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• Question 2

Write the value of the following integral:

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• Question 4

Write the adjoint of the following matrix:

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• Question 5

If f: RR be defined by, then find of fof(x).

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• Question 7

What positive values of x makes the following pair of determinant equal?

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• Question 8

A is a square matrix of order 3 and. Write the value of .

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• Question 9

Write the distance of the following plane from the origin.

2xy + 2z + 1 = 0

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• Question 10

If and are two vectors such that, then what is the angle between and?

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• Question 12

A family has 2 children. Find the probability that both are boys, if it is known that

(i) at least one of the children is a boy,

(ii) the elder child is a boy.

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• Question 13

Show that the relation S in the set A = {x ∈ Z: 0 ≤ x ≤ 12} given by S = {(a, b): a, b ∈ Z, |a − b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1.

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• Question 14

If , then find the value of A2 − 3A + 2I.

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• Question 15

Find the points on the line at a distance of 5 units from the point P (1, 3, 3).

OR

Find the distance of the point P (6, 5, 9) from the place determined by the points A (3, −1, 2), B (5, 2, 4) and C (−1, −1, 6).

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• Question 16

If and , find a vector of magnitude 6 units which is parallel to the vector

OR

Let and Find a vector which is perpendicular to both and and = 18.

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• Question 17

Solve the following differential equation:

|x| ≠ 1

OR

Solve the following differential equation:

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• Question 20

Show that the following differential equation is homogeneous, and then solve it:

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• Question 23

Find the equations of the tangent and the normal to the curve at

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• Question 24

Find the equation of the plane passing through the point P (1, 1, 1) and containing the line. Also, show that the plane contains the line

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• Question 25

Using properties of determinants, prove the following

OR

Find the inverse of the following matrix using elementary operations

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• Question 26

A bag contains 4 balls. Two balls are drawn at random, and are found to be white. What is the probability that all balls are white?

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• Question 27

Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y.

OR

Using integration, find the area of the triangle ABC, coordinates of whose vertices are A (4, 1), B (6, 6) and C (8, 4)

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• Question 28

One kind of cake required 300g of flour and 15g of fat, another kind of cake requires 150g of flour and 30g of fat. Find the maximum number of cakes which can be made from 7.5 kg of flour and 600g of fat, assuming that there is no shortage of the other ingredients used in making the cakes. Make it as an L.P.P and solve it graphically.

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• Question 29

If the length of three sides of a trapezium other than the base is 10 cm each, find the area of the trapezium, when it is maximum.

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