JEE Main Online Exam 2019: (Memory Based Paper)
JEE Main Online Exam 2019: (Memory Based Paper)
JEE Main Online Exam 2019: (Memory Based Paper)
Q.2 Average height and variance of 5 students in a class is 150 and 18 respectively. If we add one student whose
height is 156 cm then new variance is
(1) 21 (2) 24 (3) 25 (4) 20
Ans. [4]
Q.3 The value of 3(cos – sin )4 + 6(sin + cos )2 + 4 sin6 is
(1) 13 – 4 cos4 (2) 13 – 4 cos2+ 2 sin4 cos2
(3) 13 – 4 cos6 (4) 13 – 4 cos6 + 2 sin4 cos2
Ans. [3]
Q.4 If a î ĵ , b î ˆj k̂ are two vectors and c is another vector such that a c b = 0 and a . c = 0
then | c |2 =
15 19 17 21
(1) (2) (3) (4)
2 2 2 2
Ans. [2]
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Q.6 The equation of the common tangent to the parabola y2 = 4x and the circle x2 + y2 – 6x = 0 is
1 1
(1) y = ± x± 3 (2) y = x± 2
3 2
1
(3) y = 3x+ 2 (4) y = ± 3 x ±
3
Ans. [1]
x2 y2
Q.8 If 1 and e > 2. Then the range of length of latus rectum is 0,
cos 2 sin 2 2
(1) (1, 3/2) (2) (2, 3) (3) (3, ) (4) (3, 4)
Ans. [3]
Q.9 If p and q are the statement the (p q) (~ p q) is equivalent to (p ^ q) then ordered value of (, ) is
(1) , (2) , (3) , (4) ,
Ans. [3]
2 403 k
Q.11 . Then k is
15 15
(1) 8 (2) 9 (3) 10 (4) 7
Ans. [1]
1 1 x4 2
Q.12 lim is equal to -
x 0 x4
1 1 1 1
(1) (2) (3) (4)
2 2 2 8 2 4 2
Ans. [4]
Q.13 The area bounded by the curve y = x2 – 1 and tangent to it at (2, 3) and y-axis is
(1) 8/3 (2) 2/3 (3) 4/3 (4) 1/3
Ans. [1]
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Q.14 A plane parallel to y axis passing through line of intersection of planes x + y + z = 1 and
2x + 3y – z = 4, then which of the point lies on the plane
(1) (2, 3, 1) (2) (3, –1, 1) (3) (2, 1, 3) (4) (–3, 2, 1)
Ans. [2]
1 1
Q.15 If f1(x) = , f2(x) = 1 – x, f3(x) = and (f2oJof1)(x) = f3(x). Find out J(x)
x 1 x
f 3 (x ) f 2 (x)
(1) f1(x) (2) (3) f3(x) (4)
x x
Ans. [3]
5 x 1
a bx 1 x 3
Q.16 f(x) = , what is possible value of a & b if f(x) is continuous for x R
b 5x 3 x 5
30 x5
(1) a = 0, b = 10 (2) a = –5, b = 10 (3) a, b (4) a = –5, b = 0
Ans. [3]
2 3 3
Q.17 If cos–1 + cos–1 = , x > then find x
3x 4x 2 4
3 2i sin
Q.18 , , is purely imaginary. Find sum of all value of
1 2i sin 2
(1) 2/3 (2) /3 (3) 4/3 (4)
Ans. [1]
2 sin( x 2 1) sin 2( x 2 1)
Q.19 x
2 sin( x 2 1) sin 2( x 2 1)
dx , (x2 n + 1, n N) equals-
x2 1 1 x2 1
(1) loge +c
(2) log e c
2 2 2
x2 1 1 x2 1
(3) logesec + C
(4) log e sec c
2 2 2
Ans. [4]
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Q.20 If a < b < c then three circles are touching each other externally and have x-axis as a common tangent, then -
1 1 1
(1) a + c = b (2) + =
b c a
2 2 2
(3) a, b, c are in A.P. (4) a + c = b
Ans. [2]
Q.22 Find the equation of line through (–4, 1, 3) & parallel to the plane x + y + z = 3, while the line intersects
x 5 y 5 z0
another line is -
1 2 1
x4 y 1 z3 x4 y 1 z3
(1) = = (2) = =
3 2 1 1 2 3
x4 y 1 z3 x4 y 1 z3
(3) = = (4) = =
3 2 1 1 2 3
Ans. [3]
3
Q.23 cos x
0
dx =
4 8 2
(1) 0 (2) (3) (4)
3 3 3
Ans. [2]
cos – sin
Q.24 If A then A–50 at = is equal to
sin cos 12
3 / 2 1/ 2 1/ 2 3 / 2
(1) (2)
1 / 2 3 / 2 3 / 2 1 / 2
3 / 2 1/ 2 3/2 1/ 2
(3) (4)
1 / 2 3 / 2 1 / 2 3 / 2
Ans. [4]
Q.25 If 5 girls and 7 boys are in a class. How many number of groups can be made by 2 girls and 3 boys in which
two particular boys never comes together
(1) 280 (2) 310 (3) 300 (4) 305
Ans. [3]
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Q.26 There is a parabola having axis as x-axis, vertex is at a distance of 2 units from origin and focus is
at (4, 0) which of the point does not lie on the parabola.
(1) (6, 8) (2) (5, 2 6 ) (3) (8, 4 3 ) (4) (4, – 4)
Ans. [1]
dy 1
Q.27 If y(x) is solution of x + 2y = x2, y(1) = 1 then value of y is equal to
dx 2
49 45 49 45
(1) (2) (3) (4)
16 8 16 8
Ans. [3]
Q.28 If slant height of a right circular cone is 3 cm then the maximum value of cone is -
(1) 4 3 (2) 2 3 (3) ( 2 3 ) (4) ( 2 3 )
Ans. [2]
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