$∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1^{m} C_{1} & ^{m + 1} C_{1} & ^{m + 2} C_{1}^{m} C_{2} & ^{m + 1} C_{2} & ^{m + 2} C_{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ =$

m (m + 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

m (m - 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $1$
$∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 m & m + 1 & m + 2 \frac{m (m - 1)}{2} & \frac{(m + 1) m}{2} & \frac{(m + 1) (m + 2)}{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$
$= \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 m & m + 1 & m + 2 m (m - 1) & m (m + 1) & (m + 1) (m + 2) \end{matrix} ∣ ∣ ∣ ∣$
$C_{3} \to C_{3} - C_{2}; C_{2} \to C_{2} - C_{1}$
$= \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & 0 m & 1 & 1 m (m - 1) & 2 m & 2 (m + 1) \end{matrix} ∣ ∣ ∣ ∣$
$C_{3} \to C_{3} - C_{2}$
$= \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & 0 m & 1 & 0 m (m - 1) & 2 m & 2 \end{matrix} ∣ ∣ ∣ ∣ = 1$
Ans: C

Suggest Corrections

Similar questions

Q. The value of the determinant

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & ^{m} C_{1} & ^{m} C_{2} 1 & ^{m + 1} C_{1} & ^{m + 1} C_{2} 1 & ^{2 + m} C_{1} & ^{m + 2} C_{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

equals

Three points A, B, C are on the same straight line. If AB = 5 cm 6 mm and AC = 10 cm 2 mm. Then BC =?

Q. The equation

e^{x} = m (m + 1), m < 0

has

What is the area of the closed figure drawn by Rakshit on the sheet with grids of 1 sq mm each? (Consider more than half as $1 sq mm$ , less than half as $0 sq mm,$ and half as half $sq mm$ .

Q. Two waves are passing simultaneously through a string.
The equation of the waves are given by,

y_{1} = A_{1} sin k (x - v t)

and

y_{2} = A_{2} sin k (x - v t + x_{0})

where the wave number

k = 6.28 {cm}^{- 1}

and

x_{o} = 1 cm

.
The amplitudes are

A_{1} = 2.0 mm

and

A_{2} = 6.0 mm

. Find the amplitude of the resulting wave.

Join BYJU'S Learning Program

∣∣ ∣ ∣∣111mC1m+1C1m+2C1mC2m+1C2m+2C2∣∣ ∣ ∣∣=

$∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1^{m} C_{1} & ^{m + 1} C_{1} & ^{m + 2} C_{1}^{m} C_{2} & ^{m + 1} C_{2} & ^{m + 2} C_{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ =$