Organisation : West Bengal School Education
Exam : Higher Secondary HS Exam
Paper: Mathematics
Document Type : Model Question Paper
Year :
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Higher Secondary Mathematics Model Question Paper :
Mathematics – Part I :
Find the correct answer – 1
Principal, time and rate of interest – out of these three if any two remain invariant, the remaining one bears with total interest
(i) direct relation
(ii) inverse relation
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(iii) no relation
(iv) any relation
(ii) Find the correct answer – 1
m, (m-1) are factors of m3 – m. The remaining one will be
(i) m2-1
(ii) 1-m
(iii) m+1
(iv) m2 + 1
Solution :
Given, m3 – m
= m(m2 – 1)
= m(m+1)(m-1)
Since the given factors are m and (m-1), the remaining factor is (m+1)
Ans: The remaining factor is (m+1) (iii)
(iii) Determine the value of a for which the expression (a-2)x2 + 3x + 5 = 0 will not be a quadratic equation.
Solution: The expression will not be a quadratic equation,
if (a-2) = 0
i.e. a – 2 = 0
or, a = 2
Ans: For a = 2, the given expression will not be a quadratic equation.
(iv) Find the distance between the points (-3, 0) and (7, 0). 1
Length of AB = v [(x1
– x2)2 + (y1 – y2)2]
= v [( 7 + 3 )2 + (0 – 0)2]
= v 100 = 10 units
Ans: The distance is 10 units
(v) If the whole surface area and the volume of a cube are numerically equal, what is the length of its side? 1
Solution: Let the length of one side of the cube be a units.
Total surface area of the cube = 6a2 units
And, volume = a3 units
By the problem, a3 = 6a2
or, a = 6
Ans: The required length of the cube is 6 units.
(vi) Find the correct answer- 1
If 0? = ? = 90o and sin ? = cos ? then ? will be
(i) 30o
(ii) 60o
(iii) 45o
(iv) 90o
Ans: θ = 45o (iii)
2 (a) If there be a loss of 11% in selling an article at Rs. 178, at what price should it be sold to earn a profit of 11%?
Ans: The sale price of the article is Rs. 222.
(b) What should be the values of a and b for which 64×3 – 9 ax2 + 108x – b will be a perfect cube.
Ans: a = 48 and b = 729
(c) For which value of r, rx + 2y = 5 and (r – 1)x + 5y = 2 have no solution? 2
Solution: We know, if a1x + b1y=c1 and a2x + b2y=c2 are two equations then there will no solution if,
Ans: The value of r is (– 2/3 ).
(d) If x2 – x /yz = y2-yzx /z2 /xz xy , prove with reasons that x = y = z
(e) State Pythagoras’ Theorem. 2
Ans: The area of the square on the hypotenuse of a right angled triangle is equal to
the sum of areas of the squares on other two sides.
(f) Side AB of a cyclic quadrilateral ABCD is produced to X. if ? XBC = 82o and ?ADB=47o find the value of ? BAC.
(g) Show that 1o < 1c
Ans: A’s profit is Rs. 500 and B’s profit is Rs. 480.
3. Answer any two questions : 5× 2=10
(a) A and B started a business with capitals of Rs. 3000 and Rs. 4000 respectively. After 8 months, A invested Rs. 2500 more in the business and 7 months after this, total profit becomes Rs. 980. Find the share of profit for each.
(b) At 10% per annum, the difference of compound interest, compounded annually and simple interest on a certain sum of money for 3 years is Rs. 124. Find the sum of money.
(c) A person purchased some agricultural land at Rs. 720000. He sold 31 of the land at 20% loss, 52 at 25% profit. At what price should he sell the remaining land to get an overall profit of 10%.
(d) Ratio of acid and water in one container is 2:7 and the ratio of same acid and water in another container is 2:9. At what ratio, the contents of the two containers should be mixed to have the ratio of acid and water as 1:4 in the new mixture?