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Brooklyn School Dehradun Mathematics: X Science First Quarterly Examination :2023 MM- 80 Time: 2 Hrs 30 mins Note: Attempt all Questions from section A and any four questions from section B. section A Q-1 Choose the correct answers to the questions from given options : i) ii) [15] The CGST paid by the consumer to the retailer for an article which priced at Rs. 1050 is Rs 55. The rate of GST charged is : a) 10.8 % b) 10 % c) 10.47% d) 11 % The solution set for the given inequation is: 2<2x - 6 2 , x W. a) { 1,2,3,4,5} b) { 0,1,2,3,4} c) { 0,1,2,3,4,5} d) { 0,1,2,3,4,5,6} iii) The probability of head coming in the throw of coin containing tail in both the sides is given by p then the expected value of p is given by: i) P=1 ii) p < 1 iii) p > 0 iv) p=0 iv)If the roots of the given quadratic equation are real and equal then the value of discriminant is i) -1 ii) 0 v) If ( x+2) is a factor of a) 12 vi) 2 1 0 7 a)2 x 1 vii) iii) 1 1 0 iv) Infinite 3x3+2x2-4x-4. b) 18 A= : 0 1 c) -12 d) -18 then the order of matrix A is given by: b) 2 x 2 c) 1 x 2 d) 1 x 1 45,42, 39, 36,_____ are the A.P . The value of 10 th term is : a) -20 b) 18 c) -18 d) -20 viii) The total investment on Rs, 100 share available at 20 % premium is Rs 12000, then the number of shares received are : i) 1200 ii) 12 iii) 102 iv) 120 ix) If x3- x2-x-8 is divided by x-1 then the value of remainder is : a)-8 b) 5 c) -9 x) If 3 1 10 a) -3 0 7 b) 9 d) 9 8 0 + 0 7 c) -3 = 0 10 0 14 then the value of x : d) -9 xi) If the nth term of an A.P is 3n-7 , then the 12th term is : a) 29 b) -29 c) 29-n d) 36n-7 xii) What value of x will make the following terms 2x-1 ,3, 5, 7 in proportion : a) 12 b) 10 c) 13 d)11 xiii) What is the percentage of SGST in the GST: a) 100% b) 25% c) 50 % d) 35 % c) (-a, b) d) (-a, -b) xiv) Reflection of (-a,b) in the y axis is : a) (-a,-b) b) (a,-b) xv) If the probability of an event is then the value of Probability of not Event is : a) b) c) 0 d) Question 2: a) Aman deposits Rs. 1600 per month in a R.D A/C for 3 years at the rate of 9% p.a. simple interest. Find the amount Arvind will get at the time of maturity. b) Given A= c) 3 0 1 6 , = 1 0 0 1 and A2=9A+ m , find m. Solve the following quadratic equation + =5 [4] [4] [4] Q-3(a) If + , ab +cd, + are in continued proportion , prove that a,b, c and d are in proportion. [4] b) Five years ago , a woman s age was the square of her son s age . Ten years hence her age will be twice that of her son s age . [4] Find :i) the age of the son five years ago. ii) the present age of the woman. c)Use the graph sheet for this question . (Take 1 cm =1 unit along the axis) [5] The triangle ABC where A(1,2) , B(4,8) and C(6,8) is reflected in the x axis to triangle A B C . The triangle A B C is then reflected in the origin to triangle A B C . i) ii) Write down the coordinates of A ,B ,C . Write down the single transformation that maps triangle ABC on the triangle A B C . Section B( Attempt any four question from this section) Q-4(a)Cards marked with numbers 1,2,3,4, .,20 are well shuffled and a card is drawn at random . What is the probability that the number on the card is i) a prime number ii) divisible by 3 [3] iii) a perfect square number ? b) Solve the following quadratic equation: + + = [3] , p+q 0 ,p 0, q 0. c) Show that (x-1) is a factor of x3-7x+14x-8. Hence, completely factorise it. [4] Q-5 a) The following bill shows the GST rates and the marked price of articles: Aticles Marked Price Bicycle 10,590 Shoes 5980 Find the total amount to be paid for the above bill. Rate of GST 18% 24% b)Solve the following Quadratic equation : [3] 7x 2 + 2x -2 =0 (give your answer to two decimal place) 4 2 3 6 ,B= and C = , evaluate AB 4 C. 6 5 5 5 c) = Q-6 (a) x= prove that 3bx2-2ax+3b=0. [3] [4] b)Which term of the A.P 3,15,27,39 , .. will be 132 more than its 54 th term. [3] c) If = [3] = . Question 7 a) In an auditorium seats are arranged in rows and columns. The number of rows was equal to the number [4] of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 10, the total number of seats increased by 300. Find i)The number of rows in the original arrangement. ii) the number of seats in the auditorium after re-arrangement. b)Find the values of x, which satisfy the inequation. -2< - [3] , x N. Graph the solution set on the number line. c) The ratio of 11th term to the 18th term of an A.P. is 2:3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of first five terms to the sum of first 21 st terms. [3] Question 8 a) Mr. Prakesh invested Rs. 52,000 on Rs. 100 shares available at a discount of Rs. 20 paying 8 % dividend. [3] At the end of one year, he sells the shares at a premium of Rs. 20 . Find : i) the annual dividend ii) the total annual profit earned including his dividend. b) The king, queen and jack of clubs are removed from a deck of 52 playing cards and then shuffled. A card [4] is drawn from the remaining deck. Find the probability of getting: i) a heart ii)a queen iii)a club iv) 9 of red colour. c) A point P under reflection in y-axis is mapped onto P , (2,3) .i)Find the coordinates of P. ii)Find the coordinate of the image of P under reflection in the line x=-1. Question 9: a) If = = show that + + = [3] b)Find X and Y , If X + Y= 30 10 [3] [3] 10 6 and X Y = 10 0 0 10 c) If ( x 2) is a factor of the expression 2 + + 14 and when the expression is divided by (x- 3), it leaves the remainder 52. Find the values of a and b. [4] Question 10: a)A man deposits Rs. 200 per month in a recurring deposit account at 9% p.a and earned a total interest [3] Of Rs. 1764. How many installments did he pay? b) Find the nature of roots of the following quadratic equation . If the real root exist , find them. [3] 3x2-4 3x+4=0 c)If the pth, qth ,and rth term of an A.P are a,b and c respectively , then show that (a b)r + ( b c) p + (c a)q = 0. _____________________________ Paper Ends Here__________________________________ [4] The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones [5]Of radius 3.5 cm and height 7 cm. Calculate i) the radius of the sphere. ii)the number of cones recast. (Take = ). Q-3(a) The mean height of 8 students is 152 cm. Two more students of height 143 cm and 156 cm join the group.[3] What is the new mean height ? c) Use Factor Theorem to Factorise completely x3+x2-4x-4. [4] Q-4 (a) Prove the identity : [3] + = 2 cosec A. b) Section B( Attempt any four question from this section) Q-5(a)Cards marked with numbers 1,2,3,4, .,20 are well shuffled and a card is drawn at random . What is the probability that the number on the card is i) a prime number [3] ii) divisible by 3 iii) a perfect square? b)Two vertices of a triangle are (-1,4) and (5,2).If the centroid is (0,-3), find the third vertex. [3] c) Show that (x-1) is a factor of x3-7x+14x-8.Hence, completely factorise it. [4] Q-6(a)Calculate the mean and median of the numbers 2,1,0,3,1,2,3,4,3,5. [3] b)A person standing on a bank of river observes that the angle of elevation of the top of the tree standing on [4] the opposite bank is 600 When he moves 50 m away from the bank he finds that the angle of elevation to be 30 0. Calculate i)the width of the river and ii)the height of the tree. Q-7 a) How many terms of the series 3 + 3 + 3 3 + . Will make the sum 39 + 13 3 ? [3] b) Find the equation of the line parallel to the line 3x+2y=8 and passing through the point (0,1). [3] c)In a school ,the weekly pocket money of 50 students is as follows: [4] Weekly 40-50 50-60 60-70 70-80 pocket money( ) No. Of 2 8 12 14 Students Draw the Histogram on the graph paper and find the mode from the graph. 80-90 90-100 8 6 Q-8 a) A man invests 9600 on 100 shares at 80.If the company pays him 18% dividend, find: [3] i)the number of shares he buys. ii) his total dividend. iii)his percentage return on the shares. b [4] Q-9 a) Solve the equation 3x2-x-7=0 and give your answer correct to two decimal places. [3] c) A line passes through the point P(3,2) and cuts off positive intercepts, on the x-axis and the y-axis in the ratio [4] 3:4. Find the of the line. b) Mr. Lohia invests 26680 in buying 50 shares at a discount of 8%.He sells shares worth 15000 at a premium [3] of 6% and rest at a discount of 10%. Find his total gain Or loss from the transaction. paper ends Here ..
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