JEE Main Model Questions

1. The diagonals of parallelogram PQRS are along the lines x + 3y = 4 and 6x – 2y = 7. Then PQRS can be a
(A) rectangle (B) square
(C) cyclic quadrilateral (D) rhombus

2. The equation of the line perpendicular to x + y + 1 = 0 can be
(A) y − x +1 = 0 (B) y − x −1 = 0
(C) y − 2x + 2 = 0 (D) y − x − 2 = 0

3. If the co-ordinates of the vertices of a triangle are rational numbers then which of the following points of the triangle will always have rational co-ordinates
(A) centroid (B) incentre
(C) circumcentre (D) orthocentre

4. The diagonal of a parallelogram PQRS are along the lines x + 3y = 4 and 6x − 2y = 7 then PQRS must be a
A) rectangle B) square
C) cyclic quadrilateral D) rhombus

5. The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal
A) is linear
B) is homogeneous of first degree
C) has separable variable
D) is second order

6. The numbers 1, 4, 16 can be three terms, not necessarily consecutive, of
A) no A.P. B) only one G.P.
C) infinite number of A.Ps.
D) infinite number of G.Ps.

KEY: 1) BD 2) ABD 3) ACD 4) BD 5) AB 6) CD

Following are some model questions for JEE (Main) examination. The Mathematics questions along with key / answers are given below for practice.

1. If the sum of the distance of a point from two perpendicular lines in a plane is 1. Then its locus is
A) square B) circle C) straight line D) two intersections lines

2. The points (-a, -b), (0, 0), (a, b) and (a2, ab) are
A) collinear B) vertices of rectangle
C) vertices of parallelogram D) none of the above

3. The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is
A) isosceles B) equilateral C) right angled D) none

4. The point of intersection of the right bisectors of the sides AB and AC is at the minimum distance from the side BC, then the triangle is
A) equilateral B) scalene C) isosceles D) right angled

5. The equation of the straight line belonging to both the families of lines given by
x(l+4)+y(10-3l)=18-l and x(1+2m)- (1+m)y+1-2m = 0 is
A) 3x-y-5 = 0 B) 2x-3y-1 = 0
C) x+5y-23 = 0 D) 3x-y+10 = 0

6. If [x] denotes the integral part of x, then the
domain of f(x) = cos-1(x + [x]) is
A) (0,1) B) [0,1) C) [0,1] D) [-1,1]

7. A rectangle PQRS has its side PQ parallel to the line y = mx and vertices PQ and S on the lines y = a, x = b and x = -b respectively. The locus of the vertex R is
A) (m2-1)x+my+b(m2+1)+am = 0
B) (m2-1)x-my +b(m2+1)+am = 0
C) (1-m2)x-my+b(m2+1)+am = 0
D) none of these

8. All points lying inside the triangle formed by the points (1, 3) (5, 0) and (-1, 2) satisfy
A) 3x + 2y ≤ 0
B) 2x + y – 13 ≥ 0
C) 2x – 3y – 12 ≤ 0
D) -2x + y ≥ 0

9. If f(x) is a continuous and differentiable function and f(1/n) = 0 ∀ n ≥ 1 and n ∈ I, then
A) f(x) = 0, x ∈ (0, 1]
B) f(0) = 0, f ′(0) = 0
C) f ′(x) = 0 = f ′′(x), x ∈ (0, 1]
D) f(0) = 0, f ′(0) need not be zero

10. If y = f(x) and x cos y+y cos x = π then f ′′(0) is
A) 1 B) − 1 C) π D) −π

11. If f(x − y) = f(x) . g(y) − f(y) . g(x) and g(x − y) = g(x) g(y) + f(x) . f(y) ∀ x, y ∈ R. If right hand
derivative at x = 0 exists for f(x) then g′(x) at x = 0 is
A) 0 B) 1 C) − 1 D) doesn’t exist.

KEY: 1)A 2)A 3)A 4)D 5)A 6)B 7)B 8)C 9)B 10)C 11)A