Download App

STD 11 - 6. permutation and combination — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 6. permutation and combination4 Marks
Question
Four digit numbers are formed using the digits $1 , 2 , 3, 4$ (repetition is allowed). The number of such four digit numbers divisible by $11$ is
✓

Answer

c
$\mathrm{N}=\mathrm{xyz} \mathrm{w}$

$x+z=y+w=k$

$\mathrm{k}=2: \quad 1^{2}$

$\mathrm{k}=3: \quad 2^{2}$

$k=4: \quad 3^{2}$

$k=5: \quad 4^{2}$

$k=6: \quad 3^{2}$

$k=7: \quad 2^{2}$

$k=8: \quad 1^{2}$

$\Rightarrow$ Total $=44$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

In a multiple- choice test consisting of $8$ questions, each question has four options. For each of the questions, exactly one of the four options is the right answer.$A$ student answers all the questions by choosing one option for each question. The number of ways in which the student can get exactly $5$ correct answers is
→
Let $A=\{1,2,3,4,5\}$ and $B=\{1,2,3,4,5,6\}$. Then the number of functions $f: A \rightarrow B$ satisfying $f(1)+f(2)=f(4)-1$ is equal to
→
A function $f(x)$ is defined as $f(x) =\left[ {\begin{array}{*{20}{c}}  {{x^m}\,\sin \,\tfrac{1}{x}}&{x\,\, \ne \,\,0\,,\,\,\,m\,\, \in \,\,N} \\   0&{if\,\,\,\,\,x\,\, = \,\,0} \end{array}} \right. $ . The least value of $m$ for which $f ‘ (x)$ is continuous at $x = 0$ is
→
The total number of distinct $x \in \mathbb{R}$ for which $\left|\begin{array}{ccc}x & x^2 & 1+x^3 \\ 2 x & 4 x^2 & 1+8 x^3 \\ 3 x & 9 x^2 & 1+27 x^3\end{array}\right|=10$ is
→
The total number of $3 \times 3$ matrices $A$ having enteries from the set $(0,1,2,3)$ such that the sum of all the diagonal entries of $AA ^{ T }$ is $9$, is equal to........
→
Let $A$ denote the set of all $2-$digit numbers in base $10$ that are equal to four times the sum of the factorial of their digits. The sum of the numbers in $A$ is
→
If the three normals drawn to the parabola, $y ^{2}=2 x$ pass through the point $( a , 0) a \neq 0,$ then $'a'$ must be greater than
→
$(\sec A + \tan A - 1)(\sec A - \tan A + 1) - 2\tan A = $
→
Let $M$ be any $3 \times 3$ matrix with entries from the set $\{0,1,2\}$. The maximum number of such matrices, for which the sum of diagonal elements of $M ^{ T } M$ is seven, is .............
→
The number of real solutions of the equation

$\sin ^{-1}\left(\sum_{i=1}^{\infty} x^{i+1}-x \sum_{i=1}^{\infty}\left(\frac{x}{2}\right)^i\right)=\frac{\pi}{2}-\cos ^{-1}\left(\sum_{i=1}^{\infty}\left(-\frac{x}{2}\right)^i-\sum_{i=1}^{\infty}(-x)^i\right)$

lying in the interval $\left(-\frac{1}{2}, \frac{1}{2}\right)$ is. . . . .

(Here, the inverse trigonometric functions $\sin ^{-1} x$ and $\cos ^{-1} x$ assume values in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ and $[0, \pi]$, respectively.)

→