The parameter on which the value of the determinant | , * 20 c 1&… - Vidyadip

MCQ

The parameter on which the value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&a&{{a^2}}\\{\cos (p - d)x}&{\cos px}&{\cos (p + d)x}\\{\sin (p - d)x}&{\sin px}&{\sin (p + d)x}\end{array}\,} \right|$ does not depend upon

A
$a$
✓
$p$
C
$d$
D
$x$

✓

Answer

Correct option: B.

$p$

b
(b) ${C_1} \to {C_1} + {C_3} - 2{C_2}$ $\cos dx$ gives
$\Delta = \left| {\,\begin{array}{*{20}{c}}{1 + {a^2} - 2a\cos dx}&a&{{a^2}}\\0&{\cos px}&{\cos (p + d)x}\\0&{\sin px}&{\sin (p + d)x}\end{array}\,} \right|$
=$(1 + {a^2} - 2a\cos dx)\sin dx$, (which is independent of $p$).

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

If $\text{y}=\sin(\text{m}\sin^{-1}\text{x}),$ then $(1-\text{x}^2)\text{y}_2-\text{xy}_1$ is equal to:

m²y
my
-m²y
None of these

The interval in which the function $y=x^3+5 x^2-1$ is decreasing, is

Let $\bar{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}$ and $\vec{c}=\hat{j}-\hat{k}$ be three vectors such that $\vec{a} \times \vec{b}=\vec{c}$ and $\vec{a} \cdot \vec{b}=1$. If the length of projection vector of the vector $\vec{b}$ on the vector $\vec{a} \times \vec{c}$ is $l$, then the value of $3l^{2}$ is equal to $.....$

${d \over {dx}}({x^2}{e^x}\sin x) = $

If $\text{x}=2\text{ at},\text{y}=\text{at}^2,$ where a is a constant, then $\frac{\text{d}^2\text{y}}{\text{dx}^2}\text{ at}\ \text{x}=\frac{1}{2}$ is:

$\frac{1}{2}\text{a}$
1
2a
None of these

Which of the following is the integrating factor of $(\text{x}\log\text{x})\frac{\text{dy}}{\text{dx}}+\text{y}=2\log\text{x}?$

$\text{x}$
$\text{e}^{\text{x}}$
$\log\text{x}$
$\log(\log\text{x})$

If $\text{P(A)}=\frac{2}{5},\text{P(B)}=\frac{3}{10}$ and $\text{P}(\text{A}\cap\text{B})=\frac{1}{5},$ then, $\text{P}(\overline{\text{A}}|\overline{\text{B}}) \text{ P}(\overline{\text{B}}|\overline{\text{A}})$ is equal to

$\frac{5}{6}$
$\frac{5}{7}$
$\frac{25}{42}$
$1$

The area bounded by the curve $y = f(x)$ , the co-ordinate axes $\&$ the line $x = x_1$ is given by $x_1 \cdot {e^{{x_1}}}$. Therefore $f (x)$ equals:

If the rate of chage of volume of sphere is equal to the rate of change of its radius, then its radius is equal to:

$1\ \text{unit}$
$\sqrt{2\pi}\ \text{units}$
$\sqrt{2\pi}\ \text{units}$
$\frac{1}{2\sqrt{\pi}}\ \text{unit}$

Choose the correct answer from the given four options.

The domain of the function defined by $\text{f}(\text{x})=\sin^{-1}\sqrt{\text{x}-1}$ is:

[1, 2]
[-1, 1]
[0, 1]
none of these.