Joint Entrance Examination

Graduate Aptitude Test in Engineering

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1

MCQ (Single Correct Answer)

Suppose four distinct positive numbers $${a_1},\,{a_{2\,}},\,{a_3},\,{a_4}\,$$ are in G.P. Let $${b_1} = {a_1},{b_2} = {b_1} + {a_2},\,{b_3} = {b_2} + {a_{3\,\,}}\,\,\,and\,\,\,{b_4} = {b_3} + {a_4}$$.

** STATEMENT-1: ** The numbers $${b_1},\,{b_{2\,}},\,{b_3},\,{b_4}\,$$ are neither in A.P. nor in G.P. and

** STATEMENT-2 ** The numbers $${b_1},\,{b_{2\,}},\,{b_3},\,{b_4}\,$$ are in H.P.

A

STATEMENT-1 is True, STATEMENT-2 is True;

STATEMENT-2 is a correct explanation for

STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True;

STATEMENT-2 is NOT a correct explanation for

STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True

2

MCQ (Single Correct Answer)

Let $${A_1}$$, $${G_1}$$, $${H_1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \ge 2,\,Let\,{A_{n - 1}}\,\,and\,\,{H_{n - 1}}$$ have arithmetic, geometric and harminic means as $${A_n},{G_n}\,,{H_n}$$ repectively.

Which one of the following statements is correct ?

A

$${G_1} > {G_2}\, > {G_3} > ...$$

B

$${G_1} < {G_2}\, < {G_3} < ...$$

C

$${G_1} = {G_2}\, = {G_3} = ...$$

D

$${G_1} < {G_2}\, < {G_3} < ...$$ and $${G_1} > {G_2}\, > {G_3} > ...$$

3

MCQ (Single Correct Answer)

Let $$\,{V_r}$$ denote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r-1). Let $${T_r} = \,{V_{r + 1}} - \,{V_r} - 2\,\,\,and\,\,\,{Q_r} = \,{T_{r + 1}} - \,{T_r}\,for\,r = 1,2,...$$

Which one of the following is a correct statement?

A

$${Q_1},\,\,{Q_2},\,\,{Q_3},...$$ are A.P. with common difference 5

B

$${Q_1},\,\,{Q_2},\,\,{Q_3},...$$ are A.P. with common difference 6

C

$${Q_1},\,\,{Q_2},\,\,{Q_3},...$$ are A.P. with common difference 11

D

$${Q_1} = \,\,{Q_2} = \,\,{Q_3} = ...$$

4

MCQ (Single Correct Answer)

Which one of the following statements is correct ?

A

$${A_1} > {A_2}\, > {A_3} > ...$$

B

$${A_1} < {A_2}\, < {A_3} < ...$$

C

$${A_1} > {A_2}\, > {A_3} > ...$$ and $${A_1} < {A_2}\, < {A_3} < ...$$

D

$${A_1} < {A_2}\, < {A_3} < ...$$ and $${A_1} > {A_2}\, > {A_3} > ...$$

On those following papers in MCQ (Single Correct Answer)

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2016 Paper 2 Offline (1)

IIT-JEE 2012 Paper 2 Offline (1)

IIT-JEE 2009 (1)

IIT-JEE 2008 (1)

IIT-JEE 2007 (6)

IIT-JEE 2005 Screening (1)

IIT-JEE 2004 Screening (1)

IIT-JEE 2002 Screening (1)

IIT-JEE 2001 Screening (3)

IIT-JEE 2000 Screening (1)

IIT-JEE 1999 (2)

IIT-JEE 1998 (3)

IIT-JEE 1994 (1)

IIT-JEE 1990 (1)

IIT-JEE 1988 (1)

IIT-JEE 1985 (1)

IIT-JEE 1983 (1)

IIT-JEE 1982 (2)

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