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1st TERMINAL EXAMINATION SUBJECT MATHEM CLASS- X SUBJECT- MATHEMATICS SESSION: - 2024-2025 SESSION: - 2022-2023 F.M. 80 TIMESECTION- A [ATTEMPT ALL] Question:1 Choose the correct answer of the question from the given option: [1 i) ii) iii) iv) v) vi) vii) viii) ix) x) The volume of a conical tent is 462 m3 and the area of base is 154 m2. The height of the cone is: (a) 15 m (b) 12 m (c) 9 m (d) 24 m. The coordinates of the point P (-3, 5) on reflecting on x axis are: (a) (3, 5) (b) (-3,- 5) (c) (3,- 5) (d) (-3, 5) The radius of a roller 100 cm long is 14 cm. The curved surface area of the roller is: (a) 13200 cm2 (b) 15400 cm2 (c) 4400 cm2 (d) 8800 cm2 Ishika deposited 400 every month in a bank s recurring deposit account for 30 months. If she gets 1085 as interest at the time of maturity, then the rate of interest per annum is (a) 7% (b) 8% (c) 9% (d) 6% The solution to the inequation (a) { 4,5,6} (b) { x: (c) { x: (d) { x: 2 The roots of the quadratic equation 12x + 4kx+3=0 are real and equal, if (a) K= (b) 9 (c) k=3 (d) k= - 9 If ( ) ( ) ( ) (a) The mean proportional between 8 and 128 is____________ (a) 64 (b) 32 (c) 16 (d) 8 .. (a) 6 (b) -4 (c) 4 (d) 7 3 2 If (x-2) is a factor of 2x -x -px-2 find the value of p. (a) -4 (b) 5 (c) -5 (d) 2 xi) xii) ( ) ( ) ( ) (a) In the figure given below AB and DE are perpendicular to BC. If CD=6cm, AD=4cm, EC=3.6cm then the length of BE is: (a) 2.4 cm (b) 6 cm (c) 3.6 cm (d) 4.4 cm xiii) xiv) xv) Which of the following equation has 2 as the root has 2 as the root? (a) X2 4x+5=0 (b) x2 3x-12=0 (c) 2x2-7x+6=0 (d) 3x2-6x-2=0. The percentage share of SGST of total GST for an intra-State sale of an article is (a) 25% (b) 50% (c) 75% (d) 100% Assertion (A): When a cylindrical glass of radius r/2 and height h/2 is filled upto the brim with water , the water surface area of the glass is Reason (R): The volume of the cylinder is . (a) Both A and R are correct but R is the correct explanation of A. (b) Both A and R are correct but R is not the correct explanation of A. (c) A is correct but R is false (d) Both are false. QUESTION 2:(a) A manufacture buys raw material worth 7500 paying GST at the rate of 5%. He sells the finished product to a dealer at 40% profit. If the purchased and the sale both are intra-state and the rate of GST for the finished product is 12%, find: (i) the input tax (under GST) paid by the manufacturer. (ii) the output tax (under GST) collected by the manufacturer. (iii) the tax (under GST) paid by the manufacturer to the Central and State Governments. (iv) the amount paid by the dealer for the finished product. (b) Mr. Doloi opened a recurring deposit account in a bank. He deposited 2500 per month for two years. At the time of maturity he got 67500. Find: (i) the total interest earned by Mr. Doloi. (ii) the rate of interest per annum. (c) In the given figure, PQR = PST = 90 , PQ = 5 cm and PS = 2 cm. (i) Prove that PQR APST. (ii) Find Area of PQR : Area of quadrilateral SRQT. [4+4+4=12] QUESTION 3:- (a) From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: (i) the surface area of the remaining solid (ii)the volume of remaining solid (iii) the weight of the material drilled out if it weighs 7 gm per cm3. (b) Prove that: (1 + cot cosec ) (1 + tan + sec ) = 2 (c) Attempt this question on graph paper. Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes. Reflect A and B in the x-axis to A and B respectively. Plot these points also on the same graph paper. Write down: (i) the geometrical name of the figure ABB A ; (ii) the measure of angle ABB ; (iii) the image of A of A, when A is reflected in the origin. (iv) the single transformation that maps A to A . [4+4+5=13] . SECTION- B [ ATTEMPT ANY FOUR ] QUESTION 4:- (a) If a = , find the value of: (b) Eight metallic spheres, each of radius 2 cm, are melted and cast into a single sphere. Calculate the radius of the new (single) sphere. 3 2 (c) If (x 2) is a factor of 2x x + px 2, then (i) find the value of p. (ii) with this value of p, factorize the above expression completely. [3+3+4=10] QUESTION 5:(a) Prove that = cot A tan B (b) Mis. DasGupta has a recurring deposit account in a bank for 3 years at 7.5% p.a. simple interest. If She gets 8325 as interest at the time of maturity, find : (i) The monthly deposit (ii) The maturity value. (c) The speed of an ordinary train is x km per hr and that of an express train is (x + 25) km per hr. (i) Find the time taken by each train to cover 300 km. (ii) If the ordinary train takes 2 hrs more than the express train; calculate speed of the express train. [3+3+4=10] QUESTION 6:(a) Solve the equation 5x 3 =4/x and give your answer correct to 3 significant figures (b) If ax = by = cz; prove that (c) Use graph paper for this question. (i) The point P (2, -4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q. (ii) Point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R. (iii) Name the figure PQR. (iv) Find the area of figure PQR. QUESTION 7:(a) In the figure given below, CA || BD, the lines AB and CD meet at G. (i) Prove that ACO ~ BDO. [3+3+4=10] (ii) If BD = 2.4 cm, OD = 4 cm, OB = 3.2 cm and AC = 3.6 cm, calculate OA and OC. 3 2 (b) Using remainder theorem, find the value of k if on dividing 2x + 3x kx + 5 by x 2 leaves a remainder 7. (c) The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle as shown in the following figure. The tunnel is 80 m long. Calculate: (i) its volume (ii) the surface area of the tunnel (excluding the floor) and (iii) its floor area [3+3+4=10] QUESTION 8:(a) Mr. Ambarish gets 6455 at the end of one year at the rate of 14% per annum in a recurring deposit account. Find the monthly instalment. (b) If 2, 6, p, 54 and q are in continued proportion, find the values of p and q. 2 (c) Curved surface area of a cone is 308 cm and its slant height is 14 cm. Find , (i) radius of the base (ii) total surface area of the cone. [3+3+4=10] QUESTION 9:(a) Kiran purchases an article for Rs 5310 which includes 10% rebate on the marked price and 18% tax (under GST) on the remaining price. Find the marked price of the article. (b) Find the values of x, which satisfy the inequation : ,x N. Graph the solution set on the number line. (c) Prove that:[3+3+4=10]
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