If lines \(\frac{x+5}{5 \lambda+2}=\frac{4-2 y}{10}=\frac{1-3 z}{-3}\) and \(\frac{x-2}{1}=\frac{1+2 y}{4 \lambda}=\frac{2+z}{3}\) are perpendicular, then value of ' \(\lambda\) ' is

\(\frac{d^2}{d x^2}\left(\operatorname{det}\left[\begin{array}{cc}x^3 & x \\ 2 & e^x\end{array}\right]\right)\) equals

\(\int \frac{d x}{9 x^2-16}\) is equal to:

The solution of the differential equation \(y d x+\left(x-y^2\right) d y=0\) is :

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is four. The probability that it is actually four is :

If \(\vec{p}\) and \(\vec{q}\) are two unit vectors such that \(|\vec{p}+\vec{q}|=\sqrt{2}\), then which of the following are correct?
(A) \(|\vec{p}|=|\vec{q}|=1\)
(B) \(\vec{p}\) and \(\vec{q}\) are orthogonal vectors
(C) \(\vec{p}\) and \(\vec{q}\) are collinear vectors
(D) \((4 \vec{p}-\vec{q}) \cdot(2 \vec{p}+\vec{q})=7\)
Choose the correct answer from the options given below :

\(\int e^x\left(\frac{1-x}{1+x^2}\right)^2\) \(dx\) is equal to

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, so the letter "e" was dropped and ther term vitamin is used these days.
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. They must be supplied regularly in the diet as they are readily excreated in urine.
Among the following, water-soluble vitamin is

The vapour pressure of pure benzene is } \(0.900\) bar. If a non-volatile electrolytic solid is added, the vapour pressure of the solution becomes \(0.200\) bar. If the number of moles of solute and solvent in the solution are \(1\) and \(2\) respectively, what is the value of van't Hoff factor (i)?

Reaction of benzaldehyde with acetophenone in the presence of methanolic NaOH yields a major stable product as

Which one of the following drugs can not quickly reduce the symptoms of allergy?

\(t_{99\%}\) with respect to \(t_{90\%}\) for a first order reaction is :

Match List - I with List - II.

List - I	List - II
(A) To study crystal structure	(I) IR ray
(B) To study structure of nuclei	(II) X-ray
(C) Take haze photography	(III) UV-ray
(D) Can cause fluorescence	(IV) \( \gamma \)-ray

Choose the correct answer from th options given below :