Maths – Important Question Bank for Gujarat Board (GSEB) HSC 2016 Examination

1. Find the intervals in which the function f given by

  f(x) = sin x + cos x, 0 ≤ x ≤ 2π

is strictly increasing or strictly decreasing.

2. On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

3.  Write the principal value of cos-1[cos(7π/6)].

4.  Write the direction cosines of a line equally inclined to the three coordinate axes

5. In what ratio does the point (3, −1) divide the join of the points (4, 2) and (5, 5).

6. Find the general solution of the equation

sin x +sin 2x + sin 3x = 0

7. Find the square root of – 15 – 8i. Hence find the square root of – 15 + 8i

8. Solve the system of equations using matrices

x + y + z = 6

2x – y + z =3

x – 2y + 3z =6

9.  Find the area of the region enclosed by the parabolas

y2 = 4ax and x2 = 4ay for a >0.

10. A pair of dice is thrown 10 times. If getting a doublet (same number on both) is considered a success, find the probability of

(i) For successes

(ii) No success

11. Reduce the equations of the line given by 3x +2y –z – 4 = 0 and 4x + y –2z + 3 = 0 in symmetric form.

12. How many ways can 4 boys and 3 girls be seated in a row of 7 chairs if boys and girls alternate?

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

(a) the perimeter,

(b) the area of the rectangle

14.  If the sum of the lengths of the hypotenuse and a side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between them is π/3.

15. A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5,760 to invest and has a apace for at most 20 items. A fan costs him Rs. 360 and a sewing machine Rs. 240. His expectation is that he sell a fan at a profit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize the profit? Formulate this as a linear programming problem and solve it graphically.

16. Find the equation of the plane determined by the points A (3, -1, 2), B (5, 2, 4) and C (-1, -1, 6). Also find the distance of the point P(6, 5, 9) from the plane.

17. The scalar product of the vector i + j + k with the unit vector along the sum of vectors 2i + 4j -5k and λi + 2j +3k in equal to one. Find the value of λ.

18. Using geometric progression, express 0.5 as rational number.

19. Prove that: nCr + nCr-1 = n+1Cr

20. Find the co-efficient of x10 in the expansion of (1+3×2)/(1- x2)3 mentioning the condition under which the result holds.

21. Find the vertex, focus, directrix and length of latus rectum of the parabola

5×2 + 24y = 0

22. Prove that

1/2.3 + 1/4.5 + 1/6.7 + …..∞ = 1 – log 2

23.  If A and B are two events, such that

P (A) = 0.8, P (B) = 0.6, P(AÇ B) = 0.5

then find the value of

(i) P (AÈB)

(ii) P (B/A)

(iii)P (A/B)

24. Solve the following, by simplex method

Minimize z = x1 + x2

Subject to

2×1 + x2 ≥ 4

x1 + 7×2 ≥ 7

x1 ≥ 0, x2 ≥ 0

25.  Evaluate: 0π∫ [x/(a2 cos2x + b2 sin2x)] dx

Let’s try to make this a two way exercise. While we gather the question banks, you might have some inputs on this too! Please use the comments box below and post questions that you think are important from your analysis. It would help the HSC community a lot.

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