Combination

Q.

A box contains $2$ white balls, $3$ black balls and $4$ red balls. In how many ways can $3$ balls be drawn from the box, if atleast one black ball is to be included in the draw?

1. $64$

2. 24

3. $3$

4. $1$

Q.

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

1. 269

2. 271

3. 302

4. 300

Q.

How many 4-digit numbers are there with no digit repeated?

Q.

If $\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!},$ find x.

Q.

The greatest possible number of points of intersection of 8 straight lines and 4 circles is________.

___

Q.

A six-digit number is formed by repeating a three-digit number. For example$256256$, $678678$etc. Any number of this form is divisible by:

1. $7$ only

2. $11$ only

3. $13$ only

4. $1001$

Q.

How many chords can be drawn through 21 points on a circle?

Q. The total number of numbers of distinct 4 digit odd numbers if the digit used is not repeated again is

1. 2240
2. 2220
3. 2780
4. 2000

Q. What is the proof of m:n theorem?

Q. How many numbers greater than 1000 can be formed with the digits of the number 23416 [digits are not repeated in the same number]?

1. 60
2. 120
3. 180
4. 240

Q.

How many triangles can be formed by joining 10 points on a circle?

__

Q.

The number of straight lines that can be drawn through n non collinear points is ____

1. ⁿC₂

2. ⁿC₃

3. n

4. n - 1

Q.

There are 16 points in a plane out of which 6 are collinear, then how many lines can be drawn by joining these points

1. 60

2. 55

3. 106

4. 105

Q.

Locus of the middle points of the chords of the circle $x^2+y^2=a^2$ which are parallel to $y=2x$ will be

1. 

2. 

3. A circle will centre (0, 0)

4. A straight line with slope - 2

Q.

A committee consists of 5 students 3 girls and 2 boys. If the team is to be formed out of 7 boys and 5 girls, then how many ways this selection can be made?

1. C(7, 5) x C(3, 2)

2. C(5, 7) x C(2, 3)

3. C(7, 2) x C(5, 3)

4. C(7, 3) x C(5, 2)

Q. The number of triangles that can be formed by joining four points on a circle is .

1. 4
2. 6
3. 5
4. 3

Q. If PSQ is a focal chord of the ellipse $16x^2+25y^2=400$ such that SP = 8 then the length of SQ =

1. 2
2. 
3. 25
4. 16

Q.

The distance between the parallel lines $9x^2-6xy+y^2+18x-6y+8=0$ is

1. 

2. 

3. 

4. 

Q. In how many ways a team of 11 players can be selected from 15 players if-

• captain is always included in the team?
• captain is not included in the team?

1. $14C11,14C11$
2. $15C10,15C11$
3. $14C10,15C11$
4. $14C10,14C11$

Q. $f\left(n\right)=\sum _{r=1}^n[r^2\left({}^n{C}_r{-}^n{C}_{r-1}\right)+(2r+1\left){(}^n{C}_r\right)],\text{then}$

1. $f\left(30\right)=960$
2. $f\left(21\right)=483$
3. $f\left(16\right)=64$
4. $f\left(11\right)=44$

Q.

Find the numbers of chords that can be drawn through 16 points on circle.

Q. The letters of the word ‘TOSS’ are permuted in all possible ways and the words thus formed are arranged as in a dictionary, the rank of the word ‘TOSS’ is

1. 9
2. 8
3. 19
4. 10

Q.

There are 16 points in a plane out of which 6 are collinear, then how many lines can be drawn by joining these points?

1. 105

2. None of these

3. 120

4. 106

Q. 11. A polygon has 170 diagonals. How many sides will it have? A) 12 B) 17 C) 20 D) 25

Q. The condition that the straight line joining the origin to the points of intersection of the line 4x+3y=24 with the circle (x-3)^2+(y-4)^2=25 a. are coincident b. are perpendicular c. make equal angle with X-axis d.None of these

Q.

In order to prove the statement “p if and only if q” we need to show:

1. If p is false, then q is false.

2. If p is false, then q is true

3. If p is true, then q is true

4. If p is true, then q is false

Q. 11. Four cards are chosen from 52 playing cards. In how many ways: (1) Atleast one red card (2) Atleast two red card (3) Atleast three red card (4) Atmost one red card (5) Atmost two red card (6) Atmost three red card

Q.

What is the number of diagonals that can be drawn by joining the vertices of a hexagon?

1. 12

2. 9

3. 5

4. 14

Q.

In how many ways can a pack of 52 cards be formed into 4 groups of 13 cards each?

1. 

2. 

3. 

4. 

Q. A square of side a lies above the x axis and has one vertex at origin. The side passing through origin has an angle (alpha) (0<(alpha)<π/4) with the positive direction or x-axis. The equation of its diagonal passing through the origin is