DPP 51 54 PDF
DPP 51 54 PDF
DPP 51 54 PDF
28-07-08
Date : __________
Subject : Maths
51
DPP No. ____
Class : XI
M.M. 30
Time: 45 Min.
Comprehension (Q.No. 1 to 3)
Two consecutive numbers from 1, 2, 3, ......, n are removed. Artithmetic mean of the remaining
105
numbers is
.
4
1.
2.
The value of n is
(A) 7
(C*) 50
(D) 51
3.
[4]
(B) 8
(B)
50
54
[4]
(C*)
56
(D)
58
[4]
(D) 23
5.
The matrix A has x rows and (x + 5) columns. The matrix B has y rows and (11 y) columns. Both AB
and BA exist. The value of x and y is
[3]
(A) 8, 3
(B) 3, 4
(C*) 3, 8
(D) 8, 8
2
If A = 2
(A)
6.
6
1
, B = 5 , C = 1 are such that AB = C, then absolute value of |A| is
1
6
(B) 30
2
27
7.
(C)
(B) 0
(D*)
1
36
(C*) 2
(B)
(C*)
(D)
STATEMENT-1
STATEMENT-1
STATEMENT-1
STATEMENT-1
STATEMENT-1
STATEMENT-1
[3]
x 3 7
Let A = 3 x 2 and x3 62x + 84 = 0
7 2 x
STATEMENT -1 : A is singular
and
STATEMENT-2 : Every symmetric matrix of order 3 is singular.
(A)
[3]
[3]
8.
9.
If a, b R and ax2 + bx + 6 = 0, a 0 does not have two distinct real roots, then
(A*) Minimum possible value of 3a + b is 2
(B) Minimum possible value of 3a + b is 2
(C*) Minimum possible value of 6a + b is 1
(D) Minimum possible value of 6a + b is 1
[4]
[4]
29-07-08
Date : __________
Subject : Maths
52
DPP No. ____
Class : XI
M.M. 36
1.
Column I
Column II
(A)
(p)
(B)
(q)
(C)
If the set of all real values of 'x' which satisfy the inequation
(r)
(s)
Time: 45 Min.
[8]
log2 ( x 1)
> 0 is (l , 0) (, ), then (+ l ) equals to
( x 1)
(D)
Ans.
(A) (p),
(B) (q),
(C) (p),
(D) (q)
3.
4.
For three square matrix A, B & C if ABC = 0 & | A | 0, B is non-zero singular matrix, then
(A) C must be zero matrix
(B) C must be non-singular matrix
(C*) C must be singular matrix
(D) None of these
If x, y are integral solutions of 2x2 3xy 2y2 = 7, then value of |x + y| is
(A) 2
(B*) 4
(C) 6
(B)
7.
n (n 1)
2
(D) 2n2 n
(C) n2 + 2n
[3]
2 , i j
If A = [aij]3 3, such that aij = 0 , i j , then 1 + log1/2 (|A||adj A|) is equal to
(A*) 191
6.
[3]
(D) 2 or 4 or 6
cos 2
cos sin sin
4
2
n
+ ......... + f
If f() = cos sin
+ f() + f
is equal to
sin 2
cos , then f + f
3
3
3
3
sin
cos
0
(A*) n
5.
[3]
(B) 23
(C) 0
[3]
(D) does not exists
2
1 2
If A =
, then adj A is equal to
2 2 1
[3]
(B) AT
(A) A
[3]
(D*) 3AT
(C) 3A
Subjective
8.
If
1
2
1
2
1
2
1
3
1
3
1
4
+ ....... +
1
(1999 )
1
(2000 )
=x
1
,
x
[4]
x = 2000,
1
2000
2
x log10 x 3log10 x 1 > 1000
(i)
x > 1000
[6]
(ii)
(ii)
(0 , 1] [2 , )
3x 1 3
16
4
30-07-08
Date : __________
Subject : Maths
53
DPP No. ____
Class : XI
M.M. 30
Time: 45 Min.
[3]
ab bc c a
is 2
STATEMENT-1 : Least value of
2c 2a 2b
and
ab bc c a
is 8.
STATEMENT-2 : Least value of
c a b
(A)
STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is a correct explanation for
STATEMENT-1
(B)
STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1
(C)
STATEMENT-1 is True, STATEMENT-2 is False
(D*)
STATEMENT-1 is False, STATEMENT-2 is True
2.
Number of positive integers x for which f(x) = x3 8x2 + 20x 13, is a prime number, is
(A) 1
(B) 2
(C*) 3
(D) 4
3.
4.
5.
3 tan
. tan
is equal to
5
15
(B) 1/ 3
[3]
(C) 1
(D*)
The greatest integral value of k for which the equation x2 2x + k 5 = 0 possesses atleast one negative root,
is
[3]
(A) 2
(B) 3
(C*) 4
(D) 5
a b c
b
c a is
If a, b, c are sides of a scalene triangle, then value of
c a b
(A) positive
6.
tan
5
15
[3]
(B*) negative
(C) non-positive
[3]
(D) non-negative
If A is a skew symmetric matrix of order n, then the maximum number of non zero elements in A is [3]
(A)
n (n 1)
2
(B)
n (n 1) ( 2n 1)
6
(C*) n (n 1)
(D)
n2 (n 1)2
4
Consider the inequality, (x + 3)n (x 2) < 0, n N. Then the correct statement(s) is/are
(A*) the largest integral x satisfying the inequality is 1, if n is even
(B*) the least integral x satisfying the inequality is 2, if n is odd
(C) number of integral x satisfying the inequality is 3, if n is odd
(D*) number of positive integral x satisfying the inequality is 1, if n is even
[3]
Subjective
8.
a (2, 3 ] [ 3 , 2)
1
9.
a2 7
+
= 2
. Find
1 1 a 4
[5]
a=
1
3
8
, then find the value of 'a'
27
[4]
Subject : Maths
31-07-08
Date : __________
54
DPP No. ____
Class : XI
M.M. 29
Time: 45 Min.
Comprehension (Q.1 to 3)
If A is any square matrix, then |A xI| = 0 is called characteristic equation of matrix A. Its roots are called
characteristic roots of matrix A.
1.
2.
3.
0 0
a 2 4
1 2 4
1 0
0
b
3
0
2
3
Let A =
, (a < b < c), B =
and C =
( > > ).
0 0 c
0 0
3
[3]
Characteristic roots of matrix (A + B)1 are , , , where > > and A is obtained in previous question of
this paragraph, then
[3]
1
4
2
3
1
1
5
(A) = 2, = 0, = 2 (B*) = , = , = (C) = 4, = , = (D) = , = , = 0
6
3
3
8
2
4
2
Characteristic equation of matrix AT + C, where A and C are as obtained in previous questions of this
paragraph, is
[3]
(A) does not exist
(B*) x3 18x2 + 99x 162 = 0
(C) 80x3 120x2 + 53x 6 = 0
(D) 24x3 25x2 + 6x = 0
If sin x + cos x =
(A) , 2
4
5.
(B) GP
7.
1
, x [0, ], then ordered pair (x, a) is equal to
a
3
3
(B) , 1
(C) , 2
(D*) , 1
4
4
a1 a 2 a p
If a 2 a 3 a q = 0 , then p, q, r are in :
a 3 a 4 a r
(A*) AP
6.
2
Let A =
4
(B) 256
(C) HP
[3]
[3]
(D) none
1
, then |a b| is equal to
b
(C) 1024
(D*) 0
1
, then
2
[3]
[3]
5 2
STATEMENT - 1 : I + 2A + 3A2 + 4A3 + ......... = 8 3
and
9.
[4]