Joint Entrance Examination

Graduate Aptitude Test in Engineering

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1

MCQ (Single Correct Answer)

A polygon has 44 diagonals. The number of the sides is

A

10

B

11

C

12

D

13

Let number of vertices of polygon = n

Total number of line segments joining two vertices = $${}^n{C_2}$$

$$\therefore$$ Number of diagonals

= Total number of line segment $$-$$ number of sides

= $${}^n{C_2}$$ $$-$$ n = 44

$$ \Rightarrow {{n(n - 1)} \over 2} - n = 44 \Rightarrow {n^2} - 3n - 88 = 0$$

$$ \Rightarrow {n^2} - 11n + 3n - 88 = 0 \Rightarrow n(n - 11) + 3(n - 11) = 0$$

$$ \Rightarrow (n - 11)(n + 3) = 0$$

$$ \Rightarrow n - 11 = 0 \Rightarrow n = 11$$ ($$\because$$ $$n \ne - 3$$)

2

MCQ (Single Correct Answer)

The number of ways four boys can be seated around a round table in four chairs of different colours is

A

24

B

12

C

23

D

64

Number of ways in which four boys can be seated around a round table = 4! = 24.

3

MCQ (Single Correct Answer)

How many odd numbers of six significant digits can be formed with the digits 0, 1, 2, 5, 6, 7 when no digit is repeated?

A

120

B

96

C

360

D

288

For odd number, 1, 5 or 7 should be on the unit place. At the lakh's place 0 can't be there, so the lakh's place can be filled by any one of four numbers.

Rest of the four middle placed can be arranged in $${}^4{P_4}$$ ways.

So, number of odd number = 4 $$\times$$ $${}^4{P_4}$$ $$\times$$ 3

= 4 $$\times$$ 4 $$\times$$ 3 $$\times$$ 2 $$\times$$ 3 = 288.

4

MCQ (Single Correct Answer)

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?

A

26

B

28

C

27

D

25

From 8 given points $${}^8{C_2}$$ straight lines can be drawn. But 3 points are collinear. Using 3 points $${}^3{C_2}$$ straight lines can be drawn. So, total straight lines

without the straight lines using these 3 points = $${}^8{C_2}$$ $$-$$ $${}^3{C_2}$$ (as 3 points are collinear)

From 3 collinear points 1 straight line can be drawn.So, total no. of straight lines = $${}^8{C_2}$$ $$-$$ $${}^3{C_2}$$ + 1

$$ = {{8 \times 7} \over 2} - 3 + 1 = 26$$.

On those following papers in MCQ (Single Correct Answer)

Number in Brackets after Paper Indicates No. of Questions

WB JEE 2022 (1)

WB JEE 2021 (2)

WB JEE 2020 (2)

WB JEE 2019 (2)

WB JEE 2018 (3)

Trigonometric Functions & Equations

Properties of Triangle

Inverse Trigonometric Functions

Logarithms

Sequence and Series

Quadratic Equations

Complex Numbers

Permutations and Combinations

Mathematical Induction and Binomial Theorem

Matrices and Determinants

Vector Algebra

Three Dimensional Geometry

Probability

Statistics

Sets and Relations

Functions

Definite Integration

Application of Integration

Limits, Continuity and Differentiability

Differentiation

Application of Derivatives

Indefinite Integrals

Differential Equations

Straight Lines and Pair of Straight Lines

Circle

Parabola

Ellipse and Hyperbola