A and B throw a die alternatively till one of them gets a number more than 4 and wins the game. Then the probability of winning the game by B , if A starts first :

A car starts from a point at time \(t = 0\) seconds and stops at Q.
The distance \(x\) in meters covered by it in \(t\) seconds is given by
\(x = t^2 \left( 2 - \frac{t}{3} \right)\).
The time taken by it to reach Q is:

The value(s) of \(x\) for which the matrix \(A=\left[\begin{array}{ccc}x-1 & 1 & 1 \\ 1 & x-1 & 1 \\ 1 & 1 & x-1\end{array}\right]\) is singular, is/are :

If \(\left|\begin{array}{cc}3 x & 7 \\ 4 & x\end{array}\right|=\left|\begin{array}{cc}6 & -2 \\ 4 & 2\end{array}\right|\), then the value of \(x\) is :

The area of the region bounded by \(x=y^2\) and the line \(x=4\) in square units is :

In an LPP, if the objective function Z = ax + by has the same maximum value at two corner points of the feasible region, then the number of points of which \(Z_{\max }\) Occurs is:

In the given figure, shaded region represents the feasible solution to a LPP problem. The constraint represented by AD is:

Read the passage carefully and answer the Questions
Alcohols and phenols are obtained when a hydrogen atom in aliphatic and aromatic hydrocarbons respectively, is replaced by \(OH\) group. These compounds find wide applications in industry as well as in our daily life. You may notice that ordinary spirit is used for polishing wooden furniture which is chiefly a compound containing hydroxyl group. An alcohol contains one or more hydroxyl \((OH)\) group(s) directly attached to carbon atom(s), of an aliphatic system \((CH_3OH)\) while a phenol contains \(OH\) group(s) directly attached to carbon atom(s) of an aromatic system \((C_6H_5OH)\). Alcohols are prepared by the hydration of alkenes, fermentation of glucose, and reduction of carbonyl compounds. Alcohols produce alkenes upon dehydration whereas alkenes on acid catalyzed hydration convert into alcohols.
An alkyl halide can be converted into alcohol through:

Match List - I with List - II.

List - I	List - II
(A) Barrier methods	(I) Prevents physical contact between ovum and sperm
(B) IUD	(II) Sterilizes physical contact between ovum and sperm
(C) Oral Contraceptives	(III) Increases phagocytosis of sperms and suppress sperm motility:

Choose the correct answer from the options given below :

Area bounded by \(x=\frac{y^2}{4}\) and its latus rectum is:

If \(\vec{a}=\hat{i}+2 \hat{j}+2 \hat{k},|\vec{b}|=5\) and the angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{\pi}{6}\), then the area of the triangle formed by these two vectors as two sides is :

Which of the following matrices is symmetric as well as skew-symmetric?

Which of the following functions are increasing on \(x \in\left(0, \frac{\pi}{2}\right)\) ?
(A) \(f(x)=\sin x\)
(B) \(f(x)=\cos x\)
(C) \(f(x)=\tan x\)
(D) \(f(x)=\cos 3 x\)
Choose the correct answer from the options given below :