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

We had mentioned some tips for cracking the HSSC Goa Board exam here: HSC Study Tips to Crack HSC Exams.

We had also shared Important Questions Bank for HSSC Examination 2016 and students have really appreciated it and showered us with love last year.

Today, we are posting the Mathematics & Statistics* *– Important Questions Bank for Goa Board HSSC 2016 Examination to make life easy for all you HSSC students.

Without making you wait any further, please find the questions below:

**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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