List of practice Questions

The mode of the following distribution: 7, 4, 3, 5, 6, 3, 3, 2, 4, 3, 4, 3, 3, 4, 4, 2, 3.

Standard Error of the sampling distribution of a statistic is given by

The rate of activity of a person y with age t is given by (1+t) \(\frac{dy}{dx}=e^{-y}-1\). For the initial condition y = 1 at r = 0, the dy dt solution is given by,

The distance of a point whose position vector is \(\overrightarrow{u}\) from the plane\(\overrightarrow{r}.\overrightarrow{n}=d\) is, 

The integral \(∫_3^lx^3\) log(x) dx equals

The derivative \(\frac{dy}{dx} \) of the function y=x^x is

If the sets X and Y are mutually exclusive, then P(X∩Y) is

Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. The probability that first two cards are kings and third card drawn is an ace is

One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely. The probability that the card will not be a king is

The arithmetic mean and standard deviation of a series of 20 items were calculated by a student as 20 cm and 5 cm, respectively. But while calculating them an item 13 was misread as 30. The correct standard deviation is

If P (A∩B) = P(A).P(B), then event of A and B are

Given below are two statements:
Statement I: The Geometric mean of a set of n observations is the nth root of their product. 
Statement II: If X₁, X₂, X₃ ... X_n are the given n observations, then their G.M. is given by \(\sqrt{(X_1) (X_2) (X_3)....(X_n)}\) In the light of the above statements,

Consider the linear function from Z to Z: f= {(0, -5), (1, 0), (2, 5), (-1, -10)}. Then the function f(x) is

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the sphere is 42 cm and the height of the vessel is 27 cm. Find its capacity in cm³. (Use: \(\pi = \frac {22}{7}\))

Any square matrix A can be expressed as:
1. The product of a symmetric and a skew-symmetric matrices. 
2. The division of a symmetric matrix by a skew-symmetric matrix. 
3. The sum of a symmetric and a skew-symmetric matrices. 
4. The subtraction of a symmetric from a skew-symmetric matrix.

The integral \(∫_{-1}^2|x^3-x|dx\) equals to

The regression analysis confined to the study of only two variables at a time, is called as

The security guard of a hospital allows enter to 5 persons from a room for a checkup from a group of patients which has 10% Covid infected patients. The probability that there is at least one person Covid infected patients, is

Which of the following is the linear regression equation

If X is a square matrix of order NxN, then for any constant c, |cX| is equal to,

The function F(x) = [x] at x = 0 is

If X and Y are invertible matrices of same order then

A box contains 9 balls of which 4 are Golden, 3 are Silver and 2 are Steel. The balls are similar in shape and size. A ball is drawn at random from the box. The probability that it will not be a silver ball

The average marks of students in a group of 6 students is 119. The individual marks of five of them are 115, 109, 129, 117, 114. The marks of sixth student is

The standard deviation for the following distribution:

Class	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	3	7	12	15	8	3	2