## Past Exam Papers JEE Main 2013 Mathematics (offline)

/in JEE Main /by M Prakash#### Quiz-summary

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- Question 1 of 30
##### 1. Question

The real number k for which the equation, 2x

^{3}+ 3x + k = 0 has two distinct real roots in [0, 1]CorrectIncorrect - Question 2 of 30
##### 2. Question

The number of values of k, for which the system of equations :

(k + 1)x + 8y = 4k

kx + (k +3)y = 3k – 1 has no solution, isCorrectIncorrect - Question 3 of 30
##### 3. Question

CorrectIncorrect - Question 4 of 30
##### 4. Question

Let T

_{n}be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_{n+1}– T_{n}=10, then the value of n is :CorrectIncorrect - Question 5 of 30
##### 5. Question

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by If the firm employs 25 more workers, then the new level of production of items is :

CorrectIncorrect - Question 6 of 30
##### 6. Question

ABCD is a trapezium such that AB and CD are parallel and BC ⊥ CD. If ∠ADB = θ, BC = p and CD = q, then AB is equal to :

CorrectIncorrect - Question 7 of 30
##### 7. Question

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?

CorrectIncorrect - Question 8 of 30
##### 8. Question

A ray of light along x + √3y = √3 gets reflected upon reaching x-axis, the equation of the reflected ray is :

CorrectIncorrect - Question 9 of 30
##### 9. Question

The area (in square units) bounded by the curves y = √x, 2y – x + 3 = 0, xaxis and lying in the first quadrant is :

CorrectIncorrect - Question 10 of 30
##### 10. Question

CorrectIncorrect - Question 11 of 30
##### 11. Question

If ∫f(x) dx = Ψ(x), then ∫x

^{5}f(x^{3}) dx is equal to :CorrectIncorrect - Question 12 of 30
##### 12. Question

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is :

CorrectIncorrect - Question 13 of 30
##### 13. Question

CorrectIncorrect - Question 14 of 30
##### 14. Question

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is :

CorrectIncorrect - Question 15 of 30
##### 15. Question

Consider :

**Statement -I :**(p ⋀ ~ q) ⋀ (~p ⋀ q) is a fallacy.

**Statement- II:**(p → q) ↔ (~q → ~ p) is a tautology.CorrectIncorrect - Question 16 of 30
##### 16. Question

If the equations x

^{2}+ 2x + 3 = 0 and ax^{2}+ bx + c = 0, a, b, c ϵ R, have a common root, then a : b : c is :CorrectIncorrect - Question 17 of 30
##### 17. Question

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ….., is :

CorrectIncorrect - Question 18 of 30
##### 18. Question

CorrectIncorrect - Question 19 of 30
##### 19. Question

CorrectIncorrect - Question 20 of 30
##### 20. Question

If x, y, z are in A.P. and tan

^{−1}x, tan^{−1}y and tan^{−1}z are also in A.P, then :CorrectIncorrect - Question 21 of 30
##### 21. Question

The intercepts on x-axis made by tangents to the curve, which are parallel to the line y = 2x, are equal to :

CorrectIncorrect - Question 22 of 30
##### 22. Question

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is :

CorrectIncorrect - Question 23 of 30
##### 23. Question

The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point :

CorrectIncorrect - Question 24 of 30
##### 24. Question

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##### 25. Question

CorrectIncorrect - Question 26 of 30
##### 26. Question

CorrectIncorrect - Question 27 of 30
##### 27. Question

Given : A circle, 2x

^{2}+ 2y^{2 }= 5 and a parabola, y^{2}= 4√5x.Statement – I : An equation of a common tangent to these curves is y = x + √5.

Statement – II : If the line is their common tangent, then m satisfied

m

^{4}– 3m^{2}+ 2 = 0CorrectIncorrect - Question 28 of 30
##### 28. Question

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :

CorrectIncorrect - Question 29 of 30
##### 29. Question

CorrectIncorrect - Question 30 of 30
##### 30. Question

CorrectIncorrect