Page 1 :
THE REAL DESTINATION, , DIRECTOR-RASH RAJ Call :- 8579811685, SAMPLE QUESTION PAPER - 1, Class -X, Session -2021-22 (TERM 1) Time Allowed: 90 minutes, Subject- Mathematics Maximum Marks: 40, , General Instructions:, , 1. Tne question paper contains three parts A, B anc C, , 2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted, , 3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted, , 4, Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions., 5. There is no negative marking., , , , SECTION A, Section A consists of 20 questions of 1 mark each, Any 16 questions are to be attempted., , 1. Every____scan be expressed (factorised) as a product of primes, and this, factorisation is unique, apart from the order in which the prime factors occur. [1 mark], (a) Composite Number (b)PrimeNumber (c)EvenNumber (d)Odd Number, , 2. Ifaand “ are the zeros of the polynomial 4x — 2x + (k = 4), the value of kis:[1, , mark], {a)4 (b) 8 (c)o (d) None of these, , 3. Assertion: The two lines representing the two equations, x - 2y = 0 and 3x + 4y = 20, are intersecting at the point (4, 2), Reason: Each solution (x, y) of a linear equation in two variables, ax + by + c = 0,, corresponds to 2 point on the line representing the equation, and vice versa. [1 mark], (a) Both Aand R are true and R is the correct explanation of A., (b) Both A and R are true but R is not the correct explanation of A., (c) Ais true but Ris false, (d) Ais false but Ris true., , powered by, , THE REAL DESTINATION, ... Shaping tomorrow, CALL-8579811685, , THE REAL DESTINATION, .. Shaping tomorrow

Page 2 :
4. is the branch of Mathematics which deals with the position of an object lying, ina plane, described with the help of two mutually perpendicular lines. [1 mark], (a) Algebra (b)Calculus (c) Coordinate Geometry (@) Statistics, , , , , , 5. Two polygons of the same number of sides are similar, if their corresponding angles _, , , , , , , , , , , , are (i) and their corresponding sides are (ii) 5 _[1 mark! 7, (a) |. Proportional; ji. Equal (b) i. Proportional; ii. Proportional. é ~~», (c¢) & Equal; ii. Equal (a) |. Equa; ji. Proportional @ ~ p, , 6. Intriangle ABC, right-angled at B, if tan A = + then find the value of P4 C+cos, , °/>, , Asinc. a a [1 mark], {a)-1 (b) 0 (c)1 (a) Nonebt these, , 7. secA(1-sinA)(secA+tanA)=___. x SY F [1 mark], {a)1 (b) -1 (c)O @) None of these, , 8. The radii of two circles are 8 cm and6cm Leta, Find the radius of the circle, having an area equal to the sum of the areas of the two circles. [1 mark], (a) 5em (o)10cm (c) 20em (d) 15cm, , 9. State true or false: An operation which » some well-defined outcomes, is, called an experiment. [1 mark], (a) True (0) False, , 10. What are the LCM wracrot 6 and 20 by prime factorisation method? [1 mark], (a) 60, 2 ws 0,4 (c) 60,4 (d) 30, 2, , Ly, , 11. What Medrratiecies from p(x)=8x* + 14x° -— 2x" + 7x — @sothat the resulting, polynomial is exactly divisible by g(x)=4x" + 3x — 27 [1mark], (a) 12x-6 (b) 14x - 10 (c)12x-10 (d) 14x-5, , 12. Find the value of k in the system of Linear Equations in two variables kx + 4y 10, 3x +, , _ 6y =15, if these pair up to be inconsistent. [1 mark], (a) (b) 3 (c)4 (d) All options, THE REAL DESTINATION, , . Shaping tomorrow

Page 3 :
13. Point P divides the line segment joining the points A(2.1) and B(5,-8) such that, , <= = +. If Plies on the lines 2x - y +k = 0,find the value of k., , [1 mark], {a)-9 (b) -8 (c)2 (d)5, , 14. Assertion : In AABC, D and E intersects AB and AC respectively, such that DE LBC. we”, AD = 1.5cm, DB = 3cmand AE = 1cm, thenEC = 2cm. @, Reason : If a line is drawn parallel to one side of a triangle to intersect tigthantvo, sides at distinct points, the other two sides are divided in the same FRO. — [tmark], (a) Both A and R are true and R is the correct explanation of A. p, (b) Both A and R are true but Ris not the correct epienation of AL, (c) Ais true but Ris false., (d) Ais false but Ris true,, , , , 15. Evaluate sin 60 cos 30 + sin 30 cos 60. Say [1 mark], (a) -1 (b) 0 (c)1 Fa @ None of these, , 16. The outer and inner diameters of a coreularing are 34cm and 32 cm, respectively., Then, find the area of the ring. % ; [1 mark], (a) 103.71 cm* (b) 96.78 cm* (c 9937 cm* (d) 116.41 cm?, , 17. Which of the following is an example of an experiment ? [1 mark], (a) Tossing a coin ‘ (b) Throwing a die, , (c) Drawing a card he pack ofcards (d) Allof the above, , 16.7% 11 x 13.+ GeaP% 6 x5 x 4x 3x 2 x 1 + 5arecomposite numbers., TRUE or FALSE?, , [1mark], (a) True oy (b) False, 19. Inan isosceles right angled triangle, if the hypotenuse is 5./2 cm, then find the length, Of the equal sides of the triangle. [1 mark], (a) 3cm (b) 4cm (c)5cm (d) 6cm, 20. If the lines given by 3x + 2qy = 2 and 2x + Sy + 1 = O are parallel, then find tne value of q., [1 mark], THE REAL DESTINATION, , . Shaping tomorrow

Page 4 :
(a) (b) (c)-= o>, , , , dy’, SECTION B, Section B consists of 20 questions of 1 mark each. Any 16 questions are to |., , 1. Write the coordinates of the vertices of arectangle whose adth are 4, and 3 units respectively, and have one vertex at the origin. side is on the X, - axis and one of the vertices lies in the IV quadrant. [1 mark], , (c) (0, 0), (3, 0), (4,-4)and (0, -4), (d) (0, 4), (3. 4), (4,0)and (0, 3), , (a) (0, 0), (4, 0), (4,-3)and (0, -3), (0) (0,0). (-4, 0), (4,-3)and (0, -4) xy, , 2. Ifaline divides any two sides of a triang e 1€ ratio, then the line is parallel to, the third side. Itiscalled__.- [1 mark], (a) Converse of Basic Proportionality Theore, , (b) Basic Proportionality Theorem, (c) Pythagoras tl, (d) None of the above, , , , , 3. Evaluate 2tan"45° — sin’ 60., [1 mark], (a)1 (c)3 (d) 4, , , , , , 4. Ifcos (a+ B) = 0, then sin (a - B) can be reduced to [1 mark], (a) cosB (b) cos 28 (c) sina (d) sin 2a, the area of a sector of a circle with a radius 6 cmif the angle of the sector is 60°, sf om* (b) 2m’ (c) sem’ (d) 2m’, [1 mark], THE REAL DESTINATION, , .. Shaping tomorrow

Page 5 :
6. Anunbiased aie is thrown. What is the probability of getting an even number and a, , multiple of three ? [1 mark], 2, (a+ (b) + (c)= (d)+, 7. The numbers that nave either terminating or non-terminating repeating decim ®, expansion are called, , (a) Rational Number (b) Irrational Number (c) Real Number (d) Integers, , 8. Intriangle ABC, ZC «5 2B = 3(ZA+ ZB), findtheangle A. ~, [1 mark], (a) 27 (b) 18° (c)135° — (d) None of the &, , @, 9. Assertion : The value of y is 5, for which the distan points A (2, 3) and, C (10,y) is 20., Reason : Distance between two given points SS (x, ¥,) is, , @, 7 = +0,- yy) Qj [1 mark], (a) Both A and Rare true and Ris lanation of A., (b) Both A and R are true but Ris not ect explanation of A., (c) Ais true but Ris false., (d) Ais false Lr., 10. sean ee ey [1 mark], , ey," (b) 80° (c) 60 (@) 40°, . Inthe given figure below , OACB is a quadrant of a circle with centre O and radius 3.5, , cm.|fOD = 2cm, find the area of the shaded region. [1 mark], (a) 6 cm* (b) 6.35 cm* (¢)6.125cm* () 615m?, , , , THE REAL DESTINATION, .. Shaping tomorrow