**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?

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2.** Find the range of values of t for which

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

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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*(x_{1}) – *f*(x_{2})| < (x_{1} – x_{2})^{2}, for all x_{1}, x_{2} Î R. Find the equation of tangent to

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

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6. **If total number of runs scored in n matches is ((n+1)/4) (2

^{n+1}– n – 2) where n > 1, and the runs scored in the kth match are given by k. 2

^{n+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 4h^{2}. Find the locus of point P.

**8.** Evaluate

∫_{0}^{π}e^{|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 x^{2}/9 - y^{2}/4 = 1 to the circle

x^{2} + y^{2} = 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 x^{2} + y^{2} = 16 and the ellipse x^{2}/25 + y^{2}/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

x^{2} = y, x^{2} = – y and y^{2} = 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.

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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 f^{2} (0) + g^{2} (0) = 0. Prove that there exists some cÎ (–3, 3) such that g(c). gn (c) < 0.

**18.** If

,

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.