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JEE Mathematics 2010 previous year questions with solutions

61 JEE Mathematics questions from 2010 in the Quantrex bank. Featured questions below open unique solution pages. Browse by chapter on JEE Mathematics.

61 questions2010
1

Let f be a function defined on R (the set of all real numbers) such that f^ (x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4 , for all x R . If g is a function de

JEE Advanced 2010 Application of Derivatives Solution View → 2

Paragraph: Consider the polynomial f(x)=1+2 x+3 x^2+4 x^3 . Let s be the sum of all distinct real roots of f(x) and let t=|s| . Question: The real number s lies

JEE Advanced 2010 Application of Derivatives Solution View → 3

Paragraph: Consider the polynomial f(x)=1+2 x+3 x^2+4 x^3 . Let s be the sum of all distinct real roots of f(x) and let t=|s| . Question: The function f^ (x) is

JEE Advanced 2010 Application of Derivatives Solution View → 4

Let f, g and h be real-valued functions defined on the interval [0,1] by f(x)=e^ x^2 +e^ -x^2 , g(x)=x e^ x^2 +e^ -x^2 and h(x)=x^2 e^ x^2 +e^ -x^2 . If a, b an

JEE Advanced 2010 Application of Derivatives Solution View → 5

The maximum value of the expression 1 ^2 +3 +5 ^2 is

JEE Advanced 2010 Application of Derivatives Solution View → 6

Paragraph: Consider the polynomial f(x)=1+2 x+3 x^2+4 x^3 . Let s be the sum of all distinct real roots of f(x) and let t=|s| . Question: The area bounded by th

JEE Advanced 2010 Area Under Curves Solution View → 7

The area bounded by the curves y= x and y= x between the ordinates x=0 and x= 3 2 is

JEE Main 2010 Area Under Curves Solution View → 8

For r=0,1, , 10 , let A_r, B_r and C_r denote, respectively, the coefficient of x^r in the expansions of (1+x)¹⁰ , (1+x)²⁰ and (1+x)³⁰ . Then _ r=1 ¹⁰ A_r (B₁₀

JEE Advanced 2010 Binomial Theorem Solution View → 9

Two parallel chords of a circle of radius 2 are at a distance 3 +1 apart. If the chords subtend at the centre, angles of k and 2 k , where k>0 , then the value

JEE Advanced 2010 Circle Solution View → 10

Paragraph: The circle x^2+y^2-8 x=0 and hyperbola x^2 9 - y^2 4 =1 intersect at the points A and B . Question: Equation of the circle with A B as its diameter i

JEE Advanced 2010 Circle Solution View → 11

The circle x^2+y^2=4 x+8 y+5 intersects the line 3 x-4 y=m at two distinct points if

JEE Main 2010 Circle Solution View → 12

Match the statements of Column I with these in Column II. [Note : Here z takes values in the complex plane and Im (z) and Re (z) denote respectively, the imagin

JEE Advanced 2010 Complex Number Solution View → 13

Let z₁ and z₂ be two distinct complex numbers and let z=(1-t) z₁+t z₂ for some real number t with 0 < t < 1 . If (w) denotes the principal argument of a non-zer

JEE Advanced 2010 Complex Number Solution View → 14

Let be the complex number 2 3 +i 2 3 . Then the number of distinct complex number z satisfying | array ccc z+1 & & ^2 & z+ ^2 & 1 ^2 & 1 & z+ array |=0 is equal

JEE Advanced 2010 Complex Number Solution View → 15

Let f be a real-valued function defined on the interval (0, ) , by f(x)= x+ ₀^x 1+ t d t . Then which of the following statement(s) is (are) true ?

JEE Advanced 2010 Continuity and Differentiability Solution View → 16

Let f: R R be a continuous function defined by f(x)= 1 e^x+2 e^ -x . Statement-1: f(c)= 1 3 , for some c R . Statement-2: 0 < f(x) 1 2 2 , for all x R

JEE Main 2010 Continuity and Differentiability Solution View → 17

The value(s) of ₀^1 x^4(1-x)^4 1+x^2 d x is (are)

JEE Advanced 2010 Definite Integration Solution View → 18

For any real number x , let [x] denotes the largest integer less than or equal to x . Let f be a real valued function defined on the interval [-10,10] by f(x)=

JEE Advanced 2010 Definite Integration Solution View → 19

Let k be a positive real number and let aligned A & = [ array ccc 2 k-1 & 2 k & 2 k 2 k & 1 & -2 k -2 k & 2 k & -1 array ] and B & = [ array ccc 0 & 2 k-1 & k 1

JEE Advanced 2010 Determinants Solution View → 20

Consider the system of linear equations: aligned & x₁+2 x₂+x₃=3 & 2 x₁+3 x₂+x₃=3 & 3 x₁+5 x₂+2 x₃=1 aligned The system has

JEE Main 2010 Determinants Solution View → 21

Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1)=1 . If the y -intercept of the tangent at any point P(x, y) on

JEE Advanced 2010 Differential Equations Solution View → 22

Let f be a real-valued function defined on the interval (-1,1) such that e^ -x f(x)=2+ ₀^x t^4+1 d t, for all x (-1,1) and let f⁻¹ be the inverse function of f

JEE Advanced 2010 Differentiation Solution View → 23

Let f:(-1,1) R be a differentiable function with f(0)=-1 and f^ (0)=1 . Let g(x)=[f(2 f(x)+2)]^2 . Then g^ (0)=

JEE Main 2010 Differentiation Solution View → 24

Paragraph: Tangents are drawn from the point P(3,4) to the ellipse x^2 9 + y^2 4 =1 touching the ellipse at points A and B . Question: The coordinates of A and

JEE Advanced 2010 Ellipse Solution View →

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