Formatting page ...
TWK VIOYAAYA PARLE TILAK VIDYALAYA (CSE) Grade: X Date: 25.11.2024 PRELIMINARY EXAMINATION MATHEMATICS Marks: 80 Time: 3 hrs. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question The time given at the head of the question paper isthe time allowedpaper. for writing the answers. This paper consists of SIX printedpages. Section Iis compulsory. Attempt any four questions fronm Section II. the inteded marks for questions or parts of questions are given in brackets []. SECTION L(40 MARKS) (Atempt all questions fromthis section.) QUESTION 1: Choose the correct answer to all questions from the given options: [15] If zebra were younger by 5 years than what she really is, then the square of her age would have been 11 more than five times her actual age.What is her age now? i. a. 72 b. 14 C. 6 d. NIL ii. The mean proportional to 36.3 & 2.7 is: 5.0 a b 4.20 C. 3.6 d. 9.9 iii. a. If 5-4x K2-3x, xe W, then solution set is.. {1,2,3} b. {0,1,2,3} c. f..-2,-1,0, 1,2,3 } d. {x: xE R, X <=3} iv. V. The 10th term of A.P. 2,7,12,.....:. a. 40 b 42 C. 47 d. 45 Assertion: GST payable = Output GST + ITC Reason: Input Tax Credit is a provision of reducing the GST already paid on inputs in order to avoid the cascading of taxes. a. A is true, R is false b. A is false, R is true C. Both A & R are true. d. Both A & R are false. vi Naveen deposits Rs. 800 every month in a recurring deposit account for 6 months If he receives Rs.4884 at the time of maturity ,then the interest he earns is : a. vi. Rs.84 b Rs.42 C. Rs.24 d. Rs.284 Aman buys Rs.40 shares in a company which pays 15% dividend. He pays the shares at such a price that he gets 12% on his investment. At what price did he buy each share?:. a. Rs.37 b. Rs.48 C. Rs.50 d. Rs.22 Viii. Assertion: If the points A(X,1), B(8,2), C(9,4) &D(7,3) are the vertices of a parallelogram, taken in order,then the value of x is 5. Reason: Diagonals of a parallelogram bisect each other at right angles A is true, R is false b. A is false, R is true c. Both A & R are true. d. Both A & R are false. 2 Ifth lines x-my +3 =0 & 2x+3y -7 =0 are perpendicular to each other, then the value of mis :. ix. a -2/3 b. 2/3 c. -3/2 d. 3/2 Assertion: Two circles are always similar. Reason: Similar shapes have same shape & s1Ze. X. A is true, R is false b. A is false, R is true C. Both A & R are true. d. Both A & R are false. xi. XY is parallel to BC.If XY divides the triangle into two equal parts, then A 1N2 b. 1/2 C. 2+1 d AX AB equals: V2-1 xii. Ifthe radius of the base of a cone is halved, keeping the height same,what is the ratio of the volume of the new cone to that of the original cone 1:2 b. 1:3 1:4 d. 2:3 xii. If 4tan = 3, then e. 0 f I/3 4 sin 0-3cos 9 4sin 0+3cos 0 g. 2/3 h. 3/4 deprenien x v. Aboat is being rowed away from a cliff, 150 mhigh. At the top of the cliff, the angle of eleuationof the boat changes fronm 60 to 450 in 2 minutes. The speed of the boat is: a. 1.9 km/hr b. 2 km/hr C. 2.4 km/hr d. 2.5 km/hr 3 xv. The probability of anon-leap year having 53 Mondays is: a. 1/7 b. 2/7 C. 5/7 d. 6/7 QUESTION 2: a. The 2nd & 5 terms of a G.P. are - & 1/16 respectively. Find the sum of first 8terms of the G.P.[4] b. The shadow of a tower, when the angle of elevation of the sun is 45 , is found to be 10 m longer than when it was 60. Find the height of the tower. C. (4] If x - 2x + ax + bhas a factor (x+2) & leaves a remainder 9 when divided by (x+1), find values of a&b.Also factorize the expression completely. [4] QUESTION 3: a b. C. Find two nunbers whose mean proportion is 28 & the third proportional is 224. [4] Find a matrix A such that A Eliminate [4] between the following equations: q tan 0 tp sec =x & p tan +tq sec =y SECTION II(40 MARKS) (Attempt any four questions from this section) QUESTION 4: Find the ratio in which the line joiningA( 6,5) &B(4,-3) is divided by the line y=2. Also find the coordinates of the point of intersection ? [3] b. Without solving, find the values of mfor which the given equation has real &equal roots. x?+2 (m-l) x +(m+5) =0 (3] c. Calculate mean by step-deviation method: C-I 135-140 F 4 140 - 145 [4] 145 - 150 150-155 18 28 4 155-160 160-165 24 10 165-170 170-175 5 2 QUESTION 5: a. Ifthe 7 th term of A.P. is 1/9 & its 9 th term is 1/7,find 63 rd term. b. Solve the following & represent on the number line : -3 < [3] <= 2 3 , XER [3] 6 C. Find the number of coins 1.5 cm in diameter & 0.2 cm thick to be melted to form a right circular of cylinder height 10 cm & diameter 4.Scm. [4] QUESTION 6: a) The model of a building is constructed with scale factor 1:30, i) If the height of the model is 80 cm, find the actual height of the building in meters ii) If the actual volume of the tank on the top of the building is 27 m , find the actual volume of the tank on the top of the model. .[3] b) Aman buys 500, Rs. 20shares at a discount of 20% & receives a return of 10 % on his money. Calculate: i)the amount invested by him. ii) the rate of dividend paid by the company. c) In the given figure, AB | |DC, A(A0AD) =12 CM & A(A BCD) = 18 CM . Calculate: i)A(A OCD) ii)OB :0D ii) A( AOAB) A [3] [4] B QUESTION 7: a) Construct AABCwith BC= 6.5cm, AB =5.5 cm & AC= 5 cm. Construct the incircle for the given triangle. Measure the radius of the circle. [3] b) Meena has cumulative time deposit account of Rs. 340 per month at 6% per annum. If she gets Rs. 7157 at the time of maturity, find the total time for which the account was held? [3) c) A bag contains 5 black balls, 7 blue balls, 4 white balls & 6 red balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is : i)red i) black ogwhite ii) not blue iv)neither black nor blue. [4] QUESTION 8: a) The Sunm of the numerator &denominator ofa fraction is 8. If l is added to both the numerator & [4] denominator, the fraction is increasedby 1/15.Find the fraction. b) Adealer sells an electric kettle for Rs. 2150. For a particular customer he reduced the price of the kettle in such a way that the customer has to pay only Rs. 2124 including GST. If the rate of GST [3] is 18%, calculate the amount of reduction allowed by the dealer. (3] c) For the following frequency distribution, draw a histograrn &estimate the mode. Class 0-5 5-10 Frequency 2 10-15 7 25-30 20-25 15-20 10 QUESTION 9: a) The hotel bill for a number of people for overnight stay is Rs. 14400. If thee were 4more people, the bill each person had to pay would have reduced by Rs. 600. Find the number of people staying overnight. (3] b) Plot the points O(0, 0), A(-2, 2), B(4, 4), i) Reflect points A&B in the origin. ii) Write coordinates A' &B'. i) Name the figure ABAB' c) Solve: 1 2 + (x+1). (x+2) [3] 4 (x+4) Give your answer correct upto 2 decimal places. [4] QUESTION 10: a) The frequency distribution is given below: Find the median,lower quartile, upper quartile & interquartile range. [S] Weight(kg) 5-15 15 -25 25-35 35 - 45 45-55 55-65 65 -75 Frequency 6 10 16 15 24 8 7 b) Aconical vessel of radius 6 cm & height 8 cm is completely filled with water. A sphere is lowered into the water & its size is such that when it touches the sides, it is just immersed. What fraction of water overflows? 6
|
