A car is moving along the curve \(y=x^3+12\). The point(s) on the curve at which the rate of change of its y-coordiante at a certain time is 3 times the rate of change of its x-coordinate is/are

If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of \(x\)-axis, \(y\)-axis and \(z\)-axis respectively, then \(\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma\) is equal to:

Which of the following is correct about the compound annual growth rate (CAGR)?

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

If \(\left[\begin{array}{cc}2 a+b & a-2 b \\ 5 c-d & 4 c+3 d\end{array}\right]=\left[\begin{array}{cc}4 & -3 \\ 11 & 24\end{array}\right]\), then the value of \(a+2 b-3 c+4 d\) is equal to

If \(\theta\) is the angle between two unit vectors \(\hat{a}\) and \(\hat{b}\) then \(|\hat{a}-\hat{b}|=\)

The feasible region represented by the constraints of the linear programming problem :
\(x+y \leq 6, y \leq 7, x \geq 4, x, y \geq 0\) is :

Read the following passage carefully and answer the given questions.
Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location and do not spread to other parts of the body and cause little damage. The malignant tumors, on the other hand are a mass of proliferating cells called neoplastic or tumor cells. Transformation of normal cells into cancerous neoplastic cells may be induced by physical, chemical or biological agents. Ionising radiations like X-rays and gamma rays and non-ionizing radiations like UV cause cancer. Cancer-causing viruses are called oncogenic viruses which have viral oncogenes. The substances to which an immune response is produced are called allergens. The antibodies produced to these are of IgE type. Common examples of allergens are mites in dust, pollens, animal dander, etc. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells.
Which one of the following antibodies are produced in response to the allergens?

If \(\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}\), then the value of \(\cos ^{-1} x+\cos ^{-1} y\) is :

What is the approximate wavelength of the radiation emitted when the electron in an hydrogen atom jumps from n = \( \infty \) to n = 3?

Mr. X purchased a house for ₹ 7,00,000 and made a down payment of ₹ 1,50,000 .
He repays the balance in 25 years by equal monthly installments as \(9 \%\) per annum compounded monthly. The equated monthly installment (EMM) is :
[Given that \((1.0075)^{-300}=0.106\) ]

\(\cos \left(\frac{\pi}{6}-\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)\) is equal to:

Read the following passage carefully and answer the given questions
The earthworm is referred to as the farmer's friend. This is because they help in the breakdown of complex organic matter as well as in loosening of soil. Similarly, decomposers break down complex organic matter into inorganic substances like carbon dioxide, water and nutrients and the process is called decomposition. Dead plant remains such as leaves, bark, flowers and dead remains of animals, including fecal matter, constitute detritus, which is the raw material for decomposition. Some of the steps in the process of decomposition are fragmentation, catabolism, leaching, humification etc.
Process of accumulation of dark coloured amorphous substance is called: