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UTH ERNOTI OEsaL REHEARSAL EXAMINATION MATHEMATICs CLASs x SESSION 2023-2024 Maximum Marks :80 providedseparately 15 minutes. Annvers to this write during the first to allowed be question paper. You will not in reading the answers. spent be to is time This allowed for writing the time the is Paper head ofthis The time given at the Section B four questions from any and A Section on the Attempt all questions fromwork, must be clearly shown, ezd must be done rougl All working, including same sheet as the rest of the answer. marks. woring will result in lcs of brackets [] of essential Time: 2 % hours on the paper Paper must be written questions cre given in parts of Omission or questio The intended marks forMathem:ical tables are provided. SECTION A this Section.) (Attempt all questions from [15] Question 1 questions from the given options. Choose the correct answers to the correct answers only.) the (Do not copy the question, write x*y& A then the values ofz and y ure b. x=7,y =2 X=2,y =7 d. x=-2,y =7 c. x=3,y =6 + 4, then the value ofa is (ii) If (x+2) is a factor of x+ ax C. 3 a. 1 b. -2 [1] d. 2 the owner (ul) If the cost of an articie is 225,000and CGST paid by is {2250, the rate of GST is b. 10% c. 15% Page 1 [11 d. 18% (iv)Value(s) ofk for which the qundratic equation 2x -kx k=0 has cqual roots are b. 4 d. 0,8 C. 8 () The value ofx for which 2x,(x+10) and (3x+2) are the thrce consecutive terrns of an AP. 6 b. -6 d. -18 C. 18 () Ifa 6, 18 and bare in continued proportion, then the values of aand bare aa= 2,b =45 b. a d. a=2,b =55 6, b=2 d. a=2, b=54 (vil) In AABC, points P and Q are on CA and CB, respectively such that CA=16 cm, CP-10em, CB- 30 cm and CQ=25cm. Then b. PQ AB PQ| AB d. None of these (vill) The dlameter of a sphere is 6 cm. It is melted and drawn Into a wire of diameter 2mm .The length of the wire is a. 12 m b. 18 m C. 36m d. 66 m (ix) In a throw of a pair of dice. What is the probability of getting a doublet? b. (3) The point of intersection of altitudes of a triangle is called a. Centroid b. Circumcentre C. Orthocentre d. Incentre (xi) From the given figure, the value of Zx+y is 270 b. 180 C. 90 Page 2 1 [1] d. None of these equal rots s (xi)is From 125 mhigh towers the angle from the tower? a. 125 m b, 60 m (xiii) if S0 shares are ata value of the share available is a. 65 of depression of a car is 45 Then how far the car 0. premium b. 60 75 m d. of 20% in the C. 75 d. market, then the market None of these (xiv) The centroid of AABC is G(6,7). If the and (5,7) respectively. Then of coordinates of the vertlces A,B value b, (xv) a is 6 C. 3 None of these andCare (a,5), (7,9) d. 7 Assertion: The mean of first n natural numbers is Reason: is [1] a. Both Median the value of most frequent observation of Assertion and Reason are correct and the given set of data. Asserio. Reason is the correct explanation of b. Both Assertion and Recason are correct, but Reason is of Assertion. not the correct C. explanation is IfAssertion correct but is Reason d. incorrect. IfAssertion is incorrect but Reason is correct. Question 2 j Ametallic cylinder has radius 3cm and height Scm. It is its made of metal A. To reduce weight, conical hole is with lighter metal B. The drilled in the cylinder, as shown and it is conical hole has a radius of 3/2 cm and completely calculate the ratio of the metal its depth 8/9filled A to the volume of cm, the metal B in the solid. 3 Page 3 ationaboutbutterflies a fair idea JG. follow IfAARC the Deepak has a recurring deposit account ina bank. He deposits 500 per month fo years.If he gets 2s410 at the time of maturity, find a b. Ln 14 The interest paid by the bank 1ii. The rate of interest AAM b. RN Prove that cosA+sin'A coSA+sinA cosA-stnA 2 coSA-sinA 14) Question 3 ,find the ratio x:y. In the given circle with centre O, LABC=100,ZACD= 40 and CT isa tangent to the circle at C. Find ZADC and zDCT. 141 ) 2009 NFU ofst.U The table shows the distribution of the scores obtained by l60 shooters in a (competition. Use graph sheet and draw an ogive shooting for the SCores on the ii. Scores LNumber of shooters n3. x-axis and 2cm =20 shooters on 0-10 10-20 20-30 30-40 9 13 Use your graph to estimate the a) The median 3 20 26 following b) The inter quartile range c) The number of the y-axis distribution. [use 2emn=10 40-5050-60 60-7070-80 S0-90 151|90-100 30 22 shooters who obtained a score of more than Question 4 i cal. ii. 15 108 85% SECTIONB EA=.B- and C=lo , ind the matrix X such that Solve the equation 2r-5x-4 = 0 for x and give your answer corect to one place. A+X= 2B +C. Fadl Page 4 decimal .erfl ually ne naa k. He deyosit t50 per month for 4 In the following figure, CM and RN are respectively the medians of AABC and APQR iii. If AABC-APQR, Prove that a. AAMC- APNR b. =PO Question5 following frequency distribution (31 Find lower, upper and median quartiles fromn the 10 8 Marks(x) 5 6 6 10 4 7 Frequency(D5 to a dealer Sachin for 28000.The Manfacturer Poojan Mathur sells a water cooler of 1200. If the salcs are intra dealer Sachin sells it to a consumer at a profit of tax (under GST, paid by amount the find is 12%, of GST the rate state and 13] government. central to the Sachin the dealer iii. In the given figure, PQ-RQ and LRQP =72 , PC and QC are tangents to the circle with [4] centre O. Find 2PCQ. Question6 terms is -4 and the fifth term is Find a G.P. for which sum of the first two scores obtained by 25 students in a The histogram given below represents the mathematics mental test. Use the data to 4 times the third tem. i. (3) a Frame a frequency distribution table b. Calculate mean c. Detemine the modal class A 10 Page 5 20 MARKS 30 50 a k e n p a r a l l e The surface area of a solid metallie sphere is 1256 cm'. It is melted and tecast iato solid right circular cones of radius 2.5 cm nnd height cm. Calculate (0 the radius of the solid sphere (0 the number of cones recasts. (Use n-3,14). 14) Question 7 Find the cquation of the perpendicular bisector of the line segment joining the points A(2,3) and B(6,-5).Also find the point where the perpendicular bisector of AB cuts the coordinate axes. ii. Aman observes the angle of elevation of the top of a building to be30 . He walks towards it in ahorizontal line through its base. On covering 50m, the angle of clevation change to 60 . Find a) the height of the building.. b) Distance of the man from building when the angle of elevation is 30 e) (All Distance of the man from building when the angle of elevation is 60 answers should be correct to the ncarcst metre) (5) Question 8 i. Find the value of x, which satisfies the inequation 2x 31 -2s-s 1~xEN Graph the solution on the number line. ii. In the given figure, LBQR=45 and Zx =22y. Calculate the values of xand y. (31 )450 Page 6 Ouestio If the points taken in order,A(6,1), then find and D(p.3) are the vertices of a B(8,2),C(9,4) the parallelogram, parallelogram ABCD. value of p. Also find the equation of both of the diagonals di Question 9 Solve for x using the properties of proportion 3 The restaurant's bill for a number of people for overnight stay is 4800. 1f there were 4 more men, the bill each person had to pay would have reduced by 2200. Find the number of people staying overnight. 3 Draw a circle of radius 3.5 cm, mark a point P outside at a distance of 6cm from the centre. onstruct two tangents from P to the given circle Measure and write dowa the length of one tangent. 14] Question 10 Using remainder and factor theorem, factorize completely, the glven polynomial: 3r+2r-19z+6 3) Abox contains 17 cards numtered 1,2,.17 and are mixed . Acard is drawn at [31 random from the tox Find the probability that the number on the card is a) Odd b) Divisible by 2 and 3 both. ) Divisibie by 2 or 3. Using greph peper to answer the following questions (take 2em =1 nit on both axes) a) Plot the points A(4,2) and B(2,4). b) A'is the image of A, when reflected in the Y-axis. Plot it on the graph paper and write the coordinates of A' c) B' is the image of B, when reflected in the line AA' . Plot it on the graph paper and write the coordinates of B'. d) Write the geometric name of the figure ABA'B'. Page 7 14)
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