The vector equation of the line passing through the point \((-1,5,4)\) and perpendicular to the plane \(z=0\) is :

In what ratio should a shopkeeper mix two types of rice, one costing ₹ \(20\) per kg and another costing ₹ \(40\) per kg to get a rice variety costing ₹ \(28\) per kg ?

The relation R in the set \(\mathbb{R}\) of real numbers defined as \(R = \{(a, b) : a \le b^2\}\) is:

The point on the curve \(y^2=x\), where the tangent makes an angle of \(\frac{\pi}{4}\) with x-axis is:

The maximum number of equivalence relations on the set \(A=\{3,5,7\}\) is :

A can solve \(90 \%\) problems and B can solve \(70 \%\) problems of the book. A problem is selected at random from the book. The probability that the problem is solved, is equal to

The window of the house is in the form of a rectangle surmounted by a semi-circular portion, having a perimeter of 10 m as shown in figure.

If \(x\) and \(y\) represent the length and breadth of rectangular region, then the area A of the window in terms of \(x\) is :

The integrated rate equation for a first order reaction is \(\frac{kt}{2.303} = \log R_0 - \log R_t\). The straight line graph is obtained by plotting :

\(\int x^2 \tan ^{-1} x d x\)=

Match List-l with List-ll

List-l (Abbreviation used in reproductive health)	List-II (Features)
(A) IVF	(I) Sperm is directly injected into the ovum
(B) ZIFT	(II) Transfer of ovum from a doner into the fallopian tube of recipient
(C) GIFT	(III) Embryos with more than 8 blastomers is transfered into the uterus
(D) ICSI	(IV) Fertilisation outside the body

Choose the correct answer from the options given below:

Match List I with List II

LIST I (Name of interaction)	LIST II ('o' represents neutral, '+'represents benificial, '-'represents detrimental)
A. Commensalism	I. -,-
B. Competition	II. +,+
C. Mutualism	III. -,0
D. Amensalism	IV. +,0

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 -

Aryl halides are extremely less reactive towards nucleophilic substitution reaction because of