The points on the curve \(9 y^2=x^3\) where normal to the curve makes equal intercepts with the axes is/are:

Two pipes A and B can fill a tank respectively in 30 min and 45 min.
Both A and B are opened together for some time and then pipe B is turned off.
If the tank is completely filled in 20 min, find after how many minutes pipe B is turned off.

\(\int_{3 \pi / 8}^{\pi / 8} \frac{\tan ^{2025} x}{\tan ^{2025} x+\cot ^{2025} x} d x\) is equal to

The current through a \(4 / 3 \Omega\) external resistance connected to a parallel combination of two cells with emfs of 2 V and 1 V , internal resistances \(1 \Omega\) and \(2 \Omega\) respectively, is :

The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^4=\left(\frac{d^2 y}{d x^2}\right)^2\) is:

A couple has 3 children each child is equally likely to be a boy or a girl. The probability that the eldest child is a girl glven that they have atleast one boy is :

If \(A(3,2), B(1,-1)\) and \(C(2,1)\) are three vertices of a parallelogram \(A B C D\), then its area (in sq. units) is equal to

Consider the differential equation \(x d y=\left(y+2 x^3\right) d x\). Then which of the following are TRUE?
(A) It is a homogeneous differential equation.
(B) Product of the order and degree of the differential equation is one.
(C) Integrating factor is \(x\).
(D) General solution of the differential equation is \(y=x^3+C x\), where \(C\) is an arbitrary constant.
Choose the correct answer from the options given below :

Read the given passage and answer the question.
ABO blood groups in human beings are controlled by the gene I. The plasma membrane of the red blood cells has sugar polymers that protrude from its surfaces and the kind of sugar is controlled by the gene. The gene (I) has three alleles IA, IB and I. The alleles IA and IB produce a slightly different form of the sugar while allele i does not produce any sugar. Because humans are diploid organisms, each person possesses any two of the three I gene alleles, IA and IB are completely dominant over I.
Select the correct option for number of alleles present in ABO blood groups:

The function \(f(x)=4 x^3-7 x^2\) has point(s) of local minima at :

The distance of the plane \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=3\) from the origin is :

Identify the correct statements in the following:
(A) Optical fibres consist of a core and cladding
(B) Optical fibres are fabricated such that light reflected at one side of the inner surface strikes the other at an angle smaller than the critical angle.
(C) Optical fibres make use of the phenomenon of total internal reflection.
(D) Optical fibres can be used as an optical pipe
Choose the correct answer from the options given below:

The only carboxylic acid which gives positive Tollen's test is