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Important Questions for ISC Mathematics 2017

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Arijit Saha
The Bhawanipur Gujarati Education Society School (BGES), Kolkata

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ISC MATHEMATICS 2017 TEST PAPER Answer Section A and Either Section B or C SECTION A [10x3+10x5 = 80 marks] Question 1( Answer Q1 and any other five) 2 3 1 2 -1 -1 and B = 1 2 , Find (AB) 1 0 1. a) If A= b) Determine the value of k so that the line y=2x+k may touch the ellipse 3x 2 5 y 2 15. [ 23 ] [0] c) Prove that 4(cot 1 3 cos ec 5) 1 d) Evaluate Lt log sin 2 x sin x using L Hospital s Rule. [1] x 0 e) Evaluate tan x sin x cos x dx [2 tan x C ] f) Given mx-y+10=0 and -2x+5y=14 are the lines of regression of x on y and y on x respectively. Find the value of m if the coefficient of correlation between x and y is 1/ 10. [4] g) In a hostel 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both the newspapers. A student is selected at random. Find the probability that she reads neither Hindi nor English newspaper. [0.2] 1 h) Evaluate 5x 3 dx [13/10] 0 i) If p and q are complex cube roots of unity, then prove that (1+p)(1+q)(1+p2)(1+q2)=1. j) Solve the differential equation: 1 y 2 1 log x dx xdy 0. [(1+logx)2=-2tan-1y+C] Question 2 a b ax by a) Prove using the properties of determinants that: b c bx cy b 2 ac ax 2 2bxy cy 2 . ax by bx cy 0 5 1 0 3 , find the inverse of A and hence solve the following system of linear equations: b) If A= 2 0 0 3 1 5x +2y = - 1, 3z-x = 4, 3y - z = 5. [-1,2,1] Question 3 a) Solve tan 1 ( x 1) tan 1 ( x 1) tan 1 8 . 31 [1/4] b) Draw the circuit: (x+y )(x +y)(x +y ). Simplify it by the laws of Boolean. Construct the simplified circuit. [x y ]

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