Mathematics – Important Questions Bank for Jammu and Kashmir (JKBOSE + 2) HSC 2016 Examination

1.Determine graphically the minimum value of the objective function Z=-50x+20y subject to the constraints.

2x – y ≥ – 5, 3x + y ≥ 3, 2x – 3y ≤ 12, x ≥0, y ≥ 0

2.  Define definite integral of a function and find the area under y = (x + c ^2x ) between the limits 0 and 4:

3. Define reflexive, symmetric and transitive relation with an example to each

4. State Lagrange’s. Mean value theorem and interpret geometrically.

5. One kind of cake requires 200 kg of flour and 25 g of fat and another kind of requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 Kg of flour and 1 Kg of ft assuming that there is no shortage of the other ingredients used in making the cakes.

6. The side of a square sheet of metal is increasing at the rate of 4 cm per minute. At what rate is the area increasing when the side is 8 cm long?

7. Prove by vector method an angle in a semi circle is a right angle

8. Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

9. A die is rolled, if the outcome is an even number. What is the probability that it is prime number?

10. Solution of the differential equation X dy-Y dx =0 represents.

i) A rectangular hyperbola

ii) A straight line passing through origin

iii) Parabola whose vertex is at the origin

iv) Circle whose centre is at the origin

11. Define symmetric and skew symmetric matrices. Prove that every square can be expressed as a sum of symmetric and skew symmetric matrices.

12. Define differentiability and continuity of a function. What is the relationship between them, justify your answer

13. Find the equation of the plane passing through the points (1, 2, 3) and perpendicular to the plane.

2x + 3y + 4z – 5 = 0

4x + 6y + 8z – 15 = 0

14. Define bijection function and show that the function.

F : R → R defined by f(x) = X³ + 1 is a bijection

15. Calculate absolute minimum value and absolute minimum value of

F (X) = – x3 + 10 x2 – 12x ; 3 ≤ x ≤ 9

16. Solve the Differential equation x dy = y dx.

17.  A weight of 36 Kg is suspended by two ropes 6 m and 8 m long fastened to two points on some horizontal line 10 m apart. Find tension in tow ropes.

18. Define inversal law of matrices

19. Define symmetric matrix

20. Define independent event

21. Define probability distribution function.

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