Question:medium

If \[ \begin{vmatrix} p & q - y & r - z \\ p - x & q & r - z \\ p - x & q - y & r \end{vmatrix} = 0, \] then the value of \(\dfrac{p}{x} + \dfrac{q}{y} + \dfrac{r}{z}\) is

Show Hint

Use row/column operations to simplify determinants quickly.

Updated On: Apr 2, 2026

\(0\)
\(1\)
\(2\)
\(4pqr\)

Show Solution

The Correct Option is B

Solution and Explanation

Was this answer helpful?

0

Top Questions on Properties of Determinants

If \(\alpha \neq a\), \(\beta \neq b\), \(\gamma \neq c\) and \[ \begin{vmatrix} \alpha & b & c \\ a & \beta & c \\ a & b & \gamma \end{vmatrix} = 0,\] then \[ \frac{a}{\alpha - a} + \frac{b}{\beta - b} + \frac{\gamma}{\gamma - c} \] is equal to:
- JEE Main - 2024
- Mathematics
- Properties of Determinants
View Solution
If beginvmatrix p & q-y & r-z
p-x & q & r-z
p-x & q-y & r endvmatrix=0, then the value of (p)/(x)+(q)/(y)+(r)/(z) is
- BITSAT - 2021
- Mathematics
- Properties of Determinants
View Solution
If for some $c < 0$, the quadratic equation, $2cx^{2}-2\left(2c-1\right)x+3c^{2}=0$ has two distinct real roots, $\frac{1}{a}$ and $\frac{1}{b},$ then the value of the determinant. $\begin{vmatrix}1+a&1&1\\ 1&1+b&1\\ 1&1&1+c\end{vmatrix}$ is :
- JEE Main - 2020
- Mathematics
- Properties of Determinants
View Solution
If the matrix beginbmatrix 1 & 3 & λ+2
2 & 4 & 8
3 & 5 & 10 endbmatrix is singular, then λ=
- BITSAT - 2020
- Mathematics
- Properties of Determinants
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in BITSAT exam

What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?

BITSAT - 2025
Vector Algebra

In a mixture of gases, the average number of degrees of freedom per molecule is 6. If the rms speed of the molecule is \(c\), what is the velocity of sound in the gas?

BITSAT - 2025
kinetic theory

A ball is thrown vertically upward with a speed of 49 m/s. How long will it take to return to the thrower’s hand?

BITSAT - 2025
Kinematics

Two identical bodies of mass 1 kg each are moving towards each other with velocities of 5 m/s and 3 m/s, respectively. They collide elastically. What will be the velocity of the body initially moving at 5 m/s after the collision?

BITSAT - 2025
Mechanics