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JEE Mathematics 2013 previous year questions with solutions

122 JEE Mathematics questions from 2013 in the Quantrex bank. Featured questions below open unique solution pages. Browse by chapter on JEE Mathematics.

122 questions2013
1

The function f x = 2 x + x + 2 - x + 2 - 2 x has a local minimum or a local maximum at x =

JEE Advanced 2013 Application of Derivatives Solution View → 2

Paragraph: Let f:[0,1] R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f^ (x)-2 f^ (x)+

JEE Advanced 2013 Application of Derivatives Solution View → 3

Paragraph: Let f:[0,1] R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f^ (x)-2 f^ (x)+

JEE Advanced 2013 Application of Derivatives Solution View → 4

A line L : y = m x + 3 meets y - a x is at E(0,3) and the arc of the parabola y 2 = 1 6 x , 0 ≤ y ≤ 6 at the point F ⁡ x 0 y 0 .The tangent to

JEE Advanced 2013 Application of Derivatives Solution View → 5

The number of points in - ∞ , ∞ , for which x 2 - x sin x - cos x = 0 , is:

JEE Advanced 2013 Application of Derivatives Solution View → 6

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing s

JEE Advanced 2013 Application of Derivatives Solution View → 7

The area enclosed by the curves y = sin x + cos x and y = cos x - sin x over the interval 0 , π 2 is

JEE Advanced 2013 Area Under Curves Solution View → 8

Let f:[-2,3] [0, ) be a continuous function such that f(1-x)=f(x) for all x [-2,3] . If R ₁ is the numerical value of the area of the region bounded by y=f(x),

JEE Main 2013 Area Under Curves Solution View → 9

The area under the curve y=| x- x| , 0 x 2 , and above x -axis is :

JEE Main 2013 Area Under Curves Solution View → 10

The area of the region (in sq. units), in the first quadrant bounded by the parabola y=9 x^2 and the lines x=0, y=1 and y=4 , is :

JEE Main 2013 Area Under Curves Solution View → 11

The area bounded by the curve y= (x) and the lines y=0, y= (3) and x=0 is equal to:

JEE Main 2013 Area Under Curves Solution View → 12

The area (in square units) bounded by the curves y = x , 2 y - x + 3 = 0 , X -axis and lying in the first quadrant is

JEE Main 2013 Area Under Curves Solution View → 13

If 3 x = 4 x - 1 , then x =

JEE Advanced 2013 Basics of Mathematics Solution View → 14

The least integral value of x such that x-5 x^2+5 x-14 >0 , satisfies :

JEE Main 2013 Basics of Mathematics Solution View → 15

The coefficients of three consecutive terms of 1 + x n + 5 are in the ratio 5 : 10 : 14 . Then n =

JEE Advanced 2013 Binomial Theorem Solution View → 16

Circle(s) touching x -axis at a distance 3 from the origin and having an intercept of length 2 7 on y -axis is (are)

JEE Advanced 2013 Circle Solution View → 17

Statement 1: The only circle having radius 10 and a diameter along line 2 x+y=5 is x^2+y^2-6 x+2 y=0 . Statement 2: 2 x+y=5 is a normal to the circle x^2+y^2-6

JEE Main 2013 Circle Solution View → 18

If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle 60^ on the circumference of the first circle, then the radi

JEE Main 2013 Circle Solution View → 19

If the circle x^2+y^2-6 x-8 y+ (25-a^2 )=0 touches the axis of x , then a equals.

JEE Main 2013 Circle Solution View → 20

If a circle C passing through (4,0) touches the circle x^2+y^2+4 x-6 y-12=0 externally at a point (1,-1) , then the radius of the circle C is :

JEE Main 2013 Circle Solution View → 21

If each of the lines 5 x+8 y=13 and 4 x-y=3 contains a diameter of the circle x^2+y^2-2 (a^2-7 a+11 )x-2 (a^2-6 a+6 ) y+b^3+1=0 , then :

JEE Main 2013 Circle Solution View → 22

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

JEE Main 2013 Circle Solution View → 23

Given : A circle, 2 x 2 + 2 y 2 = 5 and a parabola, y 2 = 4 5 x . Statement - I : An equation of a common tangent to these curves is y = x + 5 . Statement - II

JEE Main 2013 Circle Solution View → 24

Let w ⁡ = 3 + i 2 and P = w ⁡ n : n = 1, 2, 3, … .Further H 1 = z ∈ C : Re z > 1 2 and H 2 = z ∈ C : Re z < - 1 2 , where

JEE Advanced 2013 Complex Number Solution View →

Other years

2015 · 872016 · 882017 · 882018 · 1302019 · 3492020 · 1,1412021 · 6632022 · 6502023 · 7522024 · 6342025 · 5072026 · 509
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