Roll No... KAUSHAMBI PUBLIC SCHOOL Academic Session 2024-2025 Date... PRE-BOARD EXAMINATION Total Time: 3 Hrs 00 Mins General Instructions Max Marks: 80 ALL QUESTIONS ARE COMPULSORY ‘Standard/Class: 10th Subject: MATHEMATICS Section A Fillup in the Blanks - (1 Marks) Ifin AABC, ZC = 90°, then sin (A + B) = Objective(MCQ) - (1 Marks) Assertion (A): Number zero itself is known as zero polynomial. Reason (R): Zero polynomial has only one zero. a) Both A and Rare true and Ris the correct explanation of A. b) Both A and Rare true but Ris not the correct explanation of A. ¢) Ais true but Ris false. d) Ais false but Ris true. If a, B and Y are the zeroes of the polynomial x2- x2 - 10x - 8, then aB + BY + Ya + aBY is equal to (a2 (b)2 (18 (d)-18 OR fi) ol If the sum of zeroes of the quadratic polynomial 3x? — kx + 6 is 3, then find the value of k. The zeroes of the quadratic polynomial x? + px + p, p # 0 are (a) both equal (b) both cannot be positive (0) both unequal (d) both cannot be negative Assertion (A): If kx-y-2=0 and 6x - 2y -3 = 0 are inconsistent, then k = 3 ol fl Page 1 of 6 0 terrence10. " 12, a 14, 15. 16, 17. 18. . Reason (R): a1x + byy + c2 = 0 and apx + bay + c2 = O are inconsistent if a bye eae ae a) Both A and R are correct and R is the correct explanation of A. b) Both A and R are correct but R is not the correct explanation of A. c) Ais true but Ris false. _d) Ais false but Ris true. In a square of side 10 om, its diagonal = ... (a) 15cm (b) 10v2 om (c) 20 em (d) 12m AABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 om. If ADEF ~ AABC and EF = 4.cm, then perimeter of ADEF is (75 (b) 15cm (c) 22.5cm (4) 30 cm The distance between the points (a cos 25°, 0) and (0, a cos 65°) is (aa (b) 2a ()3a (d) none of these The sum of all two digit odd numbers is (a) 2575 (b) 2475 (©) 2524 (d) 2425 If the mean of the following frequency distribution is 2.6, then the value of p is Variate (X): : = 3 4 5 Frequency (f): 4 5 y Z 2 (a3 (bs (13 (d)24 What is the minimum value of sin A, 0 < A < 90° a1 (b)o (1 @% HCF of two positive integers is always (a) a multiple of their LOM (b) a factor of their LOM (©) divisible by their LOM (d) none of these If the common difference of an AP is 7, then a5 - a2 is equal to (a) 14 (b) 20 (0) 28 (d) 35 The probability of an impossible event is (a)o (b)1 ()% (a) non-existent Subjective - (1 Marks) For what value of V the point (3, a) lies on the line represented by 2x ~ 3y = 5? How many two digits numbers are divisible by 3? Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail. S and T are points on sides PR and QR of A PQR such that 4 P= RTS. Show that A RPQ ~ ARTS. Find the 9th term from the end (towards the first term) of the A. P. 5,9, 1 + 185. f) ol fl) f) ol fl fl fl fl fl ol f Page 2 of 620. 21 22. 23. 24. 25. 26. 27. 28. Name the geometrical figure enclosed by graph of the equations x+7=0,y-2=0 [1] andx-2=0,y+7=0. OR The distance of the point P(2, 3) from the x-axis is @2 3 @©nu @s Section B Subjective - (2 Marks) If PS and PT are tangents from an external point P such that PS = 10cm and zSPT= [2] 60°. Find the length of chord ST. The 17th term of an AP exceeds its 10th term by 7. Find the common difference. [2] Express 7429 as a product of its prime factors. [2] There is a circular path around a sports field. Sonia takes 18 minutes to drive one [2] round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point? OR The length of the minute hand of a clock is 14cm. Find the area swept by the minute hand in 5 minutes. One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that [2] ‘the card will (i) be an ace, (ii) not be an ace. Section C Subjective - (3 Marks) If the mean of the following data is 18.75. Find the value of p. (3] x 10 15 P 25 30 if 6 10 7 8 2 Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old [3] as Sonu. How old are Nuri and Sonu? The sum of two digit number and the number formed by interchanging the digit is 132. [3] If 12 is added to the number, the new number become 5 times the sum of the digits. Find the number. OR Page 3 of 6 0 terrence29. 30. 31. 32. 33. 34. In the given figure, if LM || CB and LN || CD, prove that aM _AN < AB AD Find the mean of the following frequency distribution by short cut method: [3] Classinterval | 0-10[ 10-20] 20-30] 30-40] 40-50 50-60] 60-70] Frequency | 4 4 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 [3] more than the number of boys, find the number of boys and girls who took part in the quiz. ( Form the pair of linear equations of the given problems, and find solution graphically.) OR Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden. Consider A ACB, right-angled at C, in which AB = 29 units, BC = 21 units and [3] Z ABC = @ (see figure). Determine the values of (i) cos? + sin?@ (ii) cos?® - sine. Section D Subjective - (5 Marks) Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no [5] colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere (see given figure). The entire top is 5cm in height and the diameter of the top is 3.5cm. Find the area he has to colour. (Take n= 22/7) The following frequency distribution gives the monthly consumption of electricity of [5] 68 consumers of a locality. Find the median, mean and mode of the data and compare them. Find the area of the segment AYB shown in given Figure, if radius of the circle is 21cm [5] and ZAOB = 120°. (Use mt = 22/7) Page 4 of 635. 36. 37. 7 OR A chord of a circle of radius 10cm subtends a right angle at the centre. Find the area of the corresponding () minor segment (ii) major sector. (Use m= 3.14) In Figure, XY and X'Y' are two parallel tangents to a circle with centre O and another —_ [5] tangent AB with point of contact C intersecting XY at A and X'Y’ at B. Prove that zAOB 0°. ee OR A triangle ABC is drawn to circumscribe a circle of radius 4cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8m and 6cm respectively (see Figure). Find the sides AB and AC. Case-Study Basketball and soccer are played with a spherical ball. Even though an athlete dribbles [4] the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor ona court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial. i) The shape of the path traced shown is ii) Observe the following graph and answer. In the above graph, how many zeroes are there for the polynomial? ill) Write the three zeroes in the above shown graph. The speed of a motor boat is 20 km/hr. For covering the distance of 15kmthe boat [4] took 1 hour more for upstream than downstream. Page 5 of 638. ma inch i), Let speed of the stream be x km/hr. then speed of the motorboat in upstream will be : ii), What is the relation between speed distance and time? ill). Which is the correct quadratic equation for the speed of the current? Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to [4] leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the Figure). In the field, there is a pole marked as 0. 8 | | =n #6 tain) © aon * Based on the above information, answer the following questions: (i) Taking 0 as origin, coordinates of P are (-200, 0) and Q are (200, 0). PQRS being a square, what are the coordinates of R and S? (ji) What is the area of square PQRS? (iii) What is the length of diagonal PR in square PQRS? (iv) If S divides CA in the ratio k: 1, what is the value of k, where point A is (200, 800)? Page 6 of 6