Let A = [ * 20 c p& 13 - 13 &p ] and B = [ * 20 c 4q & 85 - 2 &1 … - Vidyadip

MCQ

Let $A = \left[ {\begin{array}{*{20}{c}}
p&{13}\\
{ - 13}&p
\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}
{4q}&{85}\\
{ - 2}&1
\end{array}} \right]$ where $p,q \in N$. It is given that $\left| A \right| = \left| B \right|$ and $p,q \in[1,1000]$. Then total number of ordered pairs $(p,q)$ is

✓
$31$
B
$35$
C
$41$
D
$23$

✓

Answer

Correct option: A.

$31$

a
$p^{2}+169=4 q+170$

$p^{2}=4 q+1$

Let $\mathrm{p}=(2 \mathrm{k}+1) \Rightarrow \mathrm{q}=\mathrm{k}(\mathrm{k}+1)$

$1 \leq k(k+1) \leq 1000$

Number of possible values are $31 .$

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

For $x \in R$, two real valued functions $f(x)$ and $g(x)$ are such that, $g(x)=\sqrt{x}+1$ and $f o g(x)=x+3-\sqrt{x}$. Then $f(0)$ is equal to

A $2\, m$ ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate $25\, cm/ sec$., then the rate (in $cm/sec$.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is $1\, m$ above the ground is

In a triangle $\mathrm{ABC}$, if $|\overrightarrow{\mathrm{BC}}|=3,|\overrightarrow{\mathrm{C}}|=5$ and $|\overrightarrow{\mathrm{BA}}|=7$, then the projection of the vector $\overline{\mathrm{BA}}$ on $\overline{\mathrm{BC}}$ is equal to:

If ${\sin ^{ - 1}}x + {\sin ^{ - 1}}y + {\sin ^{ - 1}}z = \frac{\pi }{2}$, then the value of ${x^2} + {y^2} + {z^2} + 2xyz$ is equal to

Let $f:(0,2) \rightarrow R$ be defined as $f( x )=\log _{2}\left(1+\tan \left(\frac{\pi x }{4}\right)\right)$ Then, $\lim _{n \rightarrow \infty} \frac{2}{n}\left(f\left(\frac{1}{n}\right)+f\left(\frac{2}{n}\right)+\ldots+f(1)\right)$ is equal to

$\smallint \frac{{{{\sin }^2}x{{\cos }^2}x}}{{{{\left( {{{\sin }^5}x + {{\cos }^3}x{{\sin }^2}x + {{\sin }^3}x{{\cos }^2}x + {{\cos }^5}x} \right)}^2}}}dx$

Let $S$ be the set of all integer solutions, $(x, y, z)$, of the system of equations

$x-2 y+5 z=0$

$-2 x+4 y+z=0$

$-7 x+14 y+9 z=0$

such that $15 \leq x^{2}+y^{2}+z^{2} \leq 150 .$ Then, the number of elements in the set $S$ is equal to

Let $S$ be the set of all real numbers and let $R$ be a relation on $S$ defined by $a R b \Leftrightarrow a^2+b^2=1$. Then, $R$ is

Corner points of the feasible region for an $\operatorname{LPP}$ are $(0,2),(3,0),(6,0),(6,8)$ and $(0,5)$

Let $F=4 x+6 y$ be the objective function. Maximum of $F-$ Minimum of $F=.....$

If A is an invertible matrix of order 3, then which of the following is not true:

$|\text{adj A}|=|\text{A}|^2$
$(\text{A}^{-1})^{-1}=\text{A}$
If BA = CA, than $\text{B}\neq\text{C},$ where B and C are square matrices of order 3
$(\text{AB})^{-1}=\text{B}^{-1}\text{A}^{-1},$ where $\text{B}\neq\big[\text{b}_{\text{ij}}\big]_{3\times3}\text{ and |B|}\neq0$