The slope of the normal to the curve \(y=x^3+3 x-2\) at its point of intersection with y-axis is:

Let [t] denote the greatest integer ≤ t and aZ = {ax : x ∈ Z, a ∈ R} (where Z is set of integer and R is set of real number). The set of points of discontinuity of the function f(x) = [2x] is given by

Let \(A=\left[a_{i j}\right]\) is given by \(A=\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 4 & -5 \\ 2 & -1 & 3\end{array}\right]\). Then the matrix \(B=\left[b_{i j}\right]\), where \(b_{i j}\) = Minor of \(a_{i j}\) is:

Two points A and B in a plane are related if OA = OB, where O is a fixed point. This relation is:

If matrices \(A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\) and \(B=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\), then \(B A\) is equal to:

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

For a Binomial distribution, \(B(n, p)\), where \(p+q=1\), the sum and product of mean and variance are 8 and 12 respectively, when the value of \(n\) is :

An armature coil consists of 20 turns of wire, each of area \( A = 0.09 \text{ m}^2 \) and total resistance \( 15 \ \Omega \).
It rotates in a magnetic field of 0.5 T perpendicular to the axis of rotation at a constant frequency \( \frac{150}{\pi} \text{ Hz} \). The value of maximum emf produced in the coil is:

When strong magnetic field is applied on a stationary electron, the electron :

Which of the following is not caused due to deficiency of hormones?

Identify the essential amino acids from the following.
(A) Threonine
(B) Serine
(C) Histidine
(D) Lysine
Choose the correct answer from the options given below :

Bt toxins are insect group specific proteins. Gene named crylAc and cryllAb control:

Read the passage carefully and answer the questions given along
Our immune system plays the major role in preventing diseases when we are exposed to disease-causing agents. Immunity is of two types: (i) Innate immunity and (ii) Acquired immunity. The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The immune system also plays an important role in allergic reactions, auto-immune diseases and organ transplantation. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs are spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa associated lymphoid tissue (MALT). It is important to note that HIV/AIDS is not spread by mere touch or physical contact; it spreads only through body fluids. AIDS has no cure, prevention is the best option. Adolescence is accompanied by several biological and behavioural changes and surveys and statistics show that use of drugs and alcohol has been on the rise especially among the youth. Factors associated with drug and alcohol abuse among adolescents are a child's natural curiosity, stress, the perception among youth that it is 'cool' or progressive to smoke, media exposure and an unstable or unsupportive family structures and peer pressure. It is best to identify the situations that may push an adolescent towards use of drugs or alcohol, and to take remedial measures well in time.
Which one of the following can never be over estimated when it comes to the complete well-being of adolescents?