WBJEE 2024 Question Paper: Download Question Paper with Answer Key PDF

1.

The function \(y=e^{kr}\) satisfies \((\frac{d^2y}{dx^2}+\frac{dy}{dx})(\frac{dy}{dx}-y)=y\frac{dy}{dx}\). It is valid for 

• exactly one value of k
• two distinct values of k
• three distinct values of k
• infinitely many values of k

2.

If 4a²+9b²-c²+12ab=0, then the family of straight lines ax+by+c=0 is concurrent at 

• (2,3)or(-2,-3)
• (-2,3)or(2,-3)
• (3,2)or(-3,2)
• (-3,2)or(2,3)

3.

The value of 'a' for which the scaler triple product formed by the vectors \(\vec\alpha=\hat{i}+a\hat{j}+\hat{k}\),  \(\vec{\beta}=\hat{j}+a\hat{k}\)  and  \(\vec{\gamma}=a\hat{i}+\hat{k}\)  is maximum, is

• 3
• -3
• \(\frac{1}{\sqrt3}\)
• \(-\frac{1}{\sqrt3}\)

4.

An electric dipole of dipole moment p is placed at the origin of the coordinate system along the z-axis. The amount of work required to move a charge 'q' from the point (a,0,0) to the point (0,0,a) is

• \(\frac{pq}{4\pi\epsilon_0a}\)
• 0
• \(-\frac{pq}{4\pi\epsilon_0a^2}\)
• \(\frac{pq}{4\pi\epsilon_0a^2}\)

5.

A train is moving along the tracks at a constant speed u. A girl on the train throws a ball of mass m straight ahead along the direction of motion of the train with speed v with respect to herself. Then,