gbshse.gov.in : HSSC Mathematics Question Paper Model Goa Board Of Secondary & Higher Secondary Education

Board : Goa Board Of Secondary & Higher Secondary Education
Subject : HSSC Mathematics
Document type : Model Question Paper
Website : gbshse.gov.in

Download Sample/Model Question Papers :
https://www.pdfquestion.in/uploads/5870-design_maths.pdf

GBSHSE HSSC Mathematics Question Paper

GOA BOARD OF SECONDARY AND HIGHER SECONDARY EDUCATION
ALTO BETIM – GOA 403521
HSSCE MATHEMATICS (754 )[ effective from March 2015]

Related : Goa Board Of Secondary & Higher Secondary Education SSC Social Science –I Question Paper Model : www.pdfquestion.in/5868.html

MODEL QUESTION PAPER
Time : 2½ hrs. Max Marks : 80

General Instructions

** This question paper contains seven main questions.
** All seven questions are compulsory.
** Answer each main question on a fresh page.
** Use of calculator is not allowed.
** Log tables will be supplied on request.
** Graphs should be drawn on the answer paper only.
** For each main questions the subquestions carry the following marks :
A = 1 mark , B = 2 marks , C = 3 marks , D = 4 marks , E = 5 marks.

Sample Questions

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

Q 5 (A) Find X if Y =I3 2 1 4 L and 2X + Y = I 1 0 +3 2 L
(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 6 (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 atleast 50 units of vitamin A and 100 units of minerals.

Q 6 (A) Choose the correct alternative from the given alternatives : The point on the curve y = x2 – 2x + 3 at which the tangent is parallel to x – axis is __
(2 , 1) (1, 1) (2 , 2) (1 , 2)
(B) Find a unit vector perpendicular to each of the vectors M^ & O^ & P Q FGH M^ & 2O Q & 3PR
(C) By using properties of determinant as far as possible , prove that

(D) A diet is to contain atleast 50 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available . Food F1 costs Rs 4 per unit of food and F2 costs Rs 6 per unit of food. One unit of food F1 contains 3 units of vitamin A and 4 units of mineral . One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem and find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

(E) Attempt any one of the following:
(i) Find the equation of the line passing through the point (3,4) which cuts X and Y axes at the points A and B respectively such that area of ? ABC is minimum .