CBSE Guess > Papers > Important Questions > Class XII > 2009 > Maths > Mathematics By Mr. Tapas

CBSE CLASS XII

Sec - A

Q. 1. Write the identity element for the binary operation * defined on the set R of all real
numbers by the rule,
Q. 2. Evaluate :

Q. 3.

Q. 4. Without expanding show that  determinants is zero ?

Q. 5. Find the value of λ ,a non-zero scaler ,

Q. 6. The radius of a circle is increasing uniformly at the rate of 4 cm / sec. find the rate at Which the area of the circle is increasing when the radius is 8 cm?

Q. 7.
Evaluate   

Q. 8. For what value of λ are the vector perpendicular to each other where :

Q. 9.

Q. 10. Find the equation of line passing throughthe point ( -1 , 2, 1) & parallel to the line

SEC – B

Q. 11. Let N denote the set of all natural numbers & R be the relation on N x N  defined by
( a , b ) R ( c , d ) <=> ad ( b + c)  =  bc ( a + d ) , Check whether R is an equivalence
Relation on N x N .

Q. 12.

OR

Q. 13.

Q. 14.
is everywhere differential , find the values of a & b .

OR

Q. 15
.

OR

Verify Rolle ‘s theorem for the function on the indicated interval :

Q. 16. Find the intervals in which    is increasing or decreasing

Q. 17.
Evaluate

Evaluate the integral as a limit of sum :

Q. 18. Solve : (x 2 + x y ) d y = ( x 2 + y 2 ) dx

Q. 19.


Q. 20. Solve y d x – ( x + 2 y 2 ) d y = 0

Q. 21. Find equation of plane through the point ( 1 , 0 , -1 ) , ( 3 , 2 , 2) & parallel to the line

Q. 22. A laboratory blood test is 99 % effective in detecting a certain disease when it is , infact, present . However , the blood test yields a false positive result for 0.5% of the healthy person tested ,  if 0.1% of the population actually has the disease , what is the probability that a person has the disease given that his test result is positive ?

Sec – C

Q. 23. Evaluate definite integeral :

Q. 24.
are two square matrix , find AB hence

solve the system of linear equation ; x – y =3 , 2x + 3 y + 4z = 17 , y + 2z = 7

OR

Find the inverse of matrix by using elementary row
transformation

Q. 25. A point on the hypotenuse of a right triangle is at a distance a b from the sides of the triangle , show that the minimum length of the hypotenuse is

OR

A figure consists of a semi – circle with a rectangle on its diameter . Given the perimeter Of the figure , find its dimension in order that the area may be maximum?   

Q. 26. Compute the area bounded by the lines x + 2y = 2 , y – x = 1 &  2 x + y =  7 ? 

Q. 27. Find the probability distribution of the number of doublets in 4 throws of a pair
of a dice?

Q. 28. Find the equations of the line of shortest distance between the lines  & also the shortest distance .

Q. 29. A brick manufacturer has two depots , A & B , with stock of 30000 & 20000 bricks respectively  He receives orders from P , Q for 15000 , 20000 & 15000 bricks respectively. The cost Of transporting 1000 bricks the builders from the depots are given below :

Paper By Mr. Tapas
Swami Vivekananda Public School, jagadhri , Haryana