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S.No. QUESTIONS 1 The prime factorisation of natural number 288 is: (a) 25 × 32 (b) 24 × 32 2 If the HCF of 360 and 64 is 8,then their LCM is: (a)2880 3 (c) 25 × 35 (d) 25 × 33 (b)2530 (c)672 (d)2780 If two positive integers A and B can be expressed as A = xy3 and B = x4y2z ; x, y being prime numbers then HCF (A, B) is : (a) x4y3 4 (b) x4y²z (b)500 (c)400 (d)200 If HCF (26, 169) = 13, then LCM (26, 169) = ? (a)26 6 (d) xy² The LCM of two numbers is 1200. Which of the following cannot be their HCF? (a)600 5 (c) xy²z (b)52 (c)338 (d)13 An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? (a)5 7 (b)6 (c)4,420 (b)2:7 (c)2:1 (b)3 (c)4 (d)1:2 (d)6 If (a × 5)n ends with the digit zero for every natural number n, then a is (a)a prime number (b)an even number (c)an odd number 11 (d)4,525 If LCM (x, 18) = 36 and HCF (x, 18) = 2, then x = (a)2 10 (b)3,515 The ratio of LCM and HCF of the least composite number and the least prime number is : (a)3:2 9 (d)8 The HCF and LCM of 12, 21, 15 respectively are : (a)3,420 8 (c)7 (d)none of these There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students: (a) 34 12 (b)52 (c)48 (d)63 Three bells ring at intervals of 4, 7 and 14 minutes. All the three rang at 7 AM. When will they ring together again? (a)7:28 AM (b)7:54 AM (c)7:32AM (d)7:40AM
The product of a non-zero rational number and an irrational number is (a)always rational 14 (b)always irrational (c)rational or irrational (d)always one The smallest irrational number by which √18 should be multiplied so as to get a rational number is (a) √3 15 (c) √2 (b) 2 (d) √18 If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is: (a) pq2 16 (c) p3q3 (b)pq (d) p2q2 On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps? (a)2540 17 (b)2560 (c)2650 (d)2520 Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags (a)98 18 (b)290 (c)350 (d)450 6×5×4×3×2×1+5 is an example of : (a)prime number (b)composite number (c)irrational number (d)none of the above 19 L.C.M of two numbers is 60 times of their H.C.F. Sum of H.C.F and L.C.M is 366. If one number is 72, then find the other number. (a)60 20 (b)20 (d)120 Two numbers are in the ratio 15:11 their HCF is 13 and LCM is 2145 then find the number. (a)205,132 21 (c)30 (b)175,305 (c)195,143 (d)230,155 The LCM of the two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find their HCF. (a)50 (b)70 (c)90 (d)40 (QUE.22 TO 30) Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(d) Assertion (A) is false but Reason (R) is true. 22 Assertion: The H.C.F. of two numbers is 16 and their product is 3072. Then their L.C.M. = 162. Reason: If a and b are two positive integers, then H.C.F. × L.C.M. = a × b. 23 Assertion: ‘2’ is an example of a rational number. Reason: The square roots of all positive integers are irrational numbers. 24 Assertion: If the HCF of two numbers is 5 and their product is 150, then their LCM is 30. Reason: For any two positive integers p and q, HCF (p, q) + LCM (p, q) = p × q 25 Assertion: (18, 25) is a pair of co-primes. Reason: Pair of co-prime has a common factor 2. 26 Assertion: √𝒙 is an irrational number, where x is a prime number. Reason: Square root of any prime number is an irrational number. 27 Assertion: 3 x 5 x 7 + 7 is a composite number. Reason: A composite number has factors one, itself and any other natural number. 28 Assertion: (2-√𝟓) is an irrational number. Reason: The sum or difference of a rational and an irrational number is irrational. 29 Assertion: 12n ends with the digit zero, where n is any natural number. Reason: Any number ends with digit zero, if its prime factor is of the form 2 𝑚 x 5 𝑛, where m and n are natural numbers. 30 Assertion: HCF of (11,17) is 1. Reason: If p and q are prime then HCF of (p,q) is always 1.
Q. NO. QUESTION 1 (a) 25 × 32 2 (a)2880 3 (d) xy² 4 (b)500 5 (c)338 6 (d)8 7 (a)3,420 8 (c)2:1 9 (c)4 10 (b)an even number 11 (b)52 12 (a)7:28 AM 13 (b)always irrational 14 (c) √2 15 (a) pq2 16 (d)2520 17 (a)98 18 (b)composite number 19 (d)120 20 (c)195,143 21 (a)50 22 (d) 23 (c) 24 (c) 25 (c) 26 (a) 27 (a) 28 (a) 29 (d) 30 (a)
SN 1 MULTIPLE CHOICE QUESTIONS ( MCQ- 30 QUESTIONS) Which of the following is not a polynomial? (a)√3 x3 - 2x - √3 2 (c) 7x2 + 5x - √2 (b) x + (d) 5 Which are the zeroes of p(x) = 6x2 – 7x – 3 (a) 5, –2 (b) –5, 2 (c) –5, –2 (d) none of these 3 The number of zeroes of the polynomial from the graph is (a) 0 (b) 1 (c) 2 (d) 3 4 Find the quadratic polynomial whose zeros are -3 and 4. (a) x2 - 7x – 12 (b) x2 + x + 12 (c)x2 – x – 12. (d) x2 + 3x – 4 5 Which are the zeroes of p(x) = x2 – 8x +15 (a) 5, –2 (b) –5, 2 (c) 5,3 (d) none of these 6 Find the sum and product of the zeroes of polynomial x2 -3x+5 (a) -3,5 (b) 2,5 (c) 3,5 (d) -3,2 7 If one of the zeroes of quadratic polynomial (k +3)x2+ 2kx + 6 is -3 ,then find value of k. (a) 10 (b) -11 (c) 11 (d) 13 8 A quadratic polynomial whose sum and product of zeroes are –5 and 6 is (a) x2 – 5x – 6 (c) x2+ 5x + 6 9 (b) x2 + 5x – 6 (d) none of the above. If the product of the zeroes of the quadratic polynomial 3 x2 + 5x +k is then the value of k is (a) -3 10 (b) -2 (c) 2 (d) 3 If one zero of the polynomial 6x2 + 37x - (k - 2) is reciprocal of the other, then, what is the value of k? (a) 4 (b) -6 (c) 6 (d) -4
The zeroes of the polynomial p(x) = x2 + 4x + 3 are given by (a) 1,3 12 (b) -1,3 (c) 1, -3 (d) -1, -3 If α and β are the zeroes of the polynomial f(x) = px2 - 2x + 3p and α + β = αβ then the value of p (b) (a) 13 (b) (b) (d) a2 – b (c) 2 (c) 3 a2 + b (d) 3 (b) a = 3, b = 1 (b) (d) more than 3 (c) a = -1, b = 5 (d) a = 5, b = -1 (c) + is (d) If α and β are the zeroes of the polynomial f(x) = x2 - ax – b, then the value of α2 + β2 (b) a2 + 2b (c) b2 – 2a b2 + 2a (d) A quadratic polynomial, the sum of whose zeroes is - 5 and their product is 6, is (a) x2 + 5x + 6 21 2 If α and β are the zeroes of the polynomial f(x) = 4x2 - 3x – 7 , then the value of (a) a2 – 2b 20 (c) If x+ 2 is factor of x2 + ax + 2b and a + b = 4, then (a) 19 (d) none The number of polynomials having zeroes -3 and 5 is (a) a = 1, b = 3 18 4 (b) a2 + 2b (a) 1 17 (c) both equal If α and β are the zeroes of the polynomial f(x) = x2 - ax – b , then the value of α2 + β2 is (a) a2 – 2b 16 (b) both positive The maximum number of zeroes a cubic polynomial can have, is (a) 1 15 (d) The zeroes of the quadratic polynomial f(x) = x2 + 99x + 127 are (a) both negative 14 (c) (c) x2 - 5x – 6 (b) x2 - 5x + 6 (d) -x2 + 5x + 6 If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and –3, then (a) a = –7, b = –1 (b) a = 5, b = –1 (c) a = 2, b = – 6 (d) a = 0, b = – 6 22 If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is (b) –10 (a) 10 23 If 2 and are two zeroes of px2+ 5x + r, then (a) p = r = 2 24 (d) –5 (c) 5 (b) p = r = - 2 (c) p = 2, r=2 (d) p = -2, r = 2 What should be subtracted from the polynomial x2 – 16x + 30, so that 15 is the zero of the resulting polynomial? (a) 30 (b) 14 (c) 15 (d) 15
Each of the following questions contains STATEMENT-1 (A) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice. (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. (c) Statement-1 is true, Statement-2 is false (d) Statement-1 is false, Statement-2 is true. 25 Statement-1 (A): The polynomial f(x) = x2 - 2x + 2 has two real zeros. Statement-2 (R): A quadratic polynomial can have at most two real zeroes. 26 Statement-1 (A): A quadratic polynomial having and as its zeroes is 6x2 - 5x + 1 Statement-2 (R): Quadratic polynomial having α and β as zeroes are given by f(x) = k{x2 (α + β) x + αβ} where k is a non-zero constant. 27 Statement-1 (A): If one root of the quadratic polynomial f(x) = (k-1)x2 – 10x + 3, k≠1 is reciprocal of the other, then k = 4 Statement-2 (R): The product of roots of the quadratic polynomial ax2 + bx +c, a ≠ 0 is 28 Statement-1 (A): If α and β are zeroes of the quadratic polynomial x2 +7x + 12, then + Statement-2(R): If α and β are zeroes of the quadratic polynomial ax2 + bx +c, then α + β = and αβ = 29 Statement-1 (A): If α, β and Ƴ are zeroes of the polynomial 6x3 + 3x2 – 5x + 1, then α-1+ β-1+ Ƴ-1= 5 Statement-2(R): If α, β and Ƴ are zeroes of the cubic polynomial ax3 + bx2 + cx + d, then α +β+Ƴ= 30 Statement-1 (A): The polynomial p(x) = x2 + 3x + 3 has two real zeroes. Statement-2(R): A quadratic polynomial can have at most two real zeroes.
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