Solutions of IIT-JEE Main Mathematics Exam 2013

Solutions of JEE (Main)—Mathematics
Paper 2013

1. The circle passing through (1, –2) and touching the axis of x at (3, 0) also passes through the point (a) (2, –5)
(b) (5, –2) (c) (–2, 5)
(d) (–5, 2) 2.
ABCD is a trapezium such that AB and CD are parallel and BC ^ CD. If –ADB = q, BC = p and CD = q, then AB is equal to
2

2

2
2
p +q p + q cos q (a) (b) 2
2
p cos q + q sin q p cos q + q sin q
2

2

2

2

( p + q ) cos q
( p + q ) sin q (c) (d)
2
p cos q + q sin q
( p cos q + q sin q) 3. Given: A circle, 2x2 + 2y2 = 5 and a parabola 4 5x. y2 = Statement-I: An equation of a common tangent to these curves is y = x + 5 . Statement-II: If the line, y = mx +

5
(m π 0) is m their common tangent, then m satisfies 2 + 2 = 0. m4–3m (a) Statement-I is true, Statement-II is true,
Statement-II is not a correct explanation for
Statement-I
(b) Statement-I is true, Statement-II is false. (c) Statement-I is false, Statement-II is true. (d) Statement-I is true, Statement-II is true,
Statement-II is a correct explanation for
Statement-I.
4. A ray of light along x + 3 y = 3 gets reflected upon reaching the x-axis, an equation of the reflected ray is (a) = x – 3 (b) 3 x – 3
3y
y=
3y
(c) = x –1

(d) y = x +

3

5. All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of
10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
(a) median
(b) mode
(c) variance
(d) mean
6. If x, y, z are in A.P. and tan–1x, tan–1y and tan–1z are also in A.P., then
(a) 2x = 3y = 6z
(b) 6x = 3y = 2z
(c) 6x = 4y = 3z (d) = z x=y 5
3
7. If Ú f(x)dx = y(x) then Ú x f(x )dx is equal to

1 3 (a) 3) – Ú x3y (x3) dx + C x y(x
3
1 3 (b) 3) – Ú x2y (x3) dx + C x y(x
3
1 3 (c) y(x3) – Ú x3y (x3) dx