IIT JEE Paper 2 Mathematics Question Paper for Examination 2013

Welcome to IIT JEE Paper 2 Mathematics Question Papers for Examination 2013 Section. All Candidates can find here IIT JEE Main Paper 2 Mathematics Mains Question Papers online.

Find online IIT JEE (Main) Paper 2 Mathematics Mains Questions:

1. A person goes to office either by car, scooter, bus or train probability of which being 1/7,3/7,2/7 and 1/7 respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is 2/9,1/9,4/9 and 1/9 respectively. Given that he reaches office in time, then what is the probability that he travelled by a car?


2.
 Find the range of values of t for which

2 sin t = (1-2x+5x2)/(3x2-2x-1),t Î [-π/2,π/2].


3.
 Circles with radii 3, 4 and 5 touch each other externally if P is the point of intersection of tangents to these circles at their points of contact. Find the distance of P from the point of contact.

4. Find the equation of the plane containing the line 2x – y + z – 3 = 0,
3x + y + z = 5 and at a distance of 1/√6 from the point (2, 1 – 1).

5. If |f(x1) – f(x2)| < (x1 – x2)2, for all x1, x2 Î R. Find the equation of tangent to

the curve y = f(x) at the point (1, 2).


6. 
If total number of runs scored in n matches is ((n+1)/4) (2n+1 – n – 2) where n > 1, and the runs scored in the kth match are given by k. 2n+1–k, where 1 < k < n. Find n.

7. The area of the triangle formed by the intersection of a line parallel to x-axis and passing through (h, k) with the lines y = x and x + y = 2 is 4h2. Find the locus of point P.

8. Evaluate

0πe|cos x| (2 sin (1/2 cos x) + 3 cos (1/2 cos x) ) sin x dx.

9. Incident ray is along the unit vector v and the reflected ray is along the unit vector w. The normal is along unit vector a outwards. Express vector w in terms of vector a and v.

10. Tangents are drawn from any point on the hyperbola x2/9 - y2/4 = 1 to the circle
x2 + y2 = 9. Find the locus of mid-point of the chord of contact.

11. Find the equation of the common tangent in 1st quadrant to the circle x2 + y2 = 16 and the ellipse x2/25 + y2/4 = 1. Also find the length of the intercept of the tangent between the coordinate axes.

12. If length of tangent at any point on the curve y = f(x) intercepted between the point and the x-axis is of length 1. Find the equation of the curve.

13. Find the area bounded by the curves
x2 = y, x2 = – y and y2 = 4x – 3.

14. If one of the vertices of the square circumscribing the circle |z – 1| = √2 is
2 + √3i. Find the other vertices of square.


15.
 If f(x – y) = f(x) . g(y) – f(y) . g(x) and g(x – y) = g(x) . g(y) + f(x). f(y) for all x, y Î R. If right hand derivative at x = 0 exists for f(x). Find derivative of g(x) at x = 0.

16. If p(x) be a polynomial of degree 3 satisfying p(–1) = 10, p(1) = –6 and p(x) has maximum at x = –1 and p’(x) has minima at x = 1. Find the distance between the local maximum and local minimum of the curve.

17. f(x) is a differentiable function and g(x) is a double differentiable function such that |f(x)| < 1 and f’(x) = g(x). If f2 (0) + g2 (0) = 0. Prove that there exists some cΠ(–3, 3) such that g(c). gn (c) < 0.

18. If
matrices-equation  ,
f(x) is a quadratic function and its maximum value occurs at a point V. A is a point of intersection of y = f(x) with x-axis and point B is such that chord AB subtends a right angle at V. Find the area enclosed by f(x) and chord AB.

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