JEE Mains 2012

JEE Mains exam papers

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Chapter 17: JEE Mains 2021 Feb 24 Shift 1

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Chapter 19: JEE Mains 2021 Aug 26 Shift 2

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Chapter 20: JEE Mains 2021 July 25 Shift 1

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Chapter 23: JEE Mains 2021 Feb 26 Shift 2

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Chapter 24: JEE Mains 2021 Feb 24 Shift 2

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Chapter 25: JEE Mains 2021 July 25 Shift 2

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Chapter 26: JEE Mains 2021 July 27 Shift 1

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Chapter 27: JEE Mains 2019

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Chapter 28: JEE Mains 2018

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Chapter 29: JEE Mains 2017

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Chapter 30: JEE Mains 2016

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Chapter 31: JEE Mains 2015

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Chapter 32: JEE Mains 2014

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Chapter 33: JEE Mains 2013

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Chapter 34: JEE Mains 2012

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Chemistry Mathematics Physics

Chapter 35: JEE Mains 2011

179 questions

Chapter 36: JEE Mains 2010

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Chapter 37: JEE Mains 2009

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Chapter 38: JEE Mains 2008

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Chapter 39: JEE Mains 2007

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Chapter 40: JEE Mains 2006

176 questions

Chapter 41: JEE Mains 2005

216 questions

Chapter 42: JEE Mains 2004

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Chapter 43: JEE Mains 2003

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Chapter 44: JEE Mains 2002

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Chapter 45: JEE Mains 2001

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Chapter 46: JEE Mains 2000

182 questions

JEE Mains 2012

Topic List

questions: 89

Verified solutions and explanations

Verified

Easy (17)Medium (47)Hard (25)

Views: 5,686

Assuming the balls to be identical except for the difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green, and 7 black balls is (a) 880 (b) 629 (c) 630 (d) 879

Topic:

Permutations and Combinations

Exam:

JEE Mains 2012

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Views: 5,497

If 100 times the 100th term of an AP with non-zero common difference equal to the 50 times its 50 th term, then the 150 th term of this AP is

$- 150$
150 times its 50 th term
150
zero

Topic:

Sequences and Series

Exam:

JEE Mains 2012

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Views: 5,182

A spherical balloon is filled with

4500 π

cubic meter of helium gas. If a leak in the balloon causes the gas to escape at the rate of

72 π cu m / min

, then the rate (in

m / min

) at which the radius of the balloon decreases 49 min after the leakage began is (a)

\frac{9}{7}

\frac{7}{9}

\frac{2}{9}

\frac{9}{2}

Topic:

Application of Derivatives

Exam:

JEE Mains 2012

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Views: 5,420

a, b \in R

be such that the function

f

f (x) = lo g ∣ x ∣ + b x^{2} + a x, x \neq = 0

has extreme values at

x = - 1

x = 2

f

has local maximum at

x = - 1

x = 2

. Statement II.

a = \frac{1}{2}

b = \frac{- 1}{4}

(a) Statement I is false, Statement II is true (b) Statement I is true, Statement II is true; Statement II is a correct explanation of Statement I (c) Statement I is true, Statement II is true; Statement II is not a correct explanation of Statement I (d) Statement I is true, Statement II is false

Topic:

Application of Derivatives

Exam:

JEE Mains 2012

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Views: 5,787

f : R \to R

is a function defined by

f (x) = [x] cos (\frac{2 x - 1}{2}) π

[x]

denotes the greatest integer function, then

f

is (a) continuous for every real

x

(b) discontinuous only at

x = 0

(c) discontinuous only at non-zero integral values of

x

(d) continuous only at

x = 0

Topic:

Continuity and Differentiability

Exam:

JEE Mains 2012

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Views: 6,023

Consider the function,

f (x) = ∣ x - 2∣ + ∣ x - 5∣, x \in R

f^{'} (4) = 0

f

is continuous in

[2, 5]

, differentiable in

(2, 5)

f (2) = f (5)

. (a) Statement I is false, Statement II is true (b) Statement II is true, Statement II is true; Statement II is a correct explanation of Statement I (c) Statement I is true, Statement II is true; Statement II is not a correct explanation of Statement I (d) Statement I is true, Statement II is false

Topic:

Continuity and Differentiability

Exam:

JEE Mains 2012

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Views: 5,362

If the integral

\int \frac{5 t a n x}{t a n x - 2} d x = x + a lo g ∣ sin x - 2 cos x ∣ + k

a

is equal to (a)

- 1

- 2

Topic:

Integrals

Exam:

JEE Mains 2012

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Views: 6,129

g (x) = \int_{0}^{x} cos 4 t d t

g (x + π)

is equal to (a)

\frac{g ( x )}{g ( π )}

g (x) + g (π)

g (x) - g (π)

g (x) \cdot g (π)

Topic:

Integrals

Exam:

JEE Mains 2012

View 2 solutions

Views: 6,104

p (t)

t

of a certain mouse species satisfies the differential equation

\frac{d p ( t )}{d t} = 0.5 (t) - 450

p (0) = 850

, then the time at which the population becomes zero is (a)

2 lo g 18

lo g 9

\frac{1}{2} lo g 18

lo g 18

Topic:

Differential Equations

Exam:

JEE Mains 2012

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Question 10

Views: 5,291

Statement I. An equation of a common tangent to the parabola

y^{2} = 163 x

and the ellipse

2 x^{2} + y^{2} = 4

y = 2 x + 23

.
Statement II. If the line

y = m x + \frac{4 3}{m}

(m \neq = 0)

is a common tangent to the parabola

y^{2} = 163 x

and the ellipse

2 x^{2} + y^{2} = 4

m

m^{4} + 2 m^{2} = 24

Statement I is false, Statement II is true
Statement I is true, Statement II is true; Statement II is a correct explanation of Statement I
Statement I is true, Statement II is true; Statement II is not a correct explanation of Statement I
Statement I is true, Statement II is false

Topic:

Conic Sections

Exam:

JEE Mains 2012

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Question 11

Views: 5,511

2 x + y = k

passes through the point which divides the line segment joining the points

(1, 1)

(2, 4)

3 : 2

k

is equal to (a)

\frac{29}{5}

(b) 5 (c) 6 (d)

\frac{11}{5}

Topic:

Straight Lines

Exam:

JEE Mains 2012

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Question 12

Views: 5,784

An ellipse is drawn by taking a diameter of the circle

(x - 1)^{2} + y^{2} = 1

as its semi-minor axis and a diameter of the circle

x^{2} + (y - 2)^{2} = 4

is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is

$4 x^{2} + y^{2} = 4$
$x^{2} + 4 y^{2} = 8$
$4 x^{2} + y^{2} = 8$
$x^{2} + 4 y^{2} = 16$

Topic:

Conic Sections

Exam:

JEE Mains 2012

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Question 13

Views: 5,392

An equation of a plane parallel to the plane

x - 2 y + 2 z - 5 = 0

and at a unit distance from the origin is (a)

x - 2 y + 2 z - 3 = 0

x - 2 y + 2 z + 1 = 0

x - 2 y + 2 z - 1 = 0

x - 2 y + 2 z + 5 = 0

Topic:

Three Dimensional Geometry

Exam:

JEE Mains 2012

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Question 14

Views: 5,781

\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4}

\frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1}

intersect, then

k

is equal to (a)

- 1

\frac{2}{9}

\frac{9}{2}

Topic:

Three Dimensional Geometry

Exam:

JEE Mains 2012

View 4 solutions

Question 15

Views: 5,366

a

b

be two unit vectors. If the vectors

c = a + 2 b

d = 5 a - 4 a

are perpendicular to each other, then the angle between

a

b

$\frac{π}{6}$
$\frac{π}{2}$
$\frac{π}{3}$
$\frac{π}{4}$

Topic:

Vector Algebra

Exam:

JEE Mains 2012

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Question 16

Views: 5,220

x_{1}, x_{2}, \dots, x_{n}

n

\overset{x}{ˉ}

be their arithmetic mean and

σ^{2}

be the variance. Statement I. Variance of

2 x_{1}, 2 x_{2}, \dots, 2 x_{n}

4 σ^{2}

. Statement II. Arithmetic mean of

2 x_{1}, 2 x_{2}, \dots, 2 x_{n}

4 \overset{x}{ˉ}

. (a) Statement I is false, Statement II is true (b) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I (c) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I (d) Statement I is true, Statement II is false

Topic:

Statistics

Exam:

JEE Mains 2012

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Question 17

Views: 5,277

Three numbers are chosen at random without replacement from numbers

{1, 2, 3, \dots, 8}

. The probability that their minimum is 3 , given that their maximum is 6 , is (a)

\frac{3}{8}

\frac{1}{5}

\frac{1}{4}

\frac{2}{5}

Topic:

Probability

Exam:

JEE Mains 2012

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Question 18

Views: 5,604

△ PQR

3 sin P + 4 cos Q = 6

4 sin Q + 3 cos P = 1

, then the angle

R

is equal to (a)

\frac{5 π}{6}

\frac{π}{6}

\frac{π}{4}

\frac{3 π}{4}

Topic:

Trigonometric Functions

Exam:

JEE Mains 2012

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Question 19

Views: 5,451

The negation of the statement "If I become a teacher, then I will open a school", is (a) I will become a teacher and I will not open a school (b) Either I will not become a teacher or I will not open a school (c) Neither I will become a teacher nor I will open a school (d) I will not become a teacher or I will open a school

Topic:

Mathematical Reasoning

Exam:

JEE Mains 2012

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Question 20

Views: 5,253

The increasing order of the ionic radii of the given isoelectronic species is

$Cl^{-}, Ca^{2 +}, K^{+}, S^{2}$
$S^{2 -}, Cl^{-}, Ca^{2 +}, K^{+}$
$Ca^{2 +}, K^{+}, Cl^{-}, S^{2 -}$
$K^{+}, S^{2 -}, Ca^{2 +}, Cl^{-}$

Topic:

Classification of Elements and Periodicity in Properties

Exam:

JEE Mains 2012

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