Joint Entrance Examination

Graduate Aptitude Test in Engineering

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1

MCQ (Single Correct Answer)

Consider the two curves $${C_1}:{y^2} = 4x,\,{C_2}:{x^2} + {y^2} - 6x + 1 = 0$$. Then,

A

$${C_1}$$ and $${C_2}$$ touch each other only at one point.

B

$${C_1}$$ and $${C_2}$$ touch each other exactly at two points

C

$${C_1}$$ and $${C_2}$$ intersect (but do not touch ) at exactly two points

D

$${C_1}$$ and $${C_2}$$ neither intersect nor touch each other

2

MCQ (Single Correct Answer)

If a continuous function $$f$$ defined on the real line $$R$$, assumes positive and negative values in $$R$$ then the equation $$f(x)=0$$ has a root in $$R$$. For example, if it is known that a continuous function $$f$$ on $$R$$ is positive at some point and its minimum value is negative then the equation $$f(x)=0$$ has a root in $$R$$.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

For $$k>0$$, the set of all values of $$k$$ for which $$k{e^x} - x = 0$$ has two distinct roots is

A

$$\left( {0,{1 \over e}} \right)$$

B

$$\left( {{1 \over e},1} \right)$$

C

$$\left( {{1 \over e},\infty } \right)$$

D

$$\left( {0,1} \right)$$

3

MCQ (Single Correct Answer)

If a continuous function $$f$$ defined on the real line $$R$$, assumes positive and negative values in $$R$$ then the equation $$f(x)=0$$ has a root in $$R$$. For example, if it is known that a continuous function $$f$$ on $$R$$ is positive at some point and its minimum value is negative then the equation $$f(x)=0$$ has a root in $$R$$.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

The positive value of $$k$$ for which $$k{e^x} - x = 0$$ has only one root is

A

$${1 \over e}$$

B

$$1$$

C

$$e$$

D

$${\log _e}2$$

4

MCQ (Single Correct Answer)

If a continuous function $$f$$ defined on the real line $$R$$, assumes positive and negative values in $$R$$ then the equation $$f(x)=0$$ has a root in $$R$$. For example, if it is known that a continuous function $$f$$ on $$R$$ is positive at some point and its minimum value is negative then the equation $$f(x)=0$$ has a root in $$R$$.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

The line $$y=x$$ meets $$y = k{e^x}$$ for $$k \le 0$$ at

A

no point

B

one point

C

two points

D

more than two points

On those following papers in MCQ (Single Correct Answer)

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2020 Paper 1 Offline (1)

JEE Advanced 2017 Paper 1 Offline (3)

JEE Advanced 2016 Paper 1 Offline (1)

JEE Advanced 2013 Paper 2 Offline (2)

IIT-JEE 2012 Paper 2 Offline (2)

IIT-JEE 2008 (3)

IIT-JEE 2007 (4)

IIT-JEE 2005 Screening (1)

IIT-JEE 2004 Screening (2)

IIT-JEE 2003 Screening (2)

IIT-JEE 2002 Screening (2)

IIT-JEE 2001 Screening (3)

IIT-JEE 2000 Screening (5)

IIT-JEE 1999 (1)

IIT-JEE 1998 (2)

IIT-JEE 1997 (1)

IIT-JEE 1995 Screening (3)

IIT-JEE 1994 (2)

IIT-JEE 1987 (2)

IIT-JEE 1986 (1)

IIT-JEE 1983 (4)

Complex Numbers

Quadratic Equation and Inequalities

Permutations and Combinations

Mathematical Induction and Binomial Theorem

Sequences and Series

Matrices and Determinants

Vector Algebra and 3D Geometry

Probability

Trigonometric Functions & Equations

Properties of Triangle

Inverse Trigonometric Functions

Straight Lines and Pair of Straight Lines

Circle

Conic Sections

Functions

Limits, Continuity and Differentiability

Differentiation

Application of Derivatives

Indefinite Integrals

Definite Integrals and Applications of Integrals

Differential Equations