List of top Questions asked in KCET

Let the functions \( f \) and \( g \) be \[ f : [0, \frac{\pi}{2}] \to \mathbb{R} \text{ given by } f(x) = \sin x \text{ and } g(x) = \cos x, \text{ where } R \text{ is the set of real numbers}. \] Consider the following statements: Statement (I): \( f \) and \( g \) are one-to-one. Statement (II): \( f + g \) is one-to-one. Which of the following is correct?
Find \[ \sec^2 \left( \tan^{-1} 2 \right) + \csc^2 \left( \cot^{-1} 3 \right) = ? \]

The equation \[ 2 \cos^{-1} x = \sin^{-1} \left( 2 \sqrt{1 - x^2} \right) \] is valid for all values of \(x\) satisfying:

Consider the following statements: Statement (I): In a LPP, the objective function is always linear. Statement (II): In a LPP, the linear inequalities on variables are called constraints. Which of the following is correct?
The maximum value of \( z = 3x + 4y \), subject to the constraints \( x + y \leq 40, x + 2y \geq 60 \) and \( x, y \geq 0 \) is:
Consider the following statements. Statement (I): If \( E \) and \( F \) are two independent events, then \( E' \) and \( F' \) are also independent. Statement (II): Two mutually exclusive events with non-zero probabilities of occurrence cannot be independent. Which of the following is correct?
If \( A \) and \( B \) are two non-mutually exclusive events such that \( P(A | B) = P(B | A) \), then:
If \( A \) and \( B \) are two events such that \( A \subseteq B \) and \( P(B) \neq 0 \), then which of the following is correct?
Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is \( \frac{2}{5} \). If she visits temple A, the probability that she meets her friend is \( \frac{1}{3} \). The probability that she meets her friend, whereas it is \( \frac{2}{7} \) if she visits temple B. Meera met her friend at one of the two temples. The probability that she met her friend at temple B is:
If \( Z_1 \) and \( Z_2 \) are two non-zero complex numbers, then which of the following is not true?
Which of the following are the techniques for detection of cancer of internal organs?
a) Radiography, MRI
b) MRI, computed tomography
c) Widal test, radiography
d) MRI, widal test
Malignant malaria is caused by
The drug prescribed to the patients who have undergone organ transplant is ____ and is produced by ____.
Read the following statements and select the correct option. Statement-I: Biocontrol refers to the use of biological methods for controlling plant diseases and pests. Statement-II: Trichoderma species are effective biocontrol agents for several plant pathogens.

Match the column-I with column-II. Choose the correct option given below.


 

Match the contents of List-I with List-II

 

The part of plasmid that codes for proteins involved in the replication of the pBR322 plasmid is
To isolate DNA from fungal cells, bacterial cells and plant cells, the enzymes required are respectively
In mature insulin, which of the peptide is not present?
A scientist wants to produce virus-free plant in tissue culture. Which part of the plant will he use as an explant? a) mature stem b) axillary meristem c) apical meristem d) mesophyll cell Choose the correct option from the following.
Some strains of Bacillus thuringiensis produce proteins that kill insects. Which one of the following is not killed by proteins of Bacillus thuringiensis?
Which one of the following population attributes, contributes to increase in population density?
If 8 individuals in a laboratory population of 80 fruit flies died during a specified time interval, the death rate in the population during that period is
Choose the correct sequence of steps involved in decomposition
With respect to limitation of Ecological pyramids, which of the following statements are correct? a) It does not take into account the same species belonging to two or more trophic levels. b) It assumes a simple food chain, something that almost never existed in nature. c) It accommodates saprophytes. d) It does not accommodate a food web. Choose the correct answer from the options given below.