# Combination

## Trending Questions

**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?

$64$

24

$3$

$1$

**Q.**

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

269

271

302

300

**Q.**

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

**Q.**

If 16!+17!=x8!, 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:

$7$ only

$11$ only

$13$ only

$1001$

**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

- 2240
- 2220
- 2780
- 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]?

- 60
- 120
- 180
- 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 ____

^{n}C_{2}^{n}C_{3}n

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

60

55

106

105

**Q.**

Locus of the middle points of the chords of the circle x2+y2=a2 which are parallel to y=2x will be

A circle will centre (0, 0)

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?

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

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

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

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

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

- 4
- 6
- 5
- 3

**Q.**If PSQ is a focal chord of the ellipse 16x2+25y2=400 such that SP = 8 then the length of SQ =

- 2
- 25
- 16

**Q.**

The distance between the parallel lines 9x2−6xy+y2+18x−6y+8=0 is

**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?

- 14 C11, 14 C11
- 15 C10, 15 C11
- 14 C10, 15 C11
- 14 C10, 14 C11

**Q.**f(n)=n∑r=1[r2(nCr−nCr−1)+(2r+1)(nCr)], then

- f(30)=960
- f(21)=483
- f(16)=64
- f(11)=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

- 9
- 8
- 19
- 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?

105

None of these

120

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:

If p is false, then q is false.

If p is false, then q is true

If p is true, then q is true

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?

12

9

5

14

**Q.**

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

**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