The function \(f ( x )=\log (\sin x )\) is ___________

Relation \(R\) on Real Numbers is defined as \(R =\{( a , b ): a \leq b \}\). The relation is :

The sum of the order and degree of the differential equation \(\frac{d^2 y}{d x^2}+\sqrt[3]{\frac{d y}{d x}}+(1+x)=0\) is :

If \(p\) is the probability of any event \(A\) then which one of the following statement is true?

The point at which the maximum value of \(x+y\), subject to constraints \(x+2 y \leq 70,2 x+y \leq 95, x \geq 0, y \geq 0\) is obtained, is :

Area of the region bounded by \(y=3 x, x\)-axis, and \(x=-1\) is :

Let * be a binary operation defined on \(Q ^{+}\)(the set of positive rational numbers) by the rule \(a * b=\frac{a b}{7}\) for all \(a, b \in Q ^{+}\). Then inverse of \(2 * 7\) is:

The correct IUPAC name of tert-butyl benzyl ether is-

Huygen's principle allows us to understand and determine.

Which of the following techniques are used for early diagnosis of diseases?
(A). Urine analysis
(B). PCR
(C). ELISA
(D). Recombinant DNA technology (RDT)
Choose the correct answer from the options given below:

The value of \(k\) for which the lines \(\frac{2 x-3}{4}=\frac{3-y}{k}=\frac{z-2}{-2}\) and \(\frac{x-2}{1}=\frac{y}{4}=\frac{5-z}{3}\) are perpendicular to each other is :

Match the statement of set of orbitals given in List-I with orbitals and energy separation given in List-II

List – I (Statements)	List-II (Orbitals and energy separation)
(A) \(t_{2 g}\) set of orbitals in octahedral crystal field and energy separation from barycentre	(I) \(d_{x^2-y^2}, d_{z^2}\) and \(3 / 5 \Delta_t\)
(B) \(e_g\) set of orbitals in octahedral crystal field and energy separation from barycentre	(II) \(d_{x y}, d_{x z}, d_{y z}\) and \(2 / 5 \Delta_t\)
(C) \(t_2\) set of orbitals in tetrahedral crystal field and energy separation from barycentre	(III) \(d_{x^2-y^2}, d_{z^2}\) and \(3 / 5 \Delta_0\)
(D) \(e\) set of orbitals in tetrahedral crystal field and energy separation from barycentre	(IV) \(d_{x y}, d_{x z}, d_{y z}\) and \(2 / 5 \Delta_0\)

Choose the correct answer from the options given below:

Read the paragraph given below and answer the question.
Sutton and Boveri argued that the pairing and separation of a pair of chromosomes would lead to the segregation of a pair of factors they carried. Sutton united the knowledge of chromosomal segregation with Mendelian principles and called it the chromosomal theory of inheritance. Following this synthesis of ideas, experimental verification of the chromosomal theory of inheritance by Thomas Hunt Morgan and his colleagues, led to discovering the basis for the variation that sexual reproduction produced. Morgan worked with the tiny fruit files, which were found very suitable for such studies. They could be grown on simple synthetic medium in the laboratory. They complete their life cycle in a short span of time and a single mating could produce a large number of progeny flies. Also, there was a clear differentiation of the sexes the male and female flies are easily distinguishable. Also, it has many types of hereditary variations that can be seen with low power microscopes.
Which statement is incorrect with respect to Drosophila.