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HIGHER MATH

HIGHER MATH

CLASS - 2

SEQUENCE AND SERIES

DIRECTIONS for questions 1 to 30: Choose the correct alternative. 1.

If a, b and c are in A.P. then which of the following is/are true? I.

b + c, c + a, a + b are in A.P.

a ( b + c ) b ( c + a ) c (a + b ) , , are in A.P.. bc ca ab 1] I only 2] II only 3] I and II

II.

2.

If a, b and c are in A.P. then which of the following is/are true? I.

bc, ca, ab are in H.P.

b + II. 1] II only 3.

c,

c + a, a + 2] I only

b are in H.P.. 3] I and II

3 2

2]

2 3

3] 2

4] 3

If five times the fifth term of an A.P. is equal to 10 times its tenth term, then find the fifteenth term of that A.P. 1] 10

6.

2] Rs.50000 4] None of the above

The ratio of the sum of the first eight numbers of a G.P. to the sum of the first four numbers of the same G.P is 97 : 81. Find the common ratio of the G.P. 1]

5.

4] None of these

Ram has borrowed some amount from Shyam and starts repaying with the first instalment Rs.1000/- and increasing the same by Rs.50/- every month. Ram had paid the amount in 30 months, then what is the amount borrowed by him? (Shyam has waived the interest payment). 1] Rs.30000 3] Rs.51750

4.

4] None of these

2] 20

3] 0

4] Data Insufficient

If a, b and c are in A.P. and x is the geometric mean of a and b and y is the geometric mean of b and c respectively, then which of the following is true? (Note: A.M. Âş Arithmetic mean) 1] b2 is A.M. between x 2 and y2. 3] x is A.M. between a and c.

2] b is A.M. between x and y. 4] y is A.M. between b and c. 1

IMS-34-UG-AL-HM-Class-2

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HIGHER MATH

7.

Find the sum of infinite terms of the following series: 1 1 1 1 + + + + ... 2´3 3´ 4 4´5 5´ 6 1] 1

8.

2]

3] 2

2] 12 years

3] 18 years

4] 19 years

The sum of first n odd numbers, beginning with unity is: 2] n2 4] Cannot be determined

1] 2n 3] n3 10.

4] None of these

A man saves Rs.4 more each year than the preceding year. If he saves Rs.20 in the first year, after how many years will his saving amount to Rs.1064? 1] 10 years

9.

1 2

Find four numbers in Arithmetic Progression such that their sum is 40 and the product of the first and the last is 64. 1] 2, 6, 10, 14 3] 4, 8, 12, 16

11.

Find the n th 1]

12.

2] 8, 12, 16, 20 4] 1, 5, 9, 13 5 20 10 20 , ------, , term of the series , 2 13 9 23

3 + 5n 20

20 3 + 5n

3]

2] 40 km

3] 36.9 km

20 3n + 5

4] 1428 km

2] 60 m 4] Cannot be determined

The three angles of a triangles are in GP. What type of triangle is it, if one of its interior angle is 60 o? 1] Equilateral triangle 3] Scalene triangle

15.

4]

A ball dropped from a height of 24 m rebounds two-third of the distance it falls. How much distance will it travel before coming to rest?. 1] 240 m 3] 120 m

14.

3n + 5 20

A body dropped from an airplane falls 10 meters in the first second of its motion, 15 meters in the second, 20 meters in the third, 25 meters in the fourth and so on. Find the distance travelled by the body if it hits the earth in 120 seconds. 1] 73.8 km

13.

2]

2] Isosceles triangle 4] Data insufficient

The three interior angles of a quadrilateral are in AP, such that the difference between the largest and the second largest angle is equal to the smallest angle considering the same three angles. Also the fourth angle is equal to one of the three angles that are in AP. At least one of the angles of the quadrilateral is 90 o. The least angle of the quadrilateral can be: 1] 40 o 3] 51.3 o

IMS-34-UG-AL-HM-Class-2

2] 45 o 4] Data insufficient

2

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HIGHER MATH

16.

Find the value of x in the following: (i) log

5

(log 5 x) = 2

1] 125

2] 625

(ii) log3 27 + log 3 x = 4 1] 3 2] 81 17.

4] 5

3] 27

4] 9

3] 3

4] 4

Find the value of log 73 54 × log 52 493 1] 1

18.

3] 3125

2] 2

Simplify: log

75 5 32 – 2log + log 16 9 243

1] log 2 3] log 3 19.

If log 2(9 – 2 x) = 10 log10 (3 – 1] 0

20.

Find the sum of log

3 + log

3

9 + log

3

4] 0 and 8

27 … up to n terms

2] 4

Find the value of x in log

Find the value of log 1] -

24.

3

3] [1] and [2]

3] 3n

4] n2 + n

3] 8

4] 16

3] 5 125

4] 625 125

3] – 1

4] -

Find the value of x in log x 2 (70 - 33x ) = 1

1] 625 5 23.

find the possible values of x.

2] ½ n(n+1)

1] 2 22.

x)

2] 3

1] 2n

21.

2] log 4 4] None of the above

If log

4 3

10

é ù êlog x ú = 4 3 ë 5 û

2] 25 125

27

1 . 81

2] – 3

6 = 0.7782, find the value of log

1] 0.7782

2] 0.3891

10

36 .

3] 1.5564

3

1 3

4] 3.1128

IMS-34-UG-AL-HM-Class-2

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HIGHER MATH

25.

Find the value of

8 log 8 8

2 log

1] 1

26.

Find the value of log

5

2

log 2 [log

2] 81

3] 3

4] 4

3] 4

4] 2

34 .

2

(log

3

(log x ))] = 2.

3]

e6 4]

e3

What is the value of log10{log 95 × log 59}? 2] 10 1

log

3

(5

3] 0

4] ¥

3] 10

4] 8

3] 6

4] 8

+ x ) + log 8 = 2 2 8

1] 22 30.

5 4 ´ log

Find the value of x, if

1] 1 29.

3

2

2] 3

1] 3 28.

.

2] 2

1] 5 27.

8

8

2] 18

log ( x + 3) + log (x + 5) = log 35

1] 2

IMS-34-UG-AL-HM-Class-2

2] 4

4

Higher Math_Class_2_stu
Higher Math_Class_2_stu

6. If a, b and c are in A.P. and x is the geometric mean of a and b and y is the geometric mean of b and c respectively, then which of the f...