Mathematics & Statistics – Important Question Bank for Goa Board HSSC 2016 Examination

Q 1 (A) Choose the correct alternative from the given alternatives :
(B) Show that the function f : R – R given by fx
(C) y log tan #$ % & ‘( , then show that
(D) Using integration , prove that dx log 3x & 4x + a3 & c
Q 2 (A) Choose the correct alternative from the given alternatives :
(B) If y = sinx, then prove that 1 + x ) *
(C) Find the value of x if the points ( 3, 2, 1 ) , ( 4, x, 5 ) , ( 4, 2, -2 )
(D) Define continuity of the function f(x) at x = a. Find the values of a and b
Q 3 (A) Choose the correct alternative from the given alternatives :
(B) If AT Is a binary operation on the set of integers A defined by
(ii) the inverse of an element in A if exists.
(C) Find the differential equation of the family of curves given by
(D) Prove that E fxdx E fx & E f2a + x C
Q 4 (A) Two cards are drawn at random without replacement from a pack of 52 cards . Find the probability that both the cards are black.
(B) A problem in mathematics is given to 3 students whose chances of solving it are ½ , – and ¼ . What is the probability that the problem is solved-
(C) Solve the differential equation 1 & edy & 1 & yedx 0
(D) Using integration , find the area of the region enclosed between
(B) Using determinants , find the equation of the line joining the points (-1,2) and
(D) Solve the following equations using matrix method 2x – 3y + 5z = 11 3x + 2y – 4z = – 5 and x + y – 2z = – 3
Q 5 (A) Choose the correct alternative from the given alternatives :
(B) Find a unit vector perpendicular to each of the vectors
(C) By using properties of determinant as far as possible , prove that
(D) A diet is to contain at least 50 units of vitamin A and 100 units of minerals.

Q 7 (A) Define “ Symmetric matrix”
(B) Find area of the triangle whose vertices are (3,8), (-4,2) and (5,1) by using
(D) By using properties of Determinants as far as possible , show that
Q No 8 (A) Select and write the correct alternative from those given below.
A matrix in which all the non-diagonal elements are zero is called ——- matrix– Scalar – Diagonal – Square – Zero
(D) Solve 2x – y + z = 3 , -x + 2y -z =- 4 , x – y + 2z = 1 by using matrix method.
Q No 9 (A) ) Select and write the correct alternative from those given below.
If R be the relation in the set N given by – (2,6) – R – (3,8 ) – R – (6,8) – R – (8,7) – R
(B) Write the constraints for the following shaded region
(C) Show that the function f : R – R given by fx
(D) Find the values of a and b such that the function defined by
f(x) = 5 , if x = 2 = ax + b , if 2 < x < 10 = 21 , if x=10 Is continuous in its domain.
Q No 10 (A) Select and write the correct alternative from those given below.
(B) Evaluate 0 9v; v dx (C) Find 02 x<2x
(D) Attempt any one of the following : (i) Evaluate 0 Log 9 x dx (ii) Evaluate 0 >- AT 1A Q No 5 (A) Select and write the correct alternative from those given below.
The difference between the resources and Liabilities of a firm is called its —–
(C) Solve the differential equation x (1 + y ) dx – y0 given that y = 0 when x = 1
Q No 11 (A) Define “ Ordinary Annuity”
(C) Form differential equation representing the given family of curves by eliminating
(D) A man is known to speak truth 3 out of 4 times . He throws a die and then reports that itis a six . Find the probability that it is actually six.
(E) Attempt any one of the following :
post office that pays 12% p.a. compounded monthly. What is the future value of amount in the account of post office at the end of 6 years- (Use log tables)
Q No 12 (A) Define “ Bill of exchange”in the ratio 3 : 2 . Calculate the gaining ratio.
(C) A , B , and C started a partnership and invested Rs.100000 , Rs. 80,000 and Rs.

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