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Class 12th CBSE Mathematics 29 Questions 100 Marks

Class 12th CBSE Mathematics 29 Questions 100 Marks

Class – XII

Subject –MATHEMATICS

Q. 1 A matrix A of order 3× 3 has determinant 5. What is the value of ?

Q. 2 For what value of x, the following matrix is singular ?

Q. 3 Evaluate the determinants.

Q. 4 What is the principal value of

?

Q.5 Give an example of a relation which is reflexive and transitive but not

Symmetric;

Q.6 The radius of a circle is increasing at the rate of 0.7 cm/s. what is the rate

of increasing of its circumference ?

Q.7 .

Q.8 Find the projection of the vector = , on the vector

= .

Q.9 Find if for a unit vector ,

Q.10 Show that the points (2,3,4), (-1,-2,1),(5,8,7) are collinear.

__SECTION – B__

Q.11 Write the function in the simplest form , x

Q12 Show that the function f(x) = is the continuous at every x

but fails to be differentiable at x = -2.

P.T.O.

Q.13 Using properties of determinants, prove that

Q.16 Find the equation of the tangent line to the curve y = x2 - 2x+7 is parallel to the line

2x - y + 9 = 0 .

Q 17 Evaluate

OR

Q.18 Evaluate .

OR

Q.19 Evaluate as the limit of the sum.

Q.20 Find the area of the parallelogram whose adjacent sides are represented

by the vectors and .

Q.21 Find the shortest distance between the lines, whose equations are

OR

Prove that the image of the point (3,-2,1) in the plane 3x – y + 4z = 2

lies on the plane, x + y + z + 4=0 .

Q .22 There are 5% defective items in a large bulk of items. What is the Probability that a

sample of 10 items will include not more than one defective items ?

P.T.O.

__SECTION - C__

23

OR

Consider f : R given by f(x) = 9x2+6x-5. Show that f is Invertible.

Find the inverse of f.

Q.24 A point on the hypotenuse of a triangle is at distance *a* and *b* from the Sides of the

triangle.

Show that the minimum length of the hypotenuse is

Q.25 Find the area of the region bounded by the curve y = x2+2, and the lines y =x, x = 0

and x = 3.

Q.26 Solve the differential equation

(tan-1y - x)dy = (1 + y2) dx.

Q.27 Find the vector equation of the line passing through the (1,2,3) and parallel to the

planes = 5 and = 6.

OR

Q.28 Two godowns A and B have grain capacity of 100 quintals and 50 quintals

respectively.They supply to 3 ration shops, D,E and F whose requirements

Are 60,50 and 40 quintals respectively. The cost of Transportation per

quintal from the godowns to the shops are given in the following table ;

How should the supplies be transported in order that the Transportation cost

is minimum ? what is the minimum cost?

Q.29 A factory has two machines A and B. past record shows that machine A produced 60%

of the items of output and machine B produced 40% Of the items. Further, 2% of the

items produced by the machine A and 1% produced by the machine B were defective.

All the items are put into One stockpile and then one item is chosen at random from

this and is Found to be defective. What is the probability that it was produced by

machine B?

Paper Submitted By:

Name: ATAL BIHARI GUPTA

Email: atalbg@gmail.com

Phone No. 9450430500

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