A die is tossed 6 times and getting 1 or 5 is considered a success.
The probability of getting at least one success in six tosses is:

A 95% confidence interval for a population mean was reported to be 152 to 160. If the standard deviation \(\sigma=15\), then the sample size is (given \(Z_{0.025}=1.96\) ) :

The maximum value of \(\sin x \cdot \cos x\) is :

Let \(A=\left[\begin{array}{ccc}0 & 2 & -5 \\ -2 & 0 & -7 \\ 5 & 7 & 0\end{array}\right]\) and \(B=\left[\begin{array}{ccc}1 & 5 & 8 \\ 2 & 7 & 4 \\ 3 & 9 & 10\end{array}\right]\) then |AB|=

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.
If the position of rocket at a certain instant of time is (5, -8, 10), then what will be the height of the rocket from the ground? (Ground is considered as xy plane)

If the area of a triangle whose vertices are (-1, 3), (1, -5) and (k, 2) where k > 0 is 30 sq. units, then the value of k is

The area enclosed between the curve \(y=x^2+2\) and x -axis between \(x=0\) and \(x=3\) is :

The sum of the order and degree of the differential equation representing the family of curves \(y=m x+m^4\), where \(m\) is arbitrary constant, is

The oxidation state, geometry and number of unpaired electrons in \([Cr(NH_3)_6]^{3+}\) is :

Other than absorption of phosphorus from soil, Glomus gives other benefits to plants like:
A. Addition of organic matter to the soil.
B. Resistance to root borne pathogens.
C. Tolerance to salinity
D. Increase in soil fertility
E. Tolerance to drought
Choose the correct answer from the options given below:

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 degradation of detritus into simpler inorganic substances by the bacterial and fungal enzymes is called as-

Match List-l with List-II

List-I(Concentration term)	List-II(Formula)
(A) Mass percentage	(I) \(\frac{\text { Volume of solute }}{\text { Volume of solution }} \times 100\)
(B) Volume percentage	(II)\(\frac{\text {Moles of a component}}{\text {Total moles of all the components } \mathrm{}}\)
(C) Mole Fraction	(III) \(\frac{\text { Moles of solute }}{\text { Mass of solvent in } \mathrm{kg}}\)
(D) Molality	(IV) \(\frac{\text { Mass of solute }}{\text { Volume of solution × Density of solution }} \times 100\)

Choose the correct answer from the options given below:

If charge is moving parallel to uniform magnetic field, its path will be: