Which one of the following options is incorrect?
For a square matrix \(A\) in the matrix equation \(A X=B\).

The maximum slope of the curve \(y=-x^3+3 x^2+9 x-27\) is:

The value of \(\left|\begin{array}{ll}\sqrt{3} / 2 & 1 / 2 \\ \sqrt{3} / 2 & 1 / 2\end{array}\right|\)

The equation of motion of a missile is x = 3t, y = - 4t, z = t where time 't' is in seconds and the distance is measured in kilometres.
At what distance will the rocket be from the point (0, 0, 0) in 5 seconds?

If the sum of the lengths of the hypotenuse and one of the other two sides of a right angled triangle is fixed, then the area of the triangle is maximum, when the angle between them is :

Maximum value of \(z=5 x+4 y\) subject to the constraints \(x-y \leq 0, x+y \leq 4, x \geq 0, y \geq 0\) occurs at the point \((a, b)\). Then \(4 a+5 b=\) \(\_\_\_\_\) ,

Which of the following differential equation represents the family of circles touching the \(x\)-axis at the origin?

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.
The process of decomposition largely requires -

Which of the following is correct about the nature of ligand?

Which of the following technique(s) is/are NOT useful in early detection of cancer?
(A) X-rays radiography
(B) Computed tomography
(C) Widal test
(D) Biopsy and histopathological studies
(E) Magnetic Resonance Imaging
Choose the correct answer from the options given below:

Microbes in human welfare Microbes are a very important component of life on earth. we use microbes and microbially derived products almost every day, like LAB to make curd, yeast to make bread, adding flavor and texture to cheese, producing antibiotics etc. The addition of LAB, improves the milk quality by increasing vit. B12. Cheese is one of the oldest food items in which microbes are used. For example, large holes in Swiss cheese are due to CO2 produced by the bacterium Propionibacterium sharmanii. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water. The greater the BOD of waste water, the more is its polluting potential. In anaerobic sludge digesters, bacteria produce a mixture of gases like methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as a source of energy. Biofertilisers are organisms that enrich the nutrient quality of the soil. The main sources of biofertilisers are bacteria, fungi and cyanobacteria. You have studied about the nodules on the roots of leguminous plants formed by the symbiotic association of Rhizobium. These bacteria fix atmospheric nitrogen into organic forms, which is used by the plant as a nutrient. Other bacteria can fix atmospheric nitrogen while free-living in the soil (examples Azospirillum and Azotobacter).
Identify, the free living bacteria in soil, which can fix the atmospheric nitrogen.

Collision theory postulates are :
A. Reactant molecules collide with each other.
B. The collisions must be of sufficient kinetic energy.
C. The collision in molecules with proper orientation.
D. Rate of reaction does not depend on temperature.
Choose the correct answer from the options given below :

A circuit containing a \( \frac{2}{\pi} \text{ H} \) inductor, a \( \frac{40}{\pi} \text{ } \mu\text{F} \) capacitor and a \( 50 \text{ } \Omega \) resistor in series are connected to an a.c. source of emf \( v = 230 \sin 314t \). The amplitude of the current in the circuit is