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 $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are three non-coplanar vectors, then $\big(\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big).\big[\big(\vec{\text{a}}+\vec{\text{b}}\big)\times\big(\vec{\text{a}}+\vec{\text{c}}\big)\big]$ equals:

$0$
$\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]$
$2\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]$
$-\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]$

$\sin \left(\tan ^{-1} x\right),|x|<1=$ __________ .

Let $y=y(x)$ be a solution curve of the differential equation, $\left(1-x^2 y^2\right) d x=y d x+x d y$.If the line $x =1$ intersects the curve $y = y ( x )$ at $y =2$ and the line $x =2$ intersects the curve $y=y(x)$ at $y=\alpha$, then a value of $\alpha$ is

In an LPP, if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then the number of points of which Zmax occurs is:

0
2
Finite
Infinite

The eqution of the plane which cute equal intercepts of unit length on the coordinate axes is:

x + y + z = 1
x + y + z = 0
x + y - z = 1
x + y + z = 2

If a line makes angle $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with x-axis and y-axis respectively, then the angle made by the line with z-axis is:

$\frac{\pi}{2}$
$\frac{\pi}{3}$
$\frac{\pi}{4}$
$\frac{5\pi}{12}$

The maximum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5x + 2y ≥ 200, x + 2y ≥ 80, x, y ≥ 0 is:

320
300
230
none of these

If a line makes an angle of $30^{\circ}$ with the positive direction of $x$-axis, $120^{\circ}$ with the positive direction of $y$-axis, then the angle which it makes with the positive direction of $z$-axis is :

The function $\sin x - bx + c$ will be increasing in the interval $( - \infty ,\,\,\infty )$, if

The slope of tangent to the curve x = t² + 3t - 8, y = 2t² - 2t - 5 at the point (2, -1) is: