Question with Answer JEE Mains
1. The quadratic equations x2 – 6x + a = 0 and x2 – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then, the common root is
(a) 1
(b) 4
(b) 4
(c) 3
(d) 2
(d) 2
Ans. d
2. How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
2. How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
(a) 8 . 6C4 . 7C4
(b) 6 . 7 . 8C4
(b) 6 . 7 . 8C4
(c) 6 . 8 . 7C4
(d) 7 . 6C4 . 8C4
(d) 7 . 6C4 . 8C4
Ans. d
3. Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then, a2 + b2 + c2 + 2 abc is equal to
(a) 2
(b) –1
(b) –1
(c) 0
(d) 1
(d) 1
Ans. d
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4. The first two terms of a geometric progression add upto 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is
(a) –4
(b) –12
(b) –12
(c) 12
(d) 4
(d) 4
Ans. b
5. Let R be the real line. Consider the following subsets of the plane R × R
5. Let R be the real line. Consider the following subsets of the plane R × R
S = {(x, y) : y = x + 1 and 0 < x < 2}
T = {(x, y) : x – y is an integer}. Which one of the following is true?
(a) Neither S nor T is an equivalence relation on R
(b) Both S and T are equivalence relations on R
(c) S is an equivalence relation on R but T is not
(d) T is an equivalence relation on R but S is not
Ans. d
6. The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept –4. Then, a possible value of k is
(a) 1
(b) 2
(b) 2
(c) –2
(d) –4
(d) –4
Ans. d
7. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then, which one of the following gives possible values of a and b?
7. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then, which one of the following gives possible values of a and b?
(a) a = 0, b = 7
(b) a = 5, b = 2
(b) a = 5, b = 2
(c) a = 1, b = 6
(d) a = 3, b = 4
(d) a = 3, b = 4
Ans. d
8. A parabola has the origin as its focus and the line x = 2 as the directrix. Then, the vertex of the parabola is at
8. A parabola has the origin as its focus and the line x = 2 as the directrix. Then, the vertex of the parabola is at
(a) (0, 2)
(b) (1, 0)
(b) (1, 0)
(c) (0, 1)
(d) (2, 0)
(d) (2, 0)
Ans. b
9. The point diametrically opposite to the point P( 1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is
(a) (3, –4)
(b) (–3, 4)
(b) (–3, 4)
(c) (–3, –4)
(d) (3, 4)
(d) (3, 4)
Ans. c
10. The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA will be
10. The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA will be
(a) 9.58
(b) 4.79
(b) 4.79
(c) 7.01
(d) 9.22
(d) 9.22
Ans. c
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