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ICSE Class X Prelims 2025 : Mathematics (St. Xavier's Institution (SXI), Panihati, Kolkata)

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1 ST. XAVIER S INSTITUTION, PANIHATI PRE-SELECTION 2024-2025 SUB: MATHEMATICS CLASS: 10 TIME: 1 HR 15 MINS MARKS: 40 [ SECTION: A] [20 MARKS] [ANSWER ALL THE QUESTIONS] . Choose the correct option for the following questions: 1 [1x8=8] + 2 = 5 and 6 = 7 are parallel, then the value of i) If the line 3 k is : a) - 9 b) 9 c) 8 d) 12 ( 2 )( 2 ) ii) 1 1 is equal to: a) 1 2 b) c) ( - 1) 2 d) , we add ( - 7) to both i ii) To solve the linear inequation 5 + 7 < 27 , sides. With the operation, the sign of inequality ______________. a) Reverse b) Remain same c) Data insufficient d) None of these 2 i v) The roots of the equation 4 5 3 = 0 are a) not real b) real and equal c) real and unequal d) cannot be determined v ) A point M is reflected in the X - axis to M (4, - 5) . M is the image of M when reflected in the Y - axis. The co-ordinate of M when M reflected in the origin, is : a) ( 4 , 5 b) ( 4 , 5 d) ( 4 , 5 ) ) c) ( 4 , 5 ) ) vi) Assertion: If = 2 and = ( 3 ) satisfies the polynomial 2 + ( + 1) + completely, then the values of a and b are 0 and (-6) respectively. Reason: If = satisfies a polynomial ( ) completely, then ( ) = 0 . ) Both assertion and reason are correct and reason is the correct a explanation of assertion. b) Both assertion and reason are correct but reason is not the correct explanation of assertion. c) Assertion is correct but reason is incorrect. d) Assertion is incorrect but reason is correct. 2 ( 2 2 ) is: v ii) If + 4 : = 4 : 1 , then : a) 1 : 4 ) 2 : 1 b c) 4 : 1 viii) If and a) 1 2 d) 1 : 2 , then the order of matrix A B is: b) 2 1 c) 2 2 d) 1 1 ) a) Find the equation of the straight line passing through the intersection 2 of 2 + 5 4 = 0 with X - axis and parallel to the line 3 7 + 8 = 0 . ) Three numbers are in AP and their sum is 15. If 1, 4 and 19 are added to b these numbers respectively, the resulting numbers are in GP. Find the numbers. c ) Use graph paper to solve this question. Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes. (i) A is the image of A when reflected in the X - axis. Write down the co-ordinates of A and plot it on the graph paper. (ii) B is the image of B when reflected in the Y - axis, followed by the reflection in the origin. Write down the co-ordinates of B and plot it on the graph paper. (iii) Write down the geometrical name of the figure AA BB . (iv) On the line segment BB identify a point D which is invariant under reflection in the X - axis and write the co-ordinates of the point D. [4+4+4] [ SECTION - B] [MARKS 20] [ANSWER ANY TWO] 2 2 2 2 3) a) Prove that: ( 1 + . ) + ( ) = . 2 , show that: 6 = 9 , where is a 2 2 unit b) If matrix. 3 2 c ) If + 13 + 66 has a factor ( 2) and leaves remainder ( 54 ) when divided by ( + 1 ) , find the values of and . With these values of and , factorise the given expression. [3+3+4] 3 4) a) Solve the following inequation and graph the solution on number line: 2 + 1 3 7 3 < 2 + 5 , b) If , are real and , then show that the roots of the equation 2 ( ) + 5 ( + ) 2( ) = 0 are real and unequal. c) If = 2 2 2 2 2 2 2 + + 2 2 2 2 , then show that 2 + = 0 . 2 + [3+3+4] ) a) The three vertices of a parallelogram taken in order are 5 ( 1 , 0 ), ( 3 , 1) and ( 2 , 2 ) respectively. Find the coordinate of the fourth vertex. ) A motor boat whose speed is 15 km/hr in still water goes 36 km b upstream and comes back to the starting point in 5 hrs. Find the speed of the stream. 2 2 2 2 c) Prove that: ( + ) + ( + ) = 7 + + [3+3+4] 0

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