A problem in Mathematics is given to two students \(X\) and \(Y\) whose chances of solving it are \(\frac{1}{3}\) and \(\frac{1}{4}\) respectively. The probability that only \(X\) solves the problem, is:

If \(\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}, \vec{a} \times \vec{b}=\vec{a} \times \vec{c}\) and \(\vec{a} \neq \overrightarrow{0}\), then the vector \(\vec{b}\) is equal to:

Find the maximum value of the function sin x(1 + cos x) is:

The area (in sq. units) of the region in the first quadrant bounded by \(y=3 \sqrt{1-x^2}, x \in[0,1]\) and the x-axis is equal to

If A and B are skew-symmetric matrices, then which of the following is not true?

If \(x^m y^n=(x+y)^{m+n}\), then \(\frac{d^2 y}{d x^2}\) is equal to:

The intercept made by the plane \(2 x-3 y+5 z+4=0\) on \(z\)-axis is :

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups. They are very essential for the body. They has to be taken various diet or in the form of medicines also.
Vitamins are classified into two groups depending upon their solubility in water or fat.
Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues Water-soluble vitamins are soluble in water. These must be supplied regularly in diet because they are readily excreated in urine and cannot be stored in our body.
Deficiency of Scurvy disease leads to

If the integral \(I=\int\left\{\log _e\left(\log _e x\right)^2+\frac{\alpha}{\log _e x}\right\} d x=x \log _e\left(\log _e x\right)^2+C\), where \(C\) is constant of integration. Then the value of \(\alpha\) is :

Which one of the following enzymes acts as molecular scissors?

The interval in which \(y=x^2 e^{-x}\) is strictly increasing is:

Identify the role of deoxyribonucleoside triphosphates in DNA replication?

If \(P, Q\) and \(R\) are three singular matrices given by
\(P=\left[\begin{array}{cc}2 & 3 a \\4 & 3\end{array}\right], Q=\left[\begin{array}{cc}b & 5 \\2 a & 6\end{array}\right]\)
and \(R=\left[\begin{array}{cc}a^2+b^2-c & 1-c \\ c+1 & c\end{array}\right]\), then the value of \((2 a+6 b+17 c)\) is: