Area of the region bounded by the curve \(x^2=4 y, x\)-axis and \(x=3\) is:

The Greatest Integer Function \(f: R \rightarrow R\) given by \(f(x)=[x], x \in R\) and \([x]\) denotes the greatest integer less than or equal to \(x\) is :

\(\int_0^{\frac{\pi}{3}} \frac{\sin x}{(2-\cos x)^2} d x=\)

The sum of order and degree of the differential equation \(\frac{\left\{1+\left(\frac{d y}{d x}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2 y}{d x^2}}= p\) is :

The programming problem
Max Z = 2x + 3y subject to the conditions \(0 \leq x \leq 3,0 \leq y \leq 4\) is:

The order and degree of the differential equation
\(x^2 \frac{d^2y}{dx^2} - 3 \left(\frac{dy}{dx}\right)^2 + y = 0\) are:

The value of the determinant \(\begin{vmatrix} 3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & 1 \end{vmatrix}\) is:

Which of the following are correct?
(A) Time series analysis does not help to understand the behavior of a variable in the past.
(B) Time series predict the future behavior of variable.
(C) Time series helps to plan future operations.
(D) The main aim of the time series analysis is to derive conclusions after arranging the time series in a systematic manner.
Choose the correct answer from the options given below:

Identify the correct sequence of structures formed during spermatogenesis in humans?
(A) Spermatozoa
(B) Secondary spermatocytes
(C) Spermatogonia
(D) Spermatid
Choose the correct answer from the options given below:

Read the Passage carefully and answer the questions
When a ligand is bound to a metal ion through a single donor atom, it is said to be a unidentate ligand but when it bind through two donor atoms, then it is said to be didentate ligand and when several donor atoms are present in a single ligand, it is said to be a polydentate ligand. When a di- or polydentate ligand uses its two or more donor atoms simultaneously to bind a single metal ion, it is said to be a chelate ligand. The number of such ligating groups is called the denticity of the ligand. ligand which has two different donor atoms and either of the two ligetes in the complex is called ambidentate ligands. The number of ligand donor atoms to which the metal is directly bonded, is called coordination number of the metal ion in the complex. Complexes in which a metal is bound to only one kind of donor groups are known as homoleptic and in which a metal is bound to more than one kind of donor groups are known as heteroleptic complexes.
Which of the following molecule/ion is not expected to behave as a ligand?

The wavelength of light coming from a sodium source is 589 nm. Its wavelength in crown glass having refractive index 1.52 is

The phase difference between the output and input of a common emitter amplifier is :

Given equation of the plane is \(5x + 2y - 3z = 17\). Then,
A. A point \((2, 2, -1)\) lies on the plane
B. The direction cosines of normal to plane are \((2, 2, -1)\)
C. Coordinates of foot of perpendicular from origin are \((5, 2, -3)\)
D. The plane does not pass through the origin
Choose the correct answer from the options given below: