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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
®
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
®
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
®
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