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Mock Test : Time :3 Hours DURGAMOYEE 2024-25, Class -X,ACADEMY Subject - Mathematics F.M. : 80 Maxinum Marks :80 Answer to this Paper must be Time allowed: 3 hours written on the write in the first 15 provided This time is to bepaper the headof the paper minutes. spent in reading the is the time allowed to separately. You will notThebe time given at allowed for writing the answers. question paper. SectionA compulsory. Attend any four The intended marks for questions fom section B. questions or parts of questions are given in brackets. | J is [Section-AJ (Attempts all questions fromthis section) Question 1. i. The degree of the zero |lx15=15) ii. The marked price of anpolynomial is - a. 1 b. 0 C. 2 d. undefined is FOUnt article 20% of GST is 12%. The cost price 25000, nd rate s 0/. amnount of SGST is abovea.the3240 C. 5000 d. 1620 i. If 2+:.<7x-4 -x and x e W then the 2 solution set is - b. {1,2,3,4,..., c. {2,3,4,...... iv, Which of the following quadratic a. v. If + 8x +15 = 0 d. 0 quantities b. ab = cd 1500 a. {0,1,2,3,. ...., d. {1,2,3} equations has the roots 3 and 5 8x -15 = ) b. x- C. x2- 8x+15 = 0 15 = 0 f(x) polynomial then remainder is - a. -2 d. b,2+2 8xC. 1 a, b, C, d are in continued then - (x+2) is a factor of a vi. Four b, proportion C. d. a. a/b-c/d a d C d vii. Matrix Aand Bhave the order m x n and pxq respectively. Then product BA exists only when - a. =1 b C. mn = pq d. mp = nq m viii. The sum of nterms of an term of the series is - a. 8arithmetic progression Sn = 6n- n2, then third b. 9 C. 1 ix. Which of the d. 5 following points is invariant with respect to the line x + 2y =7 I 2 a. (0,0) c. (7, 7/2) d. (1,3) x. The line ax + by=c (c # 0) intersect the equal distance from the origin then positive x-axis and negative y-axis at a. a-b=0 d. a-b=C b. atb=0 b. (;) C. a+b-c xi. Sis a point on the side QR of A 6cm, SR =3cm. Then area of A P R such that POR Z PSR = 2 QPR and PR = area of A SPR = a. 2 b. C. 4 d. ! 4 8 cm 6 R Cos Sine+ If xii. a. ab and = a sec + then t = b b d. a + cosec C. b. dice, the throwofa 2 single 1 In a a gettinga probabilityof is - vii numberis - 5 joined together. are b. 3 10cm length 2 a. 3 1200cm2 each of edge cubes is cuboid Two cm2, : (A) Assertion 10cm is 100 newly formed d. C. viy, composite 6 The side area of ofcube of surface total surface ofeach : Reason (R): Area option from the following Reason (R) is the correct correct true. Select the Reason (R) are and (A) Assertion correct a. Both (R)is not the Assertion (A) Reason of but explanation (R) are true (A) and Reason Assertion b.Both Assertion (A) true explanation of Reason (R) is not but true (A) is istrue (2,3) c. Assertion but Reason (R) true circle with centre O not is (A) a on Assertion lie (x,5) d. and B the points A (4,3) If (A): Assertion circle. xV. x is 2. each chord of the of mid-point then the value of correct a circle is the Reason (R) is the true. Reason (R) : Centre of are (R) Reason a. Both Assertion (A) and explanation of Assertion (A) b.Both is not the true but Reason (R) are (R) Reason Assertion (A) and correct explanation of Assertion (A) is not true true but Reason (R) c. Assertion (A) is (R) is true not true but Reason d. Assertion (A) is expression is Question 2. aftb-14 and when the + 2x3 expression the and b. i. If (x-2) is a factor of 52, find the values of a remainder a leaves divides AB in the divided by (x-3), it y-axis at B. Point P (4,-1) and A at x-axis meets ii. A line AB (4| ratio 1:2. A and B a. Find the coordinates of through P b. Find the equation of the line and perpendicular to AB and iii. In the given figure, O is the centre B AOE is the diameter of the semicircle ABCDE. If AB-BCand 2 AEC = 50 , find: a 2 CBE b. 2 CDE C. Z (4| AOB Question 3. [4] A i. In an A.P of 50 terms, the sum of first 10 terms is 210and sum of its last 15 terms is 2565. Find the A.P. ii. A conical vessel of radius 6cm and height 8cm is completely filled with water. Asphere is lowered into the water and its size is such that when it touches the sides it is just immersed. What fraction of the water overflows? [4| Pg-03/Mock Test/24/X/ Math i. The triangle OAB is reflected in the origin O to coordinates (-3, -4) and (o, -5) respectively : triangle OAB A' and B' have a. Find the coordinates of A and B. b. Drawa diagram to represent the given information. c. What kind of figure is the quadrilateral AB AB? d. Find the coordinates of A", the reflection ofA in the origin followed by reflection in the y-axis. e Find.the coordinates of B", the reflection of B in the x-axis followed by reflection in the origin. (5] [Section -B] (Attempt any four questions from this section) Question A. i.A man buys 400 ten rupee shares at a premium of 2.50 on each share. Ifthe rate of dividend is 8%, find: a. his investment b. dividend received [3] C. yield ii, Solve the following inequation,write the solution set and represent it on the real number line : 2 x- 3> x + 1-x, .xe R 5 (3] i i. Prove the following trigonometry identity : (Cosec A - Sin A) (Sec A - Cos A) = 1 CotA + tan A (4) Question 5. i. In the given figure (drawn not to scale) PQRS is a cyclic quadrilateral. PO and SR produced meet at T. a. Prove that ATPS ~ A TR b. Find SPif TP= 18cm, R = 4cm and TR = 6cm c. Find the area of quadrilateral PQRS if area of A PTS = 18cm2. (3] ii. Mr. Abir has a cumulative deposit account of Z400 per month at 10% per annum simple interest. If he gets 30100 at the time of maturity, find the total time for which the account was held. iii. The following table gives the lifetime in days of 100 electricity tubes of a certain make Life time in days Less than 50 Less than 100 Less than 150 Less than 200 Less than 250 Less than 300 No. of tubes 23 55 81 93 100 Using step deviation method, find mean lifetime of electricity tubes. (3] Pg-04/Mock Test/24/X/Math Question6. Point P(4,-1) divides AB in the ratio 1:2 meets X-axis at Aand y-axis at B. AB line B. iA Sind the coordinates of Aand [3] equation of the line through P and perpendicular to AB. X. O 0' is b. Find the touch each other at equal circles with centres Oand 0' figure, 0. ii. In this to meet a circle 0' at A. Ac 1s tangent to the circle whose centre is produced D OD AC. Find the isperpendicular to [3| value of : ADO' b. area of A a. AO' area of A ACO GST on the price of 1500. The rate of listed the at article shopkeeper payS a tax (under GST) ii. A shopkeeper sells an the and intra-state which the article is 18%. If the sales are amount inclusive of tax at the find Government, [4] of 27 to the Central wholesaler. purchased the article from the AO shopkeeper Question 7. of the water point 60m above the surface a from cloud a of elevation lake is 600, i. The angle of of its shadow in water of depression of angle the and of a lake is 30 the surface of water. Find the height of the cloud from thrown shot-put competition. The distance ii. 40 students enter for a game of (in meters) is recorded below : Distance in m No-of students 12-13| 13-14 14-15 15-16 12 16-17 9 17-18 (5] 18-19 4 1 above distribution. Use a graph paper to draw a less than type' Ogive for the Use a scale of 2cm=1m on one axis and 2cm=5 students on other axis. Hence, using your graph, find: a. the median b. upper quartile which is above 16 C. no. of students who coveradistance [5] - m. 2 Question 8. i. Agraph consists of 15 persons of which 5 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely tobe selected. Find the probability of selecting (3] a person who is - a. extremely patient b. extremely kind or honest saGwhich of the abovevalues you prefer more? i. If = Va+ 36 +Va- 36 Pg-05/ Mock Test/24/X/Math a+3h -a-35 then find the value of (3b2 2ax + 3b). ..:Anical tent is to accommodate 77 persons. Each person must have 16m of air breathe. Given tne radiusof the ternt as 7m, find the hei ht of the tent and also its curved surface area. (3] [4) Question 9. The table shows the age distribution of workers in a fa ctory Age (years) No. of workers (3] 20-24| 25-29| 30-34| 35-39 40-44 45-49 50-54 55-59 22 24 30 38 36 30 18 12 Using graphical method, find the modal age of the workers. ii. In an A.P of 50terms, the sum of first 10 terms is 210 and the sum of its last fra 25 terms is 2565. Find the A.P. [3] iii. Find the value of K for which the equation (K+1)2 - 6 (k+1) x +3(K+9) = o, K# -1, has equal roots. Hence find the roots of this equation. (4] Question 10. i. An aerdplane flying with a wind of 30km/h takes 40 minutes less to fly 3600km, than what it would have taken to fly against the same wind. Find the plane's speed of flying in still air. ii. If A = 2 find x, y sothat A2= x Aty I [3] [3| iii. Using ruler and compasses, construct a triangle ABC with AB = 5.5cm, AC=6cm and Z BAC = 1050, Hence : a. Construct the locus of points equidistant from BA and BC. b. Construct the locus of points equidistant from B andC. c. Mark the point which satisfies the above two loci as P. Measure and write the length of PC. (4] gure ST and QT are thc tangent to the circle = 64 , find () with PR diametcr. 2SPR (ii) 2SOR ( i))2STP (iv) LQTP T 640 2 R p ontaincr of radius 9 cm and hcight 8cm is illed with icc-cream. It is to be in equal cones with hemispherical tops. If the radius of each cone is 3cm ht of the icc-cream is 9 cm, then find the number of children who will get of 'k',so that the quadratic cquation (4- k)x + (2k + 4)x + (8k + 1) = given below and answer the following: (eb, teo) (60.140)
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