If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^{3}+p x+q=0\), then the value of the determinant \(\left|\begin{array}{ccc}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right|\) is

The product of the degree and order of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}-\left(\frac{d y}{d x}\right)^{3}=y^{3}\) is

If the events A and B are mutually exclusive events such that \(P(A)=\dfrac{1}{3}(3 x+1)\) and \(P(B)=\dfrac{1}{4}(1-x)\) then the possible values of \(x\) lies in the interval

If \(3 x+y+k=0\) is a tangent to the circle \(x^{2}+y^{2}=10\), the values of \(k\) are

\(\text { If } \dfrac{1}{2}\left(\dfrac{3 x}{5}+4\right) \geq \dfrac{1}{3}(x-6), x \in R \text { then }\)

Which of the following is not a homogenous function of \(x\) and \(y\)

If \(f(x)=\left\{\begin{array}{lc}x^2+1 & x \lt 0 \\ x^3-a & 0 \leq x \lt 1 \text { and it is continuous } \\ 2 b-x & x \geq 1\end{array}\right.\) \(\forall x \in R\), then

The area bounded by the curve \(y=\cos x, x=0\) and \(x=\pi\) is

A coffee roaster has 12 rare coffee beans with intensity scores ranked from 1 (mildest) to 12 (strongest). You choose 7 beans at random and line them up from mildest to strongest:
\(C_1 < C_2 < C_3 < C_4 < C_5 < C_6 < C_7\)
What is the probability that the third bean (\(C_3\)) has an intensity score of exactly 4?

The maximum number of electrons which can be held by subshell with azimuthal quantum number \(' l\) in an atom is given by

Unit vector perpendicular to \(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and lying in the plane containing \(\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) and \(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) is

Which of the following are monosaccharides?

A proton is moving along negative X axis. If a uniform magnetic field is applied parallel to the positive Z axis, then choose the correct answer from the following options;
1. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XY plane
2. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XY plane
3. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XZ plane
4. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XZ plane