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Objective Questions, , , , , , , , , , Multiple Choice Questions (a)linear (b) quadratic, , 1. Which of the following is not a (c) cubic (d) None of these, polynomial 8. Which of the following is not the graph, (a)3x+5 (b) 3y5-4y? +2y of a quadratic polynomial?, (c)x3-3 (4) — \, , x+2 J, , 2. If2isa zero of polynomial (a) (b), f(x) = — 3(a -1)x — 1, then the value, of ais [\, (a)O (b)2, (cle (a3, , |, , 3. If one of the zeroes, of the quadratic (c) | r\ (d) A, polynomial (& — 1)x? + kx + lis — 3, then / \ !, the value of k is INCERT Exemplar], , 4 4, fale (o)-3 9. The graph of a quadratic polynomial, (c)2 (d) 2 IS hesvramebennce [NCERT Exemplar], 3 3 (a) straight line (b) parabola, , 4. If one of the zeroes of the quadratic (clhyperbola {d) None of these, polynomial x” + 3x + kis 2, then the 10. If one zero of polynomial x? — 4x + lis, value of kis ICBSE 2020] 2 + V8, then other zero will be ........., (a)10 (b)-10 (a)-2+73 (b)-V3-2, (c)-7 (d)-2 (c)2-v3 (d)V3 +1, , 5. If 2 and 3 are zeroes of polynomial 11. The zeroes of the quadratic polynomial, 3x2 —2Qkx + 2m, then the values of k and (x? +5x +6) are, mare (a)-2 and-3 (b)3and4, (a)m=2andk=15 (b]m="2 andi = 9 (e)Sand2 (d)2 and, , 2 7 12. Zeroes of p(z) =z? — 27 are wo..., (c)m=9andk =~ (d)m=15 andk =9 UM sesescasesss, (a)+ 3V3 3, 6. The value of p, for which (-4) is a zero (c)+9 Le ee B, , 5a] 2 :, of the polynomial x° - 2x - (7p + 3) is 13. The zeroes of the quadratic polynomial, Bat . fle) = abx? +(b? —ac)x — bc are, , (a)3 (b)2, WP snae ab. a, (c)4 (cea (aya andé (b)— and =, 7. If the graph of a polynomial intersects (cand 2 (o)® ana =, , the X-axis at only one point, it can be a

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20, , 14. The number of polynomials having, , zeroes as—2and5is [NCERT Exemplar], , (a)1 (b)2, , (c)3 (d) more than 3, 15. 1 and 2 are the zeroes the polynomial, , x? — 3x42, , (a) True (b) False, , (c) Can't say (d) Partially true/false, 16. Every real number is the zeroes of zero, , polynomial, , (a) True (b) False, , (c) Can't say (d) Partially true/False, 17. p(x) =x —1and g(x) =x? — 2x +1, p(x), , is a factor of g(x), , (a) True (b) False, , (c) Can't Say (d) Partially True/False, , 18. The value of k for which 3 is a zero of, polynomial 2x? +4 kis .., , , , (a)21 (b)20, (c)-21 (d)18, 19. If zeroes o and B of a polynomial, , x? —7x + kare such that —B =1, then, , the value of kis, (a) 21 (b) 12, (c)9 (d)8, , 20. Sum of zeroes of Quadratic polynomial, Coefficient of x, , ~~ Coefficient of x”, (a) True (b) False, (c) Can't say (d) Partially true/false, , 21. Ifo and B are zeroes of the quadratic, polynomial x? - 6x + athe value of ‘2’,, if 30, + 2B = 20 is — 12, (a) True (b) False, (c) Can't say (d) Partially True/False, 22. If one of the zeroes of a quadratic, polynomial of the form x“ + ax + bis, , the negative of the other, then it, , (a) has no linear term and the constant term is, negative, , CBSE New Patter’, , 23., , 24., , 25., , 26., , 27, , 28., , ne Mathematics X (Term ), , (b) has no linear term and the constant term ig, , ositive, , (c) - have a linear term but the constant, term is negative, , (d) can have a linear term, term is positive, , but the constant, , If pand q are zeroes of 3x? + 2x 9,, then value of p- 9 is, , 2, (a)-3 (b)-3, et? (d) None of these, “3, , The polynomial whose zeroes are, (/2 +1) and (v2 -1) is, , (a)x?+2V2x+1 (b) x2 -2V2x+1, (c)x¢+2V2x-1 (d)x° -2V2x-1, Ifo and B are the zeroes of the, polynomial Qy? +7y +5, then the value, ofa +B + of is, , (a)-1 (b)O, , (c)1 (d)2, , Ifo and f are the zeroes of the, quadratic polynomial, , f(x) = 3x? — 5x — 2, then a? +8? is, , equal to, , (aioe (bp) 382, 27 7, , (oF (a) 328, 28 i, , Ifo and B are the zeroes of, , 2 1,, 4x" + 3x +7, then the value a +3", a, , 8, , es (o)-3, ( oe, c) 5 (ae, i ibe zeroes of the quadratic polynomi!, , (@+1)x +b are 9 and - 3, then, file 9p9 [NcERT Exem!”, , i b= =5,b=-1, , (cla=2,b=-8 (decors

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CBSE New Pattern ~ Mathematics X (Term I), , 29., , 30., , 31., , 32., , 33., , 34., , 35., , If the sum and difference of zeroes of, quadratic polynomial are — 3 and — 10,, respectively. Then, the difference of the, squares of zeroes is, (a)20, , (c)15, , (b)30, , (d)25, , If sum and product of zeroes of, quadratic polynomial are, respectively, 8 and 12, then their zeroes are, , (a)2 and6 (b)3and4, , (c)2and8 (d)2 and 5, , If m and mare the zeroes of the, polynomial 3x” +11y — 4, then find the, , mon, value of — + —, , n m, 145 145, an Ib), (a) 0 (b) 7, 145 —145, ees dj?, (c) 7 (d) 1, , If one zero of the polynomial, 3x? — 8x + 2k + lis seven times the, , other, then the value of k is, , 2 2, fae (ob), 2 3, (lo (d) 3, If sum of the squares of zeroes of the, , quadratic polynomial, fT (x) =x? -—4x+ kis 20, then the value, , of kis, , (a)-2 (b)-3, , (c)-4 (d)2, , Ifo and B are zeroes of the polynomial, , x? — p(x +1) +¢ such that, , (a +1)(8 +1) =0, then the value of ¢ is, (a)-2 (b)2, (c)-1 (d)1, , The value of k such that the polynomial, x? —(k +6) x + 2(2k —1) has sum of its, , zeroes equal to half of their product is, [CBSE 2019], , (a)-4 (b)4 (c)-7 (d)7, , 36., , 37., , 38., , 39., , 41., , 42., , 43., , 21, , The sum and the product of zeroes of, the polynomial f(x) = 4x? — 27x + 3k?, are equal the value of kis, , (a)k=3 (b)k=-3, , (c)k=+3 (d)k =2, , Ifo and B are the zeroes of the, , quadratic polynomial, f(x) =x? — 4x + 3, then the value of, , ap? +0.°B* is ;, (a) 104 (b)108, (c)112 (d)5, , The quadratic polynomial, the sum of, whose zeroes is — 5 and their product is, , 6, is [CBSE 2020], (a)x? +5x+6 (b)x¢ -5x+6, (c)? -5x-6 (d)- +5x+6, , The quadratic polynomial whose zeroes, are 2/7 and -547 is, (a)x* —3V7x-70, (c)x* + 3V7x-70, , (b) x? + 3V7x+ 70, (d)x° —3V7x +70, , . The quadratic polynomial, whose, , zeroes are 3+ V2 and 3 - V2, is, (a)? -3x+5 (b) x? -6x+7, (c)x? -7x+ 6 (d)x* -8x +12, , Ifo and B are the zeroes of the, quadratic polynomial f(x) = x? +x - 2,, then the polynomial whose zeroes are, 20. + land 28 + lis, , (a)e +9 (b)x? -4, , (c)x* -9 (a)? +4, , Ifo and B are zeroes of a quadratic, , polynomial x? —5, then the quadratic, polynomial whose zeroes are 1+ and, 1+fis, , (a) x? +2x+24, , (b) x? -2x-24, (c)x°-2x4+24, , (d) None of these, The number of value of k for which the, quadratic polynomial kx? + x + k has, equal zeroes is, (a) 4 (b)1, , (c)2 (d)3

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22, , 44. p(x) =5x° — 3x? +7x + 2, then match, the value of Column I with that of, , Column II, Column I Column IT, , A. p(l) Pp 2, B. (0) Mi, Cc. p(s) R -13, D. — p(-1) Ss. -64, E. p(-2) T. 587, , ABCODE ABCODE, {aQ TRPS (b)O RTS P, (c)O PTRS (d)T ROS P, , 45. Ifo and B are the zeroes of the, , polynomial 2x? — 4x +5, then match, the value of Column I with that of, , Column IT, Column I Column I, A. dat 1-6, Ze, a B, B. (a -B)? a. =F, 25, c. Eek 3. 7-2, a B s, dD a, B 44, Bo 5, ABCD ABC OD, (a)}4 12 3 (b)4 213, (c)1 23.4 (d)1 4 2 3, , Assertion-Reasoning MCQs, , Directions (Q. Nos. 46-55) Each of these, questions contains two statements : Assertion, (A) and Reason (R). Each of these questions, also has four alternative choices, any one of, which is the correct answer. You have to, , select one of the codes (a), (b), (c) and (d), given below., , CBSE New Patter’, , 46., , 47., , 48., , 49., , 50., , 51., , n ~ Mathematics X (Term D, , (a) Ais true, Ris true; Risa correct, , i A., explanation for /, (b) . true, Ris true: Ris not a correct, , explanation for A., (c) Ais true: R is False., (d) Ais false; R is true., , ‘Assertion (A) x” + 44 +5has two, , zeroes. :, Reason (R) A quadratic polynomial, can have atmost two zeroes., , Assertion (A) The factor of, , 3 42 gy — 2 ig L(x 7) (3 +5), , oF Qi". 2, , Reason (R) The factors are calculated, by dividing the coefficients by 2 and, expression is obtained by splitting the, middle term, , Assertion (A) A quadratic polynomial, having 4 and 3 as zeroes is x” — 7x -12, , Reason (R) The quadratic polynomial, having o. and B as zeroes is given by, , P(x) =2? —(4 +B) x+a-B, , Assertion (A) Zeroes of, f(x) =x? ~ 4x —5are 5,-1, , Reason (R) The polynomial whose, zeroes are 2+ (3,2 — J3 is x2 —4x +7, , Assertion (A) Ifo and B are the zeroes, of the polynomial x2 4 Qx —15, then, , Reason (R) Ifo, and B are the zeroes, , a quadratic polynomial ax? +bx +6,, , thena +B =~ snags - 2, a, , a, Assertion (A), 7 If on th, Polynomial p(x) = ( kv 18)e or edt, , is th ", k= 6 reciprocal of the other zero, the"

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CBSE New Pattern ~ Mathematics X (Term D, , 52., , 53., , 54., , 55., , Reason (R) If (x ~ a) and (x — 8) are, the factor of the polynomial (x), then a, and are the zeroes of the f(x), Assertion (A) If the zeroes of, , x" + px + q are two consecutive, integers, then p? —1= 4q, , Reason (R) Ifo, f are zeroes of, , (x - a) (x - 5) —c, then a, b are zeroes of, (x -a) (x -B) +e, , Assertion (A) If the zeroes of the, polynomial , ,, , f(x) =(k? + 4)x? + 4ke +(k° —9) are, equal in magnitude but opposite in sign,, then value of k is zero, , Reason (R) A quadratic polynomial, whose zeroes are o and f is, , x? +(a +B)x + 08, , Assertion (A) If mandn are the, zeroes of the polynomial 3x? +1lx-4,, then 12(m? + n*) + 145mn =0, , Reason (R) Ifo and are the zeroes of, the polynomial ax? + bx + c, then, , 3, op E = f +2, B a ac, Assertion (A) Ifx” + x —12divides, , p(x) =2° + ax? + bx — 84 exactly, then, a=-8andb=-5, , Reason (R) When a polynomial f(x) is, completely divided by (x — @), then, p(x) = 0., , Case Based MCOQs, , 56., , While playing in garden, Rohit saw a, Nest and asked her elder brother what, is that he replied that it’s a nest made, by bird to live themselves. Also he told, him that the shape of the nest formed is, parabolic. The mathematical, representation of the nest structure is, shown in the graph., , 23, , , , Based on the above information,, answer the following questions., , (i) Graph of a quadratic polynomial is, , _____ in shape., (a) straight line (b) parabolic, (c) circular (d) None of these, , (ii) The expression of the polynomial, represented by the graph is, (a)x* -49, (b)x? - 64, (c)x? -36, (d)x? -81, , (iii) Find the value of the polynomial, represented by the graph when x =8, (a)-2 (b)-1, (c)O (d)1, , (iv) The sum of zeroes of the polynomial, x? — Qe — dis, (a)-1 (b)-2, (c)2 (d)1