Page 1 :
Time Allowed: 1 hour and 30 minutes, , ATUL GAUR CLASSES, , Class - X Session -2021-22, , TERM1, Subject- Mathematics, , General Instructions:, , 1. The question paper contains three parts A, B and C., 2. Section A consists of 20 questions of 1 mark each, Attempt any 16 questions,, 3. Section B consists of 20 questions of 1 mark each. Attempt any 16 questions., , 4, Section C consists of 10 questions based on two Case Studies, Attempt any 8 cneniohory, , 5. There is no negative marking., , Section A mS, Attempt any 16 questions Ce, , 44), , The decimal expansion of the number Past ( ’, a) None of these b) non inat non-repeating, , c) terminating decimal d) non-terminating repeating decimal, The pair of equations 2x + 3y = 5 and 4x + 6y =, , a) infinitely many solutions > exactly two solutions, , , , , , ¢) no solution d) a unique solution, What should be =a omial x - 16x + 30, so that 15 is the zero of the, resulting polynomial?, , a) 15 we) b) 4, , c) 16 d) 30, , The solution re - © —Oand 2b + “2 —a+bwherex,y 4 0is, , a) x =-a? and y =-b? b) x= a? andy =-b?, x= a2 and y=b? 4) x =-a2 and y=b?, If sin® — cos@ = 0, then the value of sin'@ + cos*# is, a)i b) 3, at a+, (2+ V5)is, a) an irrational number b) not real number, , ¢) arational number d) an integer, , Maximum Marks: 40, , fi, , (1), , (1), , {1}, , 1], , i)

Page 2 :
10., , iL, , 12, , 13., , 14., , 15., , 16., , 17., , Ifa, B are the zeros of the polynomial p(x) = 4x? + 3x + 7, then + ~ 4 is equal to, , a) b) -3, , °) -t ct) q, If A (2, 2), B (-4, - 4) and C (5, -8) are the vertices of a triangle, then the length of the median, through vertex C is, , miles, , a) V113 b) 65, , ©) 85 4) ¥117, The number of zeroes of a cubic polynomial is, , a)3 b)2, , oa dt, , The sum and product of the zeroes of the polynomial f(x) = 4x* - 27x + 3k? are equal, then the, value of kis, , a) +3 bo ; g, , +1 d) +2, A die is thrown once. The probability of getting a prime number pO, , a) 7 d) 3 \, ot a3 C), , If HCF (26,169) = 13, then LCM (26,169) =, a) 13 ee, ©) 52 Qy 338, , The distance of a point from the y- ed, a) origin b) None of these, ©) abscissa \ d) ordinate, Points (1, 0) an , 0) liesion, a) line b) y-axis, c) x-axis d) linex-y=0, If one zero of the quadratic polynomial kx? + 3x + k is 2 then the value of k is, a= n=, o¢ a4, 9sec7A - Stan?A =, a)8 b9, oo d)t, , The solution of = + 4 = 2 and ax- by = a?-b? is, , a)x=aandy=b b) x= a? andy =b?, , fi), , f), , fl), , (1), , fl, , fi), , fi), , fl, , (1), , 1], , 1)

Page 3 :
18., , 19., , 20., , 21, , 22,, , 23., , 24., , 25,, , 26., , 27., , ©) x =-a2 and y=-b? d)x=-aandy=-b, , Two numbers ‘a’ and ‘b' are selected successively without replacement in that order from the, integers 1 to 10. The probability that + is an integer, is, , at ns, OF ae, , The sum of a rational and an irrational number is, , a) Can be Rational or Irrational b) Irrational, c) Always Rational d) Rational, If A(S, 3), B(11, -5) and P(12, y) are the vertices of a right triangle right angled at P, then y =, a)-1,4 b)2,4, ©)-2,4 d)2,-4, Section B &, , Attempt any 16 questions gY), Ina cyclic quadrilateral ABCD, if ZA = (2x-- 1), ZB = (y +5)®, ZC = (2y + Gy = (4x7)°, then the value of ZC is, , a) 559 b) 4250 \O, , ©) 65° 4) 115°, , A quadratic polynomial whose zeros are 3 and =, is, , a) 10x2-x+3 Mies, , ©) 40x2-x-3 > 10xt+x+3, in, , Ifa=2x3,b=2x3x 5 = d LCM (a, b,c) = 2° x 3? x 5, thenn =, , a)i b)4, 3 \ d)2, costA - si Xo, a2 ay D2sint art, 2 cos? A+1 9) 2costA-1, , The sum of the digits of a two digit number is 9, Nine times this number is twice the number, obtained by reversing the digits, then the number is, , a) 72 b) 27, c) 18 d) 81, If a and 3 are the zeroes of the polynomial x? - 6x + 8, then the value of a* + {3° is, a) 76 b) 72, c) 74 d) 80, , fl, , fi), , fi), , fn), , {1}, , a), , fi), , fi), , (1, , Two poles of height 13 m and 7 m respectively stand vertically on a plane ground ala distance [1]

Page 4 :
28., , 29., , 31., , 32,, , 33., , 35., , of 8m from each other. The distance between their tops is, , a) 11m b) 10m, com d) 12m, , The ratio in which the point (1, 3) divides the line segment joining the points (-1, 7) and (4, -3), is, , a) 2:3 b)7:2, 3:2 d)2:7, Iftan @ = ay then Spt =, ay » 4, at 3, If x = @ and y = 9 is the solution of the equations x - y = 2 and x + y = 4, then, , a)a=1and §=3 b) a=3and §=-1, , Oa=3and$=1 d)a=-3and3=1 co, , The exponent of 2 in the prime factorisation of 144, is, , o6 a3, In the given figure value of x for which DE | | BC is, a, , <, : », , o4 di, If sinA + sin? A= 1, th — of the expression (cos*A + cos*A) is, , 1, az \ bt, 3 dj2, , If the point R(x, y) divides the join of P(x, yy) and Q(x», yz) internally in the given ratio my :, Mz, then the coordinates of the point R are, , a4 b5 oP, , , , a) ( Metts aye b) ( Meticmes aes, myrmy ? msg m—me % mie, c) (mez imate may tm d) None of these, motm; * myptm,, , A child's game has 8 triangles of which 5 are blue and rest are red and 10 squares of which 6, are blue and the rest are red. One piece is lost at random. The probability that it is a square of, blue colour is, , 4 i, az Da, , 1 2, oF as, , (1, , (1), , fi), , 1), , fi), , 1), , fi)

Page 5 :
36 Asystem of linear equations is said to be consistent, if it has (1, , a) two solutions b) one or many solutions, ¢) no solution d) exactly one solution, 37. (1+ ¥'2)+(1- v2)is (11, a) a rational number b) a non-terminating decimal, c) None of these d) an irrational number, 38 = The value of (tan1° tan2° tan3° .., tan89°) is (1), a) 0 b)4, 1 dj2, 39. Iftwo different dice are rolled together, the probability of getting an even number fi), 1 1, a) ? b) q, ° 35 a5 &, 40. Ifthe endpoints of a diameter of a circle are (-4, -3) and (2, 7), then the coordi sot te fi], centre are, a) (1,-2) b) (0, 0) Cy, ©) (2, -1) d) (-1, 2) \O, Section C, Attempt any 8, , Question No. 41 to 45 are based on the given text. id the text carefully and answer the, , questions:, , Minister of a state went to city Q from city Py route via city R such that PR | RQ. PR = 2x km, e iP, , and RQ = 2(x + 7) km. He noticed that th osal to construct a 26 km highway which directly, connects the two cities P and Q., a, , NS, , axe7, , 41. Which concept can be used to get the value of x? fi), a) Converse of thales theorem b) Pythagoras theorem, c) Thales theorem d) Converse of Pythagoras theorem, , 42. The value of xis (1), a)5 b)6, a4 ays, , 43. The value of PRis (1, , a) 20km b) 25 km