Anush takes a loan of ₹ \( 150000\) @ \(16 \%\) annual interest for 5 years. His EMI (Equally Monthly Installmant) on monthly basis under flat rate system is :

If f(a - x) = f(x), then \(\int_0^a x f(x) d x\) is equal to

\(\int \frac{d x}{2 \sin ^2 x+5 \cos ^2 x}\) is equal to

If \(y = x + \tan x\), then value of \(\frac{d^2y}{dx^2}\) at \(x = \frac{\pi}{4}\) is:

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 y = - 4 a root of \(\left|\begin{array}{lll}y & 2 & 3 \\ 1 & y & 1 \\ 3 & 2 & y\end{array}\right|=0\), then the product of the other two roots is

In a LPP, let \(R\) be the feasible region.
A. If R is unbounded then a max./min. value of objective function may not exist.
B. If R is bounded then a max. and min. value of objective function will always exist.
C. If a solution exists, it must occur at a corner point.
D. If R is bounded then max. will exist but min. may or may not exist for an objective function.
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Types of inheritance)	List-II (Examples)
(A) Pleiotropy	(I) ABO blood grouping in human
(B) Polygenic inheritance	(II) Snapdragon plant
(C) Incomplete dominance	(III) Phenylketonuria
(D) Co-dominance	(IV) Human skin colour

Choose the correct answer from the options given below:

As the mass number A increases, which of the following quantities related to a nucleus does not change?

Medical termination of pregnancy (MTP) is considered relatively safe -

Assume that an electric field \( (20\hat{i}) \text{ V m}^{-1} \) exists in the region of space. If \( V_0 \) is the potential at the origin and \( V_A \) is the potential at \( x = 1 \text{ m} \), then the potential difference \( V_A - V_0 \) is :

Which of the following are autosomal recessive trait/ disorder?
(A) Thalassemia
(B) Haemophilia
(C) Sickle cell anaemia
(D) Phenylketonuria
Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions.
Theory of Evolution
The evolution of life is a gradual process through which simple organisms are transformed into complex life forms over billions of years. It involves genetic changes, adaptation to the environment, and the emergence of diversity in species. Fossil records provide evidence of extinct life forms and transitional stages. Evolution is influenced by factors such as mutation, genetic recombination, and environmental pressure, shaping the biodiversity we see today. Charles Darwin and Alfred Russel Wallace were pioneering naturalists who developed the theory of evolution by natural selection.
Which one of the following statements is not a connotation of the theory of special creation?