Formatting page ...
ST. XAVIER'S INSTITUTION, PANIHATI REARSHAL TEST -2023-24 SUBJECT - MATHEMATICS CLASS- 10 TIME2 HRS 30 MINS FM-80 Attempt all the questions fronm Sectlon- Aand any Four questions from Section B [SECTION- A(40 Marks)l [ANSWER ALL THE QUESTIONSI Question:1 [15x1=15] Choose the correct answers to the questions from the given options. (Do not copy the questions, write the answers only) i) Mr. Ravi had invested 52000 in 18% Z200 shares at a premium of 30%. What is the total number of shares bought by Mr. Ravi? a) 4 0 0 b ) 250 d) 200 c) 222 i) The equation 2x+ kx +3 = 0 has two equal roots, then the value of k is a) t y6 c) + 342 b) 4 d) + 2/6 ii) If *- (a + 1)x + 56 is divisible by (x - 7), then the value of 'a' is a) 7 b) c) 10 14 d) 14 iv) If the order of matrix A is m x pand the order of matrix B is n x m, then the order of matrix BA is, c) m x n b) n X p a) p X n d) p x m v)The nth term of an AP is given by a = 3 + 4n.Then the common difference is , a) 7 b) 3 c) 4 d) 1 vi) Point (4,0) under reflection in X-axis will be, a) (-4,0) b)-(0,4) c) (4,0) d) (0,-4) vii) The pair of equations x = a and y= b graphically represent lines which are, a) Parallel c) coincident b) Intersecting at (b,a) d) Intersecting at (a, b) vii) Corresponding sides of twosimilar triangles are in the ratio 2:3. If the area of the small triangle is 48cm , then the area of the large triangle is a) 230 cm b) 106 cm? c) 107 cm d) 108 cm ix) Volumes of the two spheres are in the ratio27: 8.Ratio of their curved surface is, a) 9:4 b) 4:9 c) 3:2 (1) d) 2:3 circular coneof height l5 cm and right a of area surface x) the curved base diameter 16 cm is, b)68t cm a) 60r cm c) 1200r cm d) 136 cm is equal to xi) V d) None of these eggs is O.035. xii) The probability of getting a bad egg in a lot of 400 a) seco + tano b) seco - tan) c) tan - sec Then the number of bad eggs in the lot is c) 21 b) 14 a) 7 d) 28 xii) Which of the following can't be calculated graphically, b) Median c) Mode a) Mean X1V) A dealer sold a laptop to a consumer at 18%, then the is SGST will be a) 5400 b) 32700 d) Quartile 30000. The rate of GST 18 c) 2700 d) 35400 xv) Assertion: Atangent to a circle is perpendicular to the radius through the point of contact. Reason: The lengths of tangents drawn from an external point to a circle are equal. Choose the correct option from the following for the given Assertion-Reason problem. a) If both assertion and reason are correct and reason is the correct explanation of assertion. b) If both assertion and reason are correct, but reason is not the correct explanation of assertion. c) If the assertion is correct but the reason is incorrect. d) If the assertion is incorrect but the reason is correct. Question -2 a) A cylindrical can whose base is horizontal and radius 3.5 cm contains sufficient water so that when a sphere is lowered in the can, the water just covers the sphere. Given that sphere just fits into the can. Calculate the depth of water in the can before the sphere was puinto the can. (Use TT = 22 7 and give your answer correct to nearest cm ) b) Laxmideposits a certain sum of money each month in a recurring deposit account in a bank. If the rate of interest is 8% p.a and she gets Z8088 from the bank after 3 years, find the value of his monthly installments. c) Prove that: 1+ tanA sin A + 1+ cot A COs A = 2(sec A + cosec A). [4 + 4 + 4= 12 ] Question-3 a) If x, y and z are in continued proportion, then provo that: (+z) b)In the given figure, O is the centre of the A circle. IfZBAD = 75 and BC= CD, find: ii) ZBCD ) BOD BOC iii) iv) OBD c) Marks obtained by 200 students in Mathematics in selection test are given below: Marks 0- 10| 10 - 2020 - 3030 -40 40 -5050- 6060 - 7070-S0 Number of 10 24 22 34 34 38 32 students Taking 2 cm =10 marks on one axis and l cnm =10 students along other axis draw an ogive of the above distribution. Use the graph toestimate the following, i)Median ii) The upper quartile iii) The number of students scoring above 65 marks. |4+ 4 + 5 = 13] [SECTION - B(40 Marks)l [ANSWER ANYFQUR QUESTIONSI Question-4 a) Findx and y, if-2 b) Solve the quadratic equation 3x-x-7=0 and g ve youranswer correct to two decimal places. c) ABC is a right angled triangle with ZABC=90 , Dis any point on AB and DE l AC. Prove that: i)AADE~ AACB (3) find DE and AD. BC = 5cm, and AE = 4cm. i ) If AC=13 cm ii ) Find area of A ADE:area of quadrilateral BCED. [3+3+ 4 =10] Question-5 a) Calculate the mean of the following data using step deviation method: Class Frequency 0-50 50 - 100 17 35 100 -150 150- 200 250-300 24 21 40 43 200-250 b) The printed price of an AC is 45000 .The wholesaler allows a discount of 10% to a dealer. The dealer sells the AC to a customer at a discount of 4% on the marked price. If thesells are intrastate and the rate of GST is 18%,find, i) amount of tax (under GST) received by the central government. ii)amount of tax (under GST) received by the state government. i) The total amount (inclusive of tax) paid by the consumer for the AC. c) In the given figure, POQ is a chord of a circle with center O and PT is a tangent. If ZQPT= 60 , find ZPRQ. [3+3+4 = 10] Question-6 a) The fourth term ofa G.P. is the sauare of its 2nd term and the first term is (-3). Find its 7th term. b) A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of the hemisphere. If the diameter of their base is 6 cm each and the slant height of the cone is 5 cm, calculate, i) height of the cone and i)volume of the solid. c) In a school the marks of Mathematics aptitude test of 50 students are as follows Marks No. of students 50 - 60 4 60- 70 70- 80 14 80 90 19 90 - 100 5 Now taking 2 cm = 10 marks on one axis and 1 cm = 2 students on the other axis draw a histogram for the above data using graph paper and locate the mode. [3+3+ 4=10] (4) a) ion-1 Quest the P(equation 3,4),Q(7,-2the) andmedianR(-2, -1)thetriangle vertices of of are the of APQR. Write down through point . a invests sum of moneyin 100 shares, paying 16% dividend and quoted at 20% i)his total Jf his annual income is premium. T576, calculate i1) rate of investment return on his investment. c) b) A man From the top of the hill, the angle of depression of two consecutive found to be 30 and 45 respectively. of two stones from the foot of the hill. [3+3 +t 4= 10] kilometre stones, due east, are Find the distance Question-8 a) Solve the inequality and graph the solution set on the number line: st14<5xER b) For what value(s) of 'p' will the following equation have real and equal roots? (p - 12)x + 2(p - 12)x + 2 = 0 c) Construct a rectangular hexagon of side 4 cm. Construct a circle circumscribing the hexagon. [3+3 + 4=10] Question-9 a) Using properties of proportion, solve for 'x: 5 +y5-x =3 b) The sum of two numbers is 8and the sum of their squares is 34. Find the numbers. c) Using ruler and a pair of compasses, i) Construct a ABC with BC =6 cm, ABC = 120 and AB = 3.5 cm. ii)In the above figure, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC. ii) Measure ZBCP. [3+3+4= 10] (5) Question-10 a) Using factor theorem factorise: + - 4x - 4. numbers are b) From a pack of 52 playing cards allcards whose random, what is the 3 are removed. Acard is now drawn at multiple of probability that the card drawn is, i) a face card ii) an even numbered red card. c) Use a graph sheet for this question, Take 2 cm = 1 unit along both the X and Y - axes. i) The point P(2, -4) is reflected about the line x = 0to get the image Q. Find the co-ordinates of Q. ii) Point Q is reflected about the liney = 0 to get the image R. Findthe co-ordinates of R. ii) Point Q is again reflected about the origin to get the image S. Find the co-ordinates of S. iv) Find the area of the figure PQRS. [3+3+4 = 10] -0 - M (G)
|
