JAWAHAR NAVODAYA VIDYALAYA, VALASAPALLE. CHITTOOR DIST.A.P.DATE:
23-08-2011 CUMULATIVE TEST -03 CLASS: XII
MAX. MARKS: 40
MATHEMATICS
TIME: 11/2 Hours
[Chapters covered: Relations & functions, Inverse
Trigonometric functions, Continuity,
Matrices and determinants] I ANSWER ALL THE QUESTIONS:
01 x 06 = 06
01. Let A be a non singular square matrix of order 3 X 3. If
|A|= 3,
Then find| adj A|.02. Without expanding find the value of
2 7 65
3 8 75
5 9 86
03. Cos-1 cos 7 = ? 604. Find gof if f(x)= |x| and g(x)= |5x
-4|05. Examine that sin |x| is a continuous function.06. Find the
principal value of cosec-1(2)II ANSWER ALL THE QUESTIONS:
04 x 04 = 16
07. If tan-1 x -1 + tan -1 x + 1 =
x -2 x + 2 4
then find the value of x.
08. Solve the equation x+a x x x x+a x = 0, a 0.
x x x+a
09. Find the value of K so that the function f is continuous at
x = 5
if f(x) = Kx + 1, x< 5
cos x , x>5 10. Let * be the binary operation on Z defined by
a * b= a
b + 1 Determine whether 1. * is associative 2. * is
commutative
3. * has an identity element, inverse element?
III ANSWER ALL THE QUESTIONS:
06 x 03 = 18
11. Solve the system of equations by matrix method.
2x-z = 3, 5x + y = 7 and y + 3z = -1.
12. a. Find the relationship between a and b so that the
function f defined by ax + 1 , if x < 3
f(x) = bx + 3 , if x > 3 is continuous at x = 3. b. Find all
points of discontinuity of f, where
sin x if x < 0 f(x) = x x+ 1, if x> 0
13. a. Prove that tan-1 (1+ x) - ( 1- x) = /4 - 1/2 [ cos-1 x] ,
x [-1/2 , 1] (1+ x) + ( 1- x)
b. Write the function tan-1 (1+ x2 ) - 1 in the simplest form.
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