All possible four digit numbers are formed using the digits 0, 1,… - Vidyadip

MCQ

All possible four digit numbers are formed using the digits $0, 1, 2, 3$ so that no number has repeated digits. The number of even numbers among them is

A
$9$
B
$18$
✓
$10$
D
None of these

✓

Answer

Correct option: C.

$10$

c
(c) In forming even numbers, the position on the right can be filled either $0$ or $2$. When $0$ is filled, the remaining positions can be filled in $3\;!$ ways and when $2$ is filled, the position on the left can be filled in $2$ ways ($0$ cannot be used) and the middle two positions in $2\;!$ ways ($0$ can be used). Therefore the number of even numbers formed $ = 3\;! + 2(2\;!) = 10$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11 - 6. permutation and combination→STD 11 - 6. permutation and combination — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the distance between $(12, 3, 4)$ and $(4, 5, 2):$

If $\text{f(x)}=\log\Big(\frac{1+\text{x}}{1-\text{x}}\Big),$ then $\text{f}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ is equal to:

If $\text{e}^{\sin\text{x}}-\text{e}^{-\sin\text{x}}-4=0,$ then $\text{x}=$

The equation of the tangent to the circle ${x^2} + {y^2} = {r^2}$ at $(a,b)$ is $ax + by - \lambda = 0$, where $\lambda $ is

The equation of the circle whose radius is $5$ and which touches the circle ${x^2} + {y^2} - 2x - 4y - 20 = 0$ externally at the point $(5, 5)$ is

Statement $1:$ $y = mx - \frac{1}{m}$ is always a tangent to the parabola, $y^2 = - 4x$ for all non-zero values of $m.$

Statement $2:$ Every tangent to the parabola, $y^2 = -4x$ will meet its axis at a point whose abscissa is non-negative.

If $y=m x+4$ is a tangent to both the parabolas, $\mathrm{y}^{2}=4 \mathrm{x}$ and $\mathrm{x}^{2}=2 \mathrm{by},$ then $\mathrm{b}$ is equal to

Suppose $a, b, c$ are real numbers, and each of the equations $x^2+2 a x+b^2=0$ and $x^2+2 b x+c^2=0$ has two distinct real roots. Then, the equation $x^2+2 c x+a^2=0$ has

There are $5$ apples, $4$ mangoes, $3$ oranges and $1$ each of $2$ other varieties of fruits. The number of ways of selecting at least one fruit of each kind is

Two dice are thrown simultaneously. The probability that sum is odd or less than $7$ or both, is