If the matrix \(\left[\begin{array}{ccc}3 & 2 a & -5 \\ -4 & 0 & b \\ -5 & 3 & 7\end{array}\right]\) is symmetric, then the value of \((a+b)\) is :

Evaluate \(: 3^{15} \bmod (7)\)

The value of \(\left|\begin{array}{llr}\sin 15^{\circ} & \cos 15^{\circ} & 2 \sin 30^{\circ} \\ \sin 30^{\circ} & \cos 30^{\circ} & \sin 45^{\circ} \\ \cos 75^{\circ} & \sin 75^{\circ} & \sin 90^{\circ}\end{array}\right|\) is

The relation \(R\) on set \(A=\{1,2,3,4,5\}\), given by \(R=\{(a, b):|a-b|\) is even \(\}\) is :

If \(x, y, z\) are all distinct and \(\left|\begin{array}{lll}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0\), then the value of \(x y z\) is :

If A is a square matrix of order \(3 \times 3\) such that \(A^2 = A\) and I is the unit matrix of order \(3 \times 3\), then the value of \((I - A)^3 + A^2 + I\) is:

If \(f(x)=\frac{1}{2 x+1}, x \neq-\frac{1}{2}\), then \(f[f(x)]\) is :

Which of the following reactions are involved in preparation of aldehydes?
(A) Gatterman-Koch reaction
(B) Etard Reaction
(C) Stephen Reaction
(D) Rosenmund Reaction
Choose the correct answer from the options given below:

Alcohol is a depressant, which means that even small amounts of alcohol slow down the actions of parts of the brain, so alcohol lengthens the time you take to respond to a stimulus.
Different people react differently to alcohol. In some people, it increase their feelings of aggression, and releases their inhibitions so that they are more likely to be violent or commit other crimes.
An alcoholic needs to drink quite large quantities of alcohol regularly. This causes many parts of the body to be damaged, because alcohol is poisonous to cells. Probably, there are many factors which decide whether or not a person becomes alcoholic. Over a long period of time, it can cause loss of memory and confusion. One way in which the damage is done is that alcohol in the body fluids draws water out of cells by osmosis.
Effect of alcohol on cells is -

\(\sin ^{-1}\left(\cos \frac{3 \pi}{5}\right)\) equals

The radius of the inner most electron orbit of a hydrogen atom is 0.53 Å. What is the radius of orbit of \(2^{\text {nd }}\) excited state ?

For which values of \(a, f(x)=a(x+\sin x)\) is an increasing function?

In Antirrhinum (Snapdragon), a red flower was crossed with a white flower and in F\(_1\) generation all pink flowers were obtained. When pink flowers were self crossed, F\(_2\) generation showed white, red and pink flowers.
Choose the correct statements for this case:
(A) This experiment does not follow the Principle of Dominance.
(B) Pink colour in F\(_1\) is due to incomplete dominance.
(C) Ratio of F\(_2\) is 1 (red): 2 (pink): 1 (white).
(D) Law of segregation does not apply in this case.
Choose the correct answer from the options given below: