Maths Class - XII 1998 (CBSE)
You are on Set no 1 Question 1 to 20

Q1) By using elementary row transformations, find the inverse of the matrix

A =

1  2 2  -1

Q2) Express the matrix 

A =

3  -4 1  -1

as the sum of a symmetric and a skew symmetric matrix.

Q3) Show the vectors - 2 + 3 ,  -2 + 3 - 4,  - 3 + 5 are coplanar.

Q4) If x = x and x = x , prove that - is parallel to - , provided and .

Q5) Verify Rolle's theorem for the function f(x) = x² - x - 6 in the interval [-2,3]

Q6) Evaluate

lim   x->

(Sin x/(x - ))

Q7) Differentiate tan^-1 [cos x/(1 + sin x)] w.r.t. x

Q8) Evaluate:- 

(log x)2 /x dx

Q9) Evaluate:- 

xex/(x + 1)2 dx

Q10) Evaluate 

8   |x - 5| dx 0

Q11) Evaluate

dx        (2 - 4x + x2)

Q12) Evaluate

/2   sin x - cos x  dx    (1 + sin x cos x) 0

Q13) Solve the differential equation. dy/dx + [(1 - y²)/(1 - x²)] = 0

Q14) Two unbiased dice are thrown. Find the probability that neither a doublet nor a total of 10 will appear.

Q15) Find the regression coefficient of y on x for the following data:
x = 24, y = 44, xy = 306, x² = 164, y² = 574, n = 4

Q16) Using the properties of determinants, Prove that

a+b+c   -c       -b -c       a+b+c   -a -b         -a     a+b+c

= 2 (a+b)(b+c)(c+a)

Q17) A variable plane passes through a fixed point (1, 2, 3). Show that the locus of the foot of the perpendicular drawn from origin to this plane is the sphere given by the equation:
x² + y² + z² - x - 2y - 3z = 0

Q18)  If a, b, c are the lengths of the sides opposite respectively to the angles A, B, C of a ABC, using vectors prove that cos c = (a² + b² - c²)/2ab

Q19) Two balls are drawn at random from a bag containing white, 3 red, 5 green and 4 black balls, one by one without replacement. Find the probability that both the balls are of different colours.

Q20)  Find the probability distribution of the number of heads in three tosses of a coin