JEE Main 2011 Maths Question Paper Set 1 With Solution

Be Paitent While your exam is being loaded

View Solution

Participate to compete with other aspirants at an all India level.

Attempt Mock Test

Participate to compete with other aspirants at an all India level.

General Instructions

Choose Your Default Language

Please read the instructions carefully

General Instructions:

- Total duration of is 60 min.
The clock will be set at the server. The countdown timer in the top right corner of screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.
The Questions Palette displayed on the right side of screen will show the status of each question using one of the following symbols:
1. You have not visited the question yet.
2. You have not answered the question.
3. You have answered the question.
4. You have NOT answered the question, but have marked the question for review.
5. The question(s) "Answered and Marked for Review" will be considered for evalution.
You can click on the ">" arrow which apperes to the left of question palette to collapse the question palette thereby maximizing the question window. To view the question palette again, you can click on "<" which appears on the right side of question window.
You can click on your "Profile" image on top right corner of your screen to change the language during the exam for entire question paper. On clicking of Profile image you will get a drop-down to change the question content to the desired language.
You can click on to navigate to the bottom and to navigate to top of the question are, without scrolling.

Navigating to a Question:

To answer a question, do the following:
1. Click on the question number in the Question Palette at the right of your screen to go to that numbered question directly. Note that using this option does NOT save your answer to the current question.
2. Click on Save & Next to save your answer for the current question and then go to the next question.
3. Click on Mark for Review & Next to save your answer for the current question, mark it for review, and then go to the next question.

Answering a Question:

Procedure for answering a multiple choice type question:
1. To select you answer, click on the button of one of the options.
2. To deselect your chosen answer, click on the button of the chosen option again or click on the Clear Response button
3. To change your chosen answer, click on the button of another option
4. To save your answer, you MUST click on the Save & Next button.
5. To mark the question for review, click on the Mark for Review & Next button.
To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.

Navigating through sections:

Sections in this question paper are displayed on the top bar of the screen. Questions in a section can be viewed by click on the section name. The section you are currently viewing is highlighted.
After click the Save & Next button on the last question for a section, you will automatically be taken to the first question of the next section.
You can shuffle between sections and questions anything during the examination as per your convenience only during the time stipulated.
Candidate can view the corresponding section summery as part of the legend that appears in every section above the question palette.

Please note all questions will appear in your default language. This language can be changed for a particular question later on.

I have read and understood the instructions. All computer hardware allotted to me are in proper working condition. I declare that I am not in possession of / not wearing / not carrying any prohibited gadget like mobile phone, bluetooth devices etc. /any prohibited material with me into the Examination Hall.I agree that in case of not adhering to the instructions, I shall be liable to be debarred from this Test and/or to disciplinary action, which may include ban from future Tests / Examinations

Proceed

Back
Total Question		Total Attempted
Correct Answers		Incorrect Answers
Score

Category: IIT-JEE 2011 Math Paper 1

Question 1:

Let

(x_{0}, y_{0})

be the solution of the following equations

{(2 x)}^{1 n 2} = {(3 y)}^{1 n 3} 3^{1 n x} = 2^{1 n} y

Then

x_{0}

(A)	$\frac{1}{6}$	(B)	$\frac{1}{3}$
(C)	$\frac{1}{2}$	(D)	6

Correct Answer : C

Category: IIT-JEE 2011 Math Paper 1

Question 2:

The value of

\int_{\sqrt{\ln 2} x}^{\sqrt{l n 3}} \frac{x \sin x^{2}}{\sin x^{2} + \sin (\ln 6 - x^{2})} d x

(A)	$\frac{1}{4} \ln \frac{3}{2}$	(B)	$\frac{1}{2} \ln \frac{3}{2}$
(C)	$\ln \frac{3}{2}$	(D)	$\frac{1}{6} \ln \frac{3}{2}$

Correct Answer : A

Category: IIT-JEE 2011 Math Paper 1

Question 3:

Let

\overset{⇀}{a} = \hat{1} + \hat{j} + \hat{k}, \overset{⇀}{b} = \hat{i} - \hat{j} + \hat{k} a n d \overset{⇀}{c} = \hat{i} - \hat{j} - \hat{k}

be three vectors. A vector

v

in the plane of

\vec{a} a n d \vec{b}

, whose projection on

\overset{⇀}{c} i s \frac{1}{\sqrt{3}}

, is given by

(A)	$\hat{i} - 3 \hat{j} + 3 \hat{k}$	(B)	$- 3 \hat{i} - 3 \hat{j} - \hat{k}$
(C)	$3 \hat{i} - \hat{j} + 3 \hat{k}$	(D)	$\hat{i} + 3 \hat{j} - 3 \hat{k}$

Correct Answer : C

Category: IIT-JEE 2011 Math Paper 1

Question 4:

Let

P = {θ : \sin θ - \cos θ = \sqrt{2} \cos θ}

and

Q = {θ : \sin θ + \cos θ = \sqrt{2} \sin θ}

be two sets. The

Correct Answer : P = Q

Category: IIT-JEE 2011 Math Paper 1

Question 5:

Let the straight line x = b divide the area enclosed by

y = {(1 - x)}^{2}, y = 0, a n d x = 0

into two parts

R_{1} (0 \leq x \leq b) a n d R_{2} (b \leq x \leq 1) s u c h t h a t R_{1} - R_{2} = \frac{1}{4}

Then b equals

(A)	$\frac{3}{4}$	(B)	$\frac{1}{2}$
(C)	$\frac{1}{3}$	(D)	$\frac{1}{4}$

Correct Answer : B

Category: IIT-JEE 2011 Math Paper 1

Question 6:

Let α and β be the roots of

x^{2} - 6 x - 2 = 0

, with α > β. If

a_{n} = α^{n} - β^{n} f o r n \geq 1

then the value of

\frac{a_{10} - 2 a_{8}}{2 a_{9}}

Correct Answer : 3

Category: IIT-JEE 2011 Math Paper 1

Question 7:

A straight line L through the point (3,-2) is inclined at an angle 60° to the line

\sqrt{3} x + y = 1

.If L also intersects the x-axis, then the equation of L is

(A)	$y + \sqrt{3} x + 2 - 3 \sqrt{3} = 0$	(B)	$y - \sqrt{3} x + 2 + 3 \sqrt{3} = 0$
(C)	$\sqrt{3} y - x + 3 + 2 \sqrt{3} = 0$	(D)	$\sqrt{3} y + x - 3 + 2 \sqrt{3} = 0$

Correct Answer : B

Category: IIT-JEE 2011 Math Paper 1

Question 8:

The vector(s) which is/are coplanar with vectors

\hat{i} + \hat{j} + 2 \hat{k} a n d \hat{i} + 2 \hat{j} + \hat{k}

and perpendicular to the vector

\hat{i} + \hat{j} + \hat{k}

is/are

(A)	$\hat{j} - \hat{k}$	(B)	$- \hat{i} + \hat{j}$
(C)	$\hat{i} - \hat{j}$	(D)	$- \hat{j} + \hat{k}$

Correct Answer : A and D

Category: IIT-JEE 2011 Math Paper 1

Question 9:

Let M and N be two 3x3 non-singular skew-symmetric matrices such that MN - NM . If

P^{T}

denotes the transpose of P, then

M^{2} N^{2} {(M^{T} N)}^{- 1} {(M N^{- 1})}^{T}

is equal to

(A)	$M^{2}$	(B)	$- N^{2}$
(C)	$- M^{2}$	(D)	$M N$

Correct Answer : A, B, C and D

Category: IIT-JEE 2011 Math Paper 1

Question 10:

Let the eccentricity of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

be reciprocal to that of the ellipse

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

. If the hyperbola passes through a focus of the ellipse, then

(A)	the equation of the hyperbola is $\frac{x^{2}}{3} - \frac{y^{2}}{2} = 1$	(B)	a focus of the hyperbola is (2, 0)
(C)	the eccentricity of the hyperbola is $\sqrt{\frac{5}{3}}$	(D)	the equation of the hyperbola is $x^{2} - 3 y^{2} = 3$

Correct Answer : B and D

Category: IIT-JEE 2011 Math Paper 1

Question 11:

Let

f : ℝ \to ℝ

be a function such that

f (x + y) = f (x) + f (y), \forall x, y \in ℝ

If f/(x) is differentiable at x = 0, then

(A)	f/(x) is differentiable only in a finite interval containing zero	(B)	f/(x) is continuous $\forall x \in ℝ$
(C)	f'(x) is constant $\forall x \in ℝ$	(D)	f/(x) is differentiable except at finitely many points

Correct Answer : B, C and D

Category: IIT-JEE 2011 Math Paper 1

Question 12:

Let a, b and c be three real numbers satisfying

[\begin{matrix} a & b & c \end{matrix}] |\begin{matrix} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \end{matrix}| = [\begin{matrix} 0 & 0 & 0 \end{matrix}] . . . . . . . . . . . . . . . (E)

If the point P(a, b, c), with reference to (E), lies on the plane 2x + y + < = 1, then the value of 7a+b+c is

Correct Answer : 6

Category: IIT-JEE 2011 Math Paper 1

Question 13:

Let a, b and c be three real numbers satisfying

[\begin{matrix} a & b & c \end{matrix}] |\begin{matrix} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \end{matrix}| = [\begin{matrix} 0 & 0 & 0 \end{matrix}] . . . . . . . . . . . . . . . (E)

Let ω be a solution of

x^{3} - 1 = 0

with

I m (ω) > 0

. If a = 2 with b and c satisfying (E), then the value of

\frac{3}{ω^{a}} + \frac{1}{ω^{b}} + \frac{3}{ω^{c}}

is equal to

Correct Answer : -2

Category: IIT-JEE 2011 Math Paper 1

Question 14:

Let a, b and c be three real numbers satisfying

[\begin{matrix} a & b & c \end{matrix}] |\begin{matrix} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \end{matrix}| = [\begin{matrix} 0 & 0 & 0 \end{matrix}] . . . . . . . . . . . . . . . (E)

Let b = 6, with v and c satisfying (E). If a and 0 are the roots of the quadratic equation

a x^{2} + b x + c = 0

, then

\sum_{n = 0}^{\infty} {(\frac{1}{α} + \frac{1}{β})}^{n}

(A)	6	(B)	7
(C)	$\frac{6}{7}$	(D)	$\infty$

Correct Answer : B

Category: IIT-JEE 2011 Math Paper 1

Question 15:

Let

U_{1} a n d U_{2}

be two urns such that

U_{1}

contains 3 white and 2 red balls, and

U_{2}

contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from

U_{1}

and put into

U_{2}

. However, if tail appears then 2 balls are drawn at random from

U_{1}

and put into

U_{2}

. Now 1 ball is drawn at random from

U_{2}

. The probability of the drawn ball from

U_{2}

being white is

(A)	$\frac{13}{30}$	(B)	$\frac{23}{30}$
(C)	$\frac{19}{30}$	(D)	$\frac{11}{30}$

Correct Answer : B

Category: IIT-JEE 2011 Math Paper 1

Question 16:

Let

U_{1} a n d U_{2}

be two urns such that

U_{1}

contains 3 white and 2 red balls, and

U_{2}

contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from

U_{1}

and put into

U_{2}

. However, if tail appears then 2 balls are drawn at random from

U_{1}

and put into

U_{2}

. Now 1 ball is drawn at random from

U_{2}

. Given that the drawn ball from

U_{2}

is white, the probability that head appeared on the coin is

(A)	$\frac{17}{23}$	(B)	$\frac{11}{23}$
(C)	$\frac{15}{23}$	(D)	$\frac{12}{23}$

Correct Answer : D

Category: IIT-JEE 2011 Math Paper 1

Question 17:

Consider the parabola

y^{2} = 8 x

. Let

∆_{1}

be the area of the triangle formed by the end points of its latus rectum and the point

P (\frac{1}{2}, 2)

on the parabola, and

∆_{2}

be the area of the triangle formed by drawing tangents at P and at the end points of the latus rectum Then

\frac{∆_{1}}{∆_{2}}

is (The answer of the questions is a single-digit integer, ranging from 0 to 9.)

Correct Answer : 2

Category: IIT-JEE 2011 Math Paper 1

Question 18:

Let

a_{1}, a_{2}, a_{3} . . . . ., a_{100}

be an arithmetic progression with

a_{1} = 3 a n d S_{p} = \sum_{i = 1}^{p} a_{1}, 1 \leq p \leq 100

For any integer n with

1 \leq n \leq 20

, let m=5n. if

\frac{S_{m}}{S_{n}}

does not depend on n, then

a_{2}

is (The answer of the questions is a single-digit integer, ranging from 0 to 9.)

Correct Answer : 3 and 9

Category: IIT-JEE 2011 Math Paper 1

Question 19:

The positive integer value of n >3 satisfying the equation

\frac{1}{\sin (\frac{π}{n})} = \frac{a}{\sin (\frac{2 π}{n})} + \frac{1}{\sin (\frac{3 π}{n})}

is (The answer of the questions is a single-digit integer, ranging from 0 to 9.)

Correct Answer : 7

Category: IIT-JEE 2011 Math Paper 1

Question 20:

Let f: [1, ∞) → [2, ∞) be a differentiable function such that /(l) = 2. If

6 \int_{1}^{x} f (t) d t = 3 x f (x) - x^{3}

for all

x \geq 1

then the value of f(2) is (The answer of the questions is a single-digit integer, ranging from 0 to 9.)

Correct Answer : None of These

Category: IIT-JEE 2011 Math Paper 1

Question 21:

If z is any complex number satisfying

|z - 3 - 2 i| \leq 2

, then the minimum value of |2z-6 + 5i| is (The answer of the questions is a single-digit integer, ranging from 0 to 9.)

Correct Answer : 5

Category: IIT-JEE 2011 Math Paper 1

Question 22:

The minimum value of the sum of real numbers

a^{- 5}, a^{- 4}, 3 a^{- 3}, 1, a^{8} a n d a^{10} w i t h a > 0

is (The answer of the questions is a single-digit integer, ranging from 0 to 9.)

Correct Answer : 8

Category: IIT-JEE 2011 Math Paper 1

Question 23:

Let

f (θ) = \sin (\tan^{- 1} (\frac{\sin θ}{\sqrt{\cos 2 θ}}))

, where

- \frac{π}{4} < θ < \frac{π}{4}

Then the value of

\frac{d}{d (\tan θ)} (f (θ))

is (The answer of the questions is a single-digit integer, ranging from 0 to 9.)

Correct Answer : 1

Not Visited	0	Not Answered
Answered	0	Marked for Review
Answered & Marked for Review (will be considered for evaluation)

JEE Main 2011 Maths Question Paper Set 1 With Solution

View Solution

Attempt Mock Test

General Instructions

Please read the instructions carefully

General Instructions:

Navigating to a Question:

Answering a Question:

Navigating through sections:

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7:

Question 8:

Question 9:

Question 10:

Question 11:

Question 12:

Question 13:

Question 14:

Question 15:

Question 16:

Question 17:

Question 18:

Question 19:

Question 20:

Question 21:

Question 22:

Question 23:

Exam Summary

Are you sure you want to submit for final marking? No changes will be allowed after submission.

Thank you, Submitted Successfully.

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7:

Question 8:

Question 9:

Question 10:

Question 11:

Question 12:

Question 13:

Question 14:

Question 15:

Question 16:

Question 17:

Question 18:

Question 19:

Question 20:

Question 21:

Question 22:

Question 23:

Are you sure you want to submit for final marking?
No changes will be allowed after submission.