Question with Answer JEE Mains

1. If PS is the median of the triangle with vertices P (2, 2), Q (6, –1) and R (7, 3), then equation of the line passing through (1, –1) and parallel to PS is
(a) 4x – 7y – 11 = 0
(b) 2x + 9y + 7 = 0 
(c) 4x + 7y + 3 = 0
(d) 2x – 9y – 11 = 0
Ans. b
 
2. . Let a, b, c and d be non-zero numbers. If the point of intersection of the lines  4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes, then
(a) 2bc – 3ad = 0
(b) 2bc + 3ad = 0 
(c) 2ad – 3bc = 0
(d) 3bc + 2ad = 0
Ans. c

3. The locus of the foot of perpendicular drawn from the centre of the ellipse x2 + 3y2 = 6 on any tangent to it is
(a) (x2 – y2)2 = 6x2 + 2y2
(b) (x2 – y2)2 = 6x2 – 2y2
(c) (x2 + y2)2 = 6x2 + 2y2
(d) (x2 + y2)2 = 6x2 – 2y2
Ans. c
4. The statement ~ (p → ~ q) is
(a) equivalent to p → q
(b) equivalent to ~p → q
(c) a tautology
(d) a fallacy
Ans. a
5.  If [a × bb × cc × a] = l[a b c]2, then l is equal to
(a) 0
(b) 1
(c) 2
(d) 3
Ans. b

6. If f and g are differentiable functions in (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c Î ]0,1[
(a) 2f'(c) = g'(c)
(b) 2f'(c) = 3g'(c)
(c) f'(c) = g'(c)
(d) f'(c) = 2g'(c)
Ans. d
7. If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A–1AT, then BBT is equal to
(a) 1 + B
(b) 1
(c) B–1
(d)  (B–1)T
Ans. b
8. Which one is classified as a condensation polymer?
(a) Dacron
(b) Neoprene
(c) Teflon
(d) Acrylonitrile
Ans. a

9. Which one of the following bases is not present in DNA?
(a) Quinoline
(b) Adenine
(c) Cytosine
(d) Thymine
Ans. a
10. Considering the basic strength of amines in aqueous solution, which one has the smallest pKb value?
(a) (CH3)2NH
(b) CH3NH2
(c) (CH3)3N
(d) C6H5NH2
Ans. a
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