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ICSE Class X Prelims 2024 : Mathematics (Sanskriti the Gurukul, Kamrup)

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Ronak Ajitsaria
Sanskriti the Gurukul, Kamrup
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Pre-Board EXAMINATION 2023-24 STD-X MATHEMATICS Time: 2 MM-80 Section-A (All questions are compulsory) 1) Choose the correct answers to the questions from the given options. [Do not copy the question. Write the correct answer only] (15) a) A dice is rolled once. Find the probability of getting a prime number : i) 1/6 ii)1/3 iii)1/2 iv)1/4 b) MRP of an article is 10,000 and discount is 10 % and GST is 5%, calculate amount of bill i) 9450 ii) 9405 iii) 9054 iv) 9045 c) Solve: 2(x-4) < 1, x {1,2,3, .10} i) {1} ii) {1,2} iii) {1,2,3,4} iv) none of these d) In the given figure, AB is a chord of the circle such that =50 . If AT is a tangent to the circle at the point A, then = i) 65 ii) 60 iii) 50 iv) 40 e) If x, 5.4, 5, 9 are in proportion then x is: i) 3 ii)9.72 iii)25 iv)25/3 2 f) Which is a factor of p(x)= 4 + 3 i)x+1 ii)x+2 iii)x-2 iv)x-1 g) Which of the following is Row Matrix? 2 6 2 1 0 ] ] i)[2 4] ii)[ iii)[ ] iv)[ 4 1 1 0 1 h) Assertion(A): The 10th term from the end of the A.P.: 100,95,90,85 .10 is 55. Reason(R): The nth term from the end of the A.P. having last term and common difference is ( 1) i) Both (A) and (R) are true and (R) is the correct explanation of (A) (ii) Both (A) and (R) are true but (R) is not the correct explanation of (A) (iii) (A) is true but (R) is false (iv) (A) is false but (R) is true i) Which of the following points is invariant with respect to the line y = -2 i)(3,2) ii) (3,-2) iii)(2,3) iv)(-2,3) j) If P(3 , 4) is the mid-point of the line segment joining the points Q(-6, 5) and R(-2, 3),then the value of ` is i)-4 ii)-6 iii)12 iv)-12 k) The equation of a line passing through the point (-2, 3) and having X-intercept 4 units is i)x+2y=8 ii)x+2y=4 iii)2x+y=8 iv)x+y+4=0 l) If in two triangles DEF and ABC, = = , then i) ~ ii) ~ iii) ~ iv) ~ 2 m) ( 1)(1 2 ) is equal to i) -1 ii) 1 iii) 0 iv) 2 n) One of the roots of the quadratic equation 2 8 + 5 = 0 is 7.3166. The root of the equation correct to 4 significant figures is : i) 7.3166 ii)7.317 iii)7.3167 iv)7.32 o) Assertion (A) : The point on the x-axis which is equidistant from (2, -5) and (2, 9) is (8, 0). Reason (R) : Points lies on the y-axis are always of the form (0, y). (i) Both (A) and (R) are true and (R) is the correct explanation of (A) (ii) Both (A) and (R) are true but (R) is not the correct explanation of (A) (iii) (A) is true but (R) is false (iv) (A) is false but (R) is true 2) a) A circus tent is made of canvas and is in the form of right circular cylinder and a right circular cone surmounted it. The diameter and height of the cylindrical part of the tent are 126m and 5m respectively. The total height of the tent is 21m. Find the total cost of the canvas, if canvas used costs 36 per square meter. (4) b) Using componendo and dividendo, find the value of x. 3 +4 + 3 5 3 +4 3 5 =9 (4) c) Using the remainder theorem factorize completely the following polynomial. 3 3 + 2 2 19 + 6. (4) 3) a) Rishi has a cumulative time deposit account in Bank of Baroda. He deposits 200 for a period of 3 years. If at the time of maturity he gets 8088, find the rate of interest.(4) b) Solve the following inequation, write the solution set and represent it on number line: 3 2 113 < 16 , . (4) c) Use graph paper for this question. The point P (4,2) was reflected in the origin to get the image P . (i) Write down the co-ordinates of P . (ii) If M is the foot of the perpendicular from P to the x-axis, find the co-ordinates of M. (iii) If N is the foot of the perpendicular from P to the x-axis, find the co-ordinates of N. (iv) Name the figure PMP N. (v)Find the area of the figure PMP N. (5) Section- B (Attempt any four questions ) 4) a) A company with 500 shares of nominal value ` 120 declares and annual dividend of 15%. Calculate: (i) the total amount of dividend paid by the company. (ii) annual income of Mr. Sharma who holds 80 shares of the company. (iii)If the return percent of Mr. Sharma from his shares is 10%, find the market value of each share. (3) b) In the adjoining figure, CE is a tangent to the circle at point C. ABCD is a cyclic quadrilateral. If = 93 and = 35 ,find i) ii) iii) (3) c) Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown. [4] (a)Construct a in which BC =6.5 cm, = 60 , AB= 5 cm. (b) Construct the locus of points at a distance of 3.5 cm from A. (c) Construct the locus of points equidistant from AC and BC . (d) Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY. (4) 5) a) The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7:15. Find the numbers.(3) b) A wholesaler buys a machine from the manufacturer for 25000. He marks the price of the machine 20 % above his cost price and sells it to a retailer at 10% discount on the marked price. If the rate of GST is 18% and assuming that all transactions occur within the same state, calculate i)the marked price of the machine ii)retailer s cost price inclusive GST iii)the CGST and SGST payable by the wholesaler to the government. (3) c) Using ruler and compasses only, construct a triangle with sides 5cm, 4cm, 3cm. Draw its incircle and measure its radius. (4) 6) a) Using a graph paper, draw an ogive for the following distribution which shows the marks obtained in the General Knowledge paper by 100 students. Marks No. of students 010 5 1020 10 2030 20 3040 25 4050 15 5060 12 6070 9 7080 4 Use the ogive to estimate (i) the median. (ii) (ii) the number of students, who score marks above 65. (5) b) From the top of a building AB ,60m high, the angle of depression of the top and bottom of a vertical lamp post CD are observed to be 30 and 60 respectively. Find (i) the horizontal distance between AB and CD. (II) the height of the lamp post. (5) 1 1 7) a) The 4th and the 7th terms of a G.P. are and 27 729 respectively. Find the sum of first 6 terms of the G.P. (3) b) A die is thrown once. What is the probability of getting (i) an even number (ii)a number greater than 2 (iii) getting number 6. (3) c) Following is the distribution of earnings of 200 workers in a flour mill: Monthly 80-100 100-120 120-140 140-160 wages( ) Number of 20 30 20 40 workers Find the average earning of a worker by step deviation method. 160-180 90 (4) 8) a) PQR is triangle. S is a point on the side QR of such that = . Given QP= 8 cm, PR= 6 cm and SR= 3 cm. (i) Prove ~ . (ii) Find the length of QR and PS. (iii) 9) a) In the given figure, diameter and chord of a circle meet at P . PT is a tangent to the circle at T and CD= 7.8 cm, PD=5cm, PB= 4cm.Find (3) b) The distance from A to B by two different routes are 75 km and 77km. A motor car taking the longer route travels on the average 6 km per hour faster than one taking the shorter route and does the journey in 15 minutes less. Find the speed of each car. (3) c) Find the mode of the distribution given below, by drawing a histogram. (Take 2cm=20 units on x-axis and 2cm=5 units on y-axis.) Classes 0-20 20-40 40-60 60-80 frequency 15 6 18 10 (4) (i) AB , (ii) the length of tangent PT. 3 2 5 b)Find x and y, if [ ] [ ] =[ ]. 4 1 12 c) Find the roots of quadratic equation: 2 + 3 3 = 0, giving your answer correct to two significant figures. 10) a) Prove that: ( + )2 + ( + )2 = 7+ 2 + 2 (3) (3) (4) (3) b) Find the equation of line which is passes through the origin and perpendicular to the line y+5x=3. (3) c) A copper sphere having a radius of 6cm is melted and then recast into a cylindrical wire of radius 2mm. Calculate the length of the wire. (4) *******************************

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