Important Questions To Study For Karnataka II PUC Mathematics Exam

Important Topics To Study

1. Types of relations
2. Principal value branches
3. Invertible matrices
4. Determinant of a square matrix
5. Derivatives of composite functions
6. Tangents
7. Integrals
8. Algebra of vectors
9. Types of LPP
10. Probability distribution of variables

Important 1 Mark Questions

1. Find the principal value of cosec ^ -1 (-root 2).
2. If A is a square matrix with |A| = 8, then find the value of |AA'|.
3. Define collinear vectors.
4. Find the direct cosines of a line which makes equal angles with the positive coordinate axes.

Important 2 Marks Questions

1. Find the values of k, if area of triangle is 4 sq cm. Units and vertices are (k,0), (4,0) and (0,2) using determinant.

2. Find the approximate change in the volume of a cube of size x metres caused by increasing the side by 3%.

3. Verification of Rolle's theorem for various functions provided.

4. Find the probability distribution of number of heads in two tosses of a coin.

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Important 3 Marks Questions

1. Show that the relation R in A (set of real numbers) is defined as R = [(a,b):a<=b] is reflexive and transitive but not symmetric.

2. Form the differential equation of the family of circles having centre on y axis and radius 3 units.

3. If A and B are symmetric matrices of the same order, then show that AB is symmetric if and only if AB = BA.

4. Given that the two numbers appearing on throwing two dice are different. Find the probability of the event 'the sum of numbers on the dice is 4'.

Important 5 Marks Questions

1. Let f:N->R be a function defines as f(x) = 4x^2 + 12x + 15. Show that f:N-> S, where S is the range pf f, is invertible. Find the inverse of f.

2. The length x of a rectangle is decreasing at the rate of 5cm/minute and the width y is increasing at the rate of 4cm/minute. Whe x = 8cm and y=6cm, find the rate of change of the perimeter and the area of the rectangle.

3. Derive the equation of a plane perpendicular to a given vector and passing through a given point both in vector and Cartesian form.

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Important 10 Marks Questions

1. Show that | x x^2 yz
                     y y^2 zx
                     z z^2 xy| = (x-y)(y-z)(z-x)(xy+yz+zx)

2. Minimise and maximise z = 600x + 400y
Subject to the constraints:
x+2y<=12
2x+y<=12
4x+5y>=20 and x>=0, y>=0 by graphical method.