{6}(n + 1)(6{n^2} + 14n + 7)$$

$$\frac{n}{6}(n + 1)(2n + 1)(3n + 1)$$

$$4{n^3} + 4{n^2} + n$$

None of these

## Questions 49 of 50

Question:If the $${n^{th}}$$ term of a series be $$3 + n\,(n - 1)$$, then the sum of $$n$$ terms of the series is

$$\frac{{{n^2} + n}}{3}$$

$$\frac{{{n^3} + 8n}}{3}$$

$$\frac{{{n^2} + 8n}}{5}$$

$$\frac{{{n^2} - 8n}}{3}$$

## Questions 50 of 50

Question:The sum to $$n$$ terms of $$(2n - 1) + 2\,(2n - 3)$$ $$+ 3\,(2n - 5) + .....$$ is

$$(n + 1)\,(n + 2)\,(n + 3)/6$$
$$n\,(n + 1)\,(n + 2)/6$$
$$n\,(n + 1)\,(2n + 3)\,$$
$$n\,(n + 1)\,(2n + 1)/6$$