QUIZ-II
31. The number of real solutions of the equation $\large sine^x = 5^x + 5^{-x}$ is
(A) 0
(B) 1
(C) 2
(D) infinitely many
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32. The equation (x – 3)9 + (x – 32)9 + …..(x – 39)9 = 0 has
(A) all real equation
(B) real root namely 3, 32, …..39
(C) one real & of imaginary roots
(D) None of these
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33. The set of all real numbers x for which x2 – |x + 2| + x > 0 is
(A) (–∞, –2)∪ (2, ∞)
(B) (–∞, –√2)∪ (√2, ∞)
(C) (–∞, –1) ∪ (1, ∞)
(D) (√2, ∞)
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34. If f(x) = x2 + 2bx + 2c2 and g(x) = -x2 – 2cx + b2, such that minimum f(x) > maximum g(x), then the relation b and c, is
(A) no real value of b and c
(B) 0 < c < b√2
(C) |c| > |b| √2
(D) |c| < |b|√2
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35. If one of the roots of the equation 2x2 – 6x + k = 0 is (α + 5i ) / 2 , then the values of α and k are
(A) α = 3 , k = 8
(B) α = 3/2 , k = 17
(C) α = –3 , k = –17
(D) α = 3 , k = 17
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36. The set of all x in the interval [0 , π] for which 2sin2 x – 3 sin x + 1 ≥ o is
(A) {π/2}
(B) φ
(C) [0 , π/4]
(D) [0 , π/6 ] ∪ [5π/6 , 0] ∪ {π/2}
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37. Let a > 0, b > 0 then both roots of the equation ax2 + bx + c = 0
(A) are real and negative
(B) have negative real parts
(C) have positive real parts
(D) none of these
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38. The number of positive integral solutions of x4 – y4 = 3789108 is
(A) 0
(B) 1
(C) 2
(D) 4
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39. The set of values for which x3 + 1 ≥ x2 + x is
(A) x ≤ 0
(B) x ≥ 0
(C) x ≥ –1
(D) –1 ≤ x ≤ 1
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40. If a ≤ 0, then the roots of x2 – 2a|x – a| – 3a2 = 0 is
(A) (-1+√6)a , a(1 –√2 )
(B) (√6-1) , (√2 – 1)
(C) a
(D) none of these
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41. If the roots of the equation x2 – 2ax + a2 + a -3 = 0 are less than 3 then
(A) a < 2
(B) 2 ≤ a ≤ 3
(C) 3 < a ≤ 4
(D) a > 4
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42. If a1 , a2 , a3 (a1 > 0) are in G. P. with common ratio r, then the value of r, for which the inequality 9a1 + 5 a3 > 14 a2 holds, can not lie in the interval
(A) [1, ∞)
(B) [1, 9/5]
(C) [4/5, 1]
(D) [5/ 9, 1]
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43. Let p(x) = 0 be a polynomial equation of least possible degree, with rational coefficients, having 3√7 + 3√(49) as one of its roots. Then the product of all the roots of p(x) = 0 is
(A) 7
(B) 49
(C) 56
(D) 63
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44. If α and β are the roots of x2 – 3px + p2 = 0 such that α2 + β2 = 7/4 then values of p are
(A) 2, 1
(B) 2, 1/2
(C) 1/2 , 1
(D) 1/2 , –1/2
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45. For all ‘x’, x2 + 2ax + 10 – 3a > 0, then the interval in which ‘a’ lies is
(A) a < – 5
(B) – 5 < a < 2
(C) a > 5
(D) 2 < a < 5
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46. If (m2 -3) x2 + 3mx + 3m + 1= 0 has roots which are reciprocals of each other, then the value of m equals to
(A) 4
(B) 1
(C) 2
(D) None of these
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47. If the two equation x2 – cx + d = 0 and x2 – ax + b = 0 have one common root and the second has equal roots then 2(b + d) is equal to
(A) 0
(B) a + c
(C) ac
(D) –ac
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48. If the inequality $\large \frac{mx^2 + 3x+4}{x^2 + 2x + 2} < 5 $ is satisfied for all x ∈ R , then
(A) 1 < m < 5
(B) -1 < m < 5
(C) 1< m < 6
(D) m < 71/24
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49. If the roots of the equation $\large \frac{a}{x+a + k} + \frac{b}{x+b + k} = 2 $ are equal in magnitude but opposite in sign, then the value of k is
(A) – (a+b)/4
(B) (a+b)/4
(C) (a+b)/2
(D) 0
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50. The number of solutions of the equation n-|x| |m – |x|| = 1
(where m, n > 1 and n > m) is
(A) 0
(B) 1
(C) 2
(D) 4
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Click to See All Answers :
41. A 42. B 43. C 44. D 45. B 46. A 47. C 48. D 49. A 50. C