Jee 2014 Booklet4 Hwt Sequence & Series
February 12, 2017 | Author: varunkohliin | Category: N/A
Short Description
Jee 2014 Booklet4 Hwt Sequence & Series...
Description
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : SQS [1]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
log32 , log 62 , log122 are in : (A)
2.
A.P.
4.
a positive integer
divisible by n
(C)
equal to n
44
1 n
(D)
never less than n
(D)
None of these
(B) (D)
A.P. H.P.
27
(B)
27
(C)
13.5
(D)
–13.5
ab n
(B)
ab n 2
(C)
ab 2n
(D)
None of these
(C)
log5 2
(D)
1 log 2 5
(C)
4
(D)
None of these
If log 2 5.2 x 1 , log 4 21 x 1 and 1 are in A.P., then x equals : (B)
log 2 5
The value of 0.16
1 log5 2
1 1 1 1 log2.5 . . . . 33 3 32
2
(B)
3
is :
If A1, A2 be two AM’s and G1, G2 be two GM’s between a and b, then (A)
10.
None of these
The product of n geometric means between a and b is :
(A) 9.
(D)
If x, 2 x 2 , 3 x 3 are in G.P., then the fourth term is :
(A) 8.
(B)
a b c , , will be in : bc ca ab no specified sequence G.P.
(A) 7.
H.P.
If a, b, c are in H.P., then
(A) 6.
(C)
The third term of G.P. is 4. The product of first five terms is : (A) 43 (B) 45 (C)
(A) (C) 5.
G.P.
The product of n positive numbers is unity. Then their sum is : (A)
3.
(B)
ab 2ab
(B)
2ab ab
A1 A2 is equal to : G1 G2 ab ab
(D)
ab ab
–5050
(D)
–5000
(C)
Coefficient of x99 in the expansion of x 1 x 2 . . . . . x 100 is : (A)
5050
VMC/Sequence & Series
(B)
5000
(C)
36
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : SQS [2]
ROLL NO.
START TIME :
STUDENT’S SIGNATURE :
END TIME :
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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
If A and G be the AM and GM respectively between two numbers, then the numbers are :
A G 2 A2
(A) 2.
1
16 : 7 1
(B)
1
6.
7.
8.
7 : 16
G A2 G 2
(C)
74 : 169
(D)
None of these
(B)
x2
(C)
x2
(D)
None of these
A>H>G
(C)
GG>H (B)
(A) *9.
A A2 G 2
1
1
5.
(C)
x 2 . x 4 . x 8 . x 16 . . . . . to is equal to :
(A) 4.
A A2 G 2
If the ratio between the sums of n terms of two A.P.’s is 3n 8 : 7 n 15 , then the ratio between their 12th term is : (A)
3.
(B)
pth term is zero
Sum of the series : 12 32 52 . . . . . .20 terms : (A)
10660
VMC/Sequence & Series
(B)
10330
(C)
37
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : SQS [3]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with ‘*’ may have More than One correct option. 1.
x 1 x y 1 y 2
(A)
n
(C)
1 x
(B)
2
n 2 y2 1 yn 1 x 1 x x y 1 x 1 y
n
(D)
1 y
None of these
n
1 I r 3 1 , then I r is equal to : r
(A)
4.
n
y 1 y
r 1
3.
x y
n
If
2
x y
x2 1 xn
2.
Sum of n terms of series : x y x 2 xy y 2 x3 xy 2 x 2 y y 3 . . . . .
r 1
1 n 2 1 3
(B)
1 n 1 3
(C)
3 1 1 4 3
n
Let positive numbers a, b, c, d be in A.P. then abc, abd, acd, bcd are : (A) not in A.P. or G.P. or H.P. (B) in A.P. (C) in G.P. a b c , , bca c ab b ac 3 (C) 2
(D)
None of these
(D)
in H.P.
(D)
2
If a, b, c are the sides of a triangle, then : (A)
3
(B)
5.
The harmonic mean and geometric mean of two positive numbers are in the ratio 4 : 5, then two numbers are in the ratio. (A) 4:1 (B) 3:1 (C) 2:1 (D) 1:3
6.
Sum of integers from 1 to 100 that are divisible by 2 or 5 is : (A) 3050 (B) 3150 (C)
7.
9.
None of these
2
(B)
3
(C)
4
(D)
5
If the sum of first 2n terms of the A.P. 2, 5, 8, . . . . is equal to the sum of first n terms of the A.P. 57, 59, 61 . . . . . then n equals : (A) 10 (B) 12 (C) 11 (D) 13 Coefficient of x0 in x a x b x c x d x e . . . . x x0 is : (A)
*10.
(D)
If x > 0 and log 2 x log 2 2 log 2 4 x log 2 8 x . . . . . . = 4 then x equals : (A)
8.
3250
product of roots
(B)
sum of roots
(C)
A.M. ≥ G.M. for a, b where a and b are : (A) Natural numbers (B) Rational numbers (C)
VMC/Sequence & Series
38
1
Integers
(D)
depends on roots and number of roots
(D)
Positive rational numbers
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : SQS [4]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
If the length of sides of a right triangle are in A.P. then the sines of the acute angle are :
1 3 , 2 2
(A) 2.
If
a, b, c are in A.P. (B)
1 12
1 22
1 32
....
If x
tr
r 1
(A)
3 4 , 5 5
5 1 , 2
(D)
5 1 2
a b, b c, c a are in A.P.
2 8
(D)
2 12
(C)
xy z y x z
(D)
None of these
(C)
4n n 1
(D)
R
(C)
Integer
(D)
natural number
385
(C)
1115
(D)
3025
(C)
(B)
(B)
n
a b , then : n0
xyz x y z
1 n n 1 n 2 , the value of 12 2n n 1
a, b, c are in H.P. (D)
n
t
1
is :
r 1 r
n 1
n 1!
3n n2
2 x 2 x 2 for x :
(A) 7.
2 6
b n , 0 a b 1 and z
x yz x y z n
6.
(B)
n0
(A) If
a, b, c are in G.P. (C)
an , y
n0
5.
(C)
1 1 1 2 , then value of 2 2 2 . . . . is : 6 1 3 5
2 4
(A)
4.
2 1 , 3 3
If log a c log a c 2b 2 log a c , then : (A)
3.
(B)
R
(B)
If n 55 then n is equal to : (A) 506 (B) 2
Statement True or False for Q.8 - 10 8.
n! n n
10.
ba bc 3. If a, b, c are in H.P. then ba bc
VMC/Sequence & Series
9.
If a and c are positive and b is negative than a, b, c can be in G.P.
39
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : SQS [5]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. Paragraph for Q.1 - 3 The sum of the squares of 3 distinct real numbers which are strictly in G.P. is s2. If their sum is s. 1.
2 lies in :
1 1 3 , 0 0 , 3 (C)
1 3 , 3
(D)
1 3 , 1 1, 3
If 2 2 then the value of [r] is : (A) 0 (B)
1
(C)
2
(D)
3
If r = 2 then value of 2 is : (A) 0 (B)
1
(C)
2
(D)
3
4
(D)
64
(A) 2. 3.
4.
1 3 , 1
(B)
If a b c 12 a, b, c 0 then maximum value of abc is : (A)
16
(B)
12
(C)
5.
The sum of infinite numbers of terms of a G.P. is 15 and the sum of their squares is 45. Then third term of the G.P. is : (A) 5 (B) 10/3 (C) 20/9 (D) 40/27
6.
If
1 1 1 1 0 b a c then : a c a b cb
(A) 7.
a, b, c are in A.P. (B)
a, b, c are in H.P. (C)
a, b, c are in G.P. (D)
a, b, c are in AG.P.
Sum of the series 1.2 + 2.3 + 3.4 + . . . . n terms : (A)
3n n 1 n 2 3
(B)
n n 1 n 2 3
(C)
n 1 n 2 2n 1 3
(D)
None of these
Statement True or False for Q.8 - 10 8.
If a, b, c, d are in G.P. then ax 2 c divides ax3 bx 2 cx d .
9.
Only solution for system of equations :
1 x x 2 x3 . . . . .x 23 0 is 10.
and
1 x x 2 x3 . . . . .x19 0
x 1
If a, b, c are in G.P. then a b, 2b, c d are in H.P.
VMC/Sequence & Series
40
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : SQS [6]
ROLL NO.
START TIME :
STUDENT’S SIGNATURE :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. Paragraph for Q.1 - 3 Suppose p is the first of n A.M’s between two positive numbers a and b ; q the first of n H.M’s between the same two numbers. 1.
P is : (A)
2.
(B)
na b n 1
(C)
nb a n 1
(D)
nb a n 1
Value of q is : (A)
3.
na b n 1
ab n 1
(B)
b an
ab n 1 a bn
(C)
ab n 1 b an
(D)
ab n 1 a bn
If pq f x then f x is : x
b
(D)
a2
558
(D)
650
1025th term in the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8 . . . . . . . is : (A) 29 (B) 210 (C) 211
(D)
212
Sum of the series upto 10 terms is 4 + 44 + 444 + 4444 + . . . . . 10 terms ? (A) 100 (12345679) (B) 200 (12345679) (C) 300 (12345679)
(D)
400 (12345679)
(A) 4. 5. 6.
ab
(B)
a
(C)
Maximum value of the sum of the A.P. 50, 48, 46, 44, . . . . . is : (A) 648 (B) 450 (C)
Statement True or False for Q.7 - 10 7.
The number 111 . . . . 11 (91 times) is a prime number.
8.
If H n 1
9.
If 0.272727 . . . . . , x, 0.727272 are in HP then x must be an irrational number.
10.
If a 2b c 4 then maximum value of ab 2 c exists when a = b = c = 1.
1 1 1 n 1 1 2 3 . . . . . , then H n n . . . . . 2 3 n n 2 3 4
VMC/Sequence & Series
41
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : SQS [7]
ROLL NO.
START TIME :
STUDENT’S SIGNATURE :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with ‘*’ may have More than One correct option. 1.
Find 10th term of the series 8, 8 17
(A) 2.
4.
x 2 2 Ax G 2 0 (B)
(C)
8 21
(D)
8 10
x 2 2 Ax G 2 0 (C)
x 2 Ax G 2 0
(D)
None of these
(D)
440
If f n 1 1! 2 2! 3 3! 4 4! . . . . upto n terms, then : f n n! 1
If a (A)
f n n! 1
(C)
f n n 1 ! 1 (D)
is the A.M. between ‘a’ and ‘b’, then : b n 1 n is odd (B) n is even
(C)
n is perfect square (D)
n is not a perfect square
(C)
1771
(D)
1881
(C)
1 2 5
(D)
1 2 4
(D)
–1
(D)
2
a b n
6.
8 19
Sum of the series utpo 10 terms is 1.2 + 2.3 + 3.4 + . . . . . . 10 terms : (A) 110 (B) 220 (C) 330
(A) *5.
(B)
If A is arithmetic mean and G is geometric mean of a and b then a, b are roots of the equation. (A)
3.
8 8 , ..... 3 5
n 1
(B)
f n n 1 ! 1
n
Sum of the series upto 11 terms is :
12 32 52 . . . . 11 terms : (A) 7.
1551
Sum to 5 terms of the series
(B)
1 3 7 15 is : 2 4 8 16
4
(A) 8.
9.
*10.
1 2 5
1661
5
4
(B)
1 2 4
Minimum value of logb a log a b is : (a > 1, b > 1) (A) 1 (B) 2
(C)
3 y If cos x y , cos x and cos x y are in H.P., then cos x . sec is equal to : 2 1 1 (A) (B) (C) 2 2 2
5
If x > 0, then sum of the series e x e2 x e3 x . . . . . is : (A)
always negative
VMC/Sequence & Series
(B)
always positive
(C)
42
always less than 1 (D)
always greater than one
HWT/Mathematics
Vidyamandir Classes
DATE :
IITJEE :
NAME :
MARKS : 10
TIME : 25 MINUTES
TEST CODE : SQS [8]
ROLL NO.
START TIME :
STUDENT’S SIGNATURE :
END TIME :
TIME TAKEN:
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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
2.
1 1 1 are in : , , 1 x 1 x 1 x (A) A.P. (B)
4.
(C)
G.P.
(D)
None of these
(C)
4
(D)
None of these
Least value of log100 a log a 0.0001, a 1 is : (A)
3.
H.P.
2
(B)
3
A monkey while trying to reach the top of a pole of height 12 meters takes every jump of 2 meters but slips 1 meter while holding the pole. The number of jumps required to reach the top of the pole, is : (A) 6 (B) 10 (C) 11 (D) 12 x2 x
(A)
tan 2 x2 x
is always greater than or equal to :
2tan
(B)
2
(C)
1
(D)
sec 2
5
5.
r r 1 r 2 r 3 is equal to : r 1
1 x x 1 x 2 x 3 x 4 5 1 x x 1 x 2 x 3 x 4 7
(A) (C)
6.
If 1.05
49
50
11.658 , then
1.05
n
(B) (D)
1 x x 1 x 2 x 3 x 4 10 9! 5!
equals :
n 1
(A) 7.
8.
208.34
(B)
212.12
(C)
212.16
(D)
213.16
An infinite G.P. has first term x and sum 5, then x belongs to : (A) 0 x5 (B) 0 x 10 (C)
5 x 5
(D)
10 x 10
For two unequal numbers, AM = 4 and GM = 2. Then HM is : (A) 1 (B) 2 (C)
3
(D)
4
9.
After inserting n AM’s between 2 and 38, the sum of the resulting progression is 200. The value of n is : (A) 10 (B) 9 (C) 8 (D) None of these
10.
Sum of integers from 1 to 100 which are divisible by 2 or 5 is : (A) 3000 (B) 3010 (C)
VMC/Sequence & Series
43
3150
(D)
3050
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : SQS [9]
ROLL NO.
START TIME :
STUDENT’S SIGNATURE :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Number of common terms of two sequences 17 , 21, 25, . . . .417 and 16, 21, 26, . . . .466 are : (A) (C)
2.
If
4.
5.
19 22
3 9
(B) (D)
a
(A)
2 3
2r 1
(C)
22 3
2 3
(A) (C)
2
2
55 110
2
16 (B) (D)
2
2
(D)
i
j
1 is : n n 1 2n 1 6
(B)
n n 1 2
n n 1 n n 1 n 2 (D) 6 2 If a, b, c are positive then minimum value of (C)
2
9.
alog b log c blog c log a clog a log b is : (A) 3 (B) 1 (C) 6 (D) 16
25 is :
n
10.
–55 –110
r 1
a, b, c are three positive numbers and abc2 has the 1 greatest value . Then : 64 1 1 1 1 (A) a b ,c (B) a b ,c 2 4 4 2 1 a b c (C) (D) None of these 3
VMC/Sequence & Series
(C)
2 100
2
2
x
(B)
(A)
3
x 1 x 4 x 9 x
i 1 j 1 k 1
8
Coefficient of x in
, then the common difference of the A.P.
(A)
n
8.
2
(D)
and
is :
2 5 2 11 . . . . is : 3 6 3 24
(B)
2r
r 1
6 81
2 12 If first two terms of a H.P. are and respectively, 5 13 then the largest term is : (A) 6 (B) 12 (C) 5 (D) 17/3
Sum to infinity of the series
a
100
42
4
2
6.
(B) (D)
Let an be nth term of an A.P. and
r 1
3 d 3 2d . . . 8 , then the value of d 3
is : (A) (C) 3.
20 21
100
7.
44
r 2 r 1 is equal to : r 1!
(A)
n n 1!
(B)
1 n 1 n 1!
(C)
n 1 n 1!
(D)
None of these
HWT/Mathematics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : SQS [10]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
2.
Fifth term of a G.P. is 2, then the product of its 9 terms is : (A) 256 (B) 512 (C)
(A) 3.
7.
9.
6 2
(C)
20 5n 3
(D)
20 5n 2
(D)
None of these
(D)
8
2 6 18 54 . . . . . is :
(B)
121 2
3 1
(C)
243
3 1
2
(B)
4
(C)
6
1 5
2 5
(B)
(C)
3 5
(D)
4 5
If H.M. and G.M. of two positive numbers are in the ratio 12 : 13, then the numbers are in the ratio : (A) 1:2 (B) 2:3 (C) 3:5 (D) 4:9 Sum to n terms of the series 1 1 2 1 2 3 . . . . . n terms is :
1 n n 1 n 2 2
(B)
1 n n 1 n 2 3
(C)
1 n n 1 2n 1 (D) 4
If n!, 3(n!) and (n + 1)! are in G.P., then n!, 5(n!) and (n + 1)! are in : (A) A.P. (B) G.P. (C) H.P. Sum to infinity of the series 1 (A)
10.
204
Sum of an infinite G.P. is 20 and sum of their squares is 100. The common ratio of the G.P. is :
(A) 8.
121
20 5n 4
(B)
(A) 6.
(D)
Harmonic mean of the roots of the equation 5 2 x 2 4 2 x 8 2 2 0 is : (A)
5.
15 5n 3
Sum to 10 terms of the series (A)
4.
1024
1 17 11 20 nth term of sequence 2 , , , . . . . . is : 2 13 9 23
16 35
(A)
H.P.
VMC/Sequence & Series
(D)
None of these
(D)
17 6
(D)
None of these
4 7 10 . . . . . is : 5 52 53
(B)
If a, b, c . . . . . . are in G.P. and
1 n n 1 n 2 6
1 ax
(B)
11 8 1 y
(C)
35 16
1
b c z . . . . , then x, y, z are in : G.P.
(C)
45
A.P.
HWT/Mathematics
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