NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

WB JEE 2009

MCQ (Single Correct Answer)

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

A
10
B
11
C
12
D
13

Explanation

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

WB JEE 2008

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

Explanation

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

3

WB JEE 2008

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

Explanation

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

WB JEE 2008

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

Explanation

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

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

Questions Asked from Permutations and Combinations

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)

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12