List of top Mathematics Questions asked in Karnataka PGCET

Match the following List-I with List-II.

\[ \begin{array}{|c|l|c|l|} \hline \text{List-I} & & \text{List-II} & \\ \hline (a) & \text{Mean} & (i) & \text{List of individual values} \\ \hline (b) & \text{Median} & (ii) & \text{Value appears most often} \\ \hline (c) & \text{Mode} & (iii) & \text{Average for complete data} \\ \hline (d) & \text{Frequency Distribution} & (iv) & \text{Location average} \\ \hline \end{array} \]

The following table shows the number of working hours and the number of employees employed in a small-scale industry. 

\[ \begin{array}{|c|c|} \hline \text{Number of Working Hours} & \text{Number of Employees} \\ \hline 3-5 & 7 \\ \hline 5-7 & 10 \\ \hline 7-9 & 16 \\ \hline 9-11 & 47 \\ \hline 11-13 & 12 \\ \hline 13-15 & 8 \\ \hline \text{Total} & 100 \\ \hline \end{array} \]

Statements:

(i) Average number of working hours of employees is 9.42 hours. 
(ii) The number of workers working less than nine hours is 33. 
(iii) The number of workers working more than average working hours is 67.

In a cross-sectional study conducted at a clinic, the researcher is interested to know what proportion of the patients is suffering from tuberculosis and HIV.

\[ \begin{array}{|c|c|c|} \hline & \text{Tuberculosis (Yes)} & \text{Tuberculosis (No)} \\ \hline \text{HIV +ve} & 16 & 4 \\ \hline \text{HIV -ve} & 24 & 456 \\ \hline \end{array} \]

The probability that a person selected is not suffering from both tuberculosis and HIV is:

A person has 2 parents, 4 grandparents, 8 great grandparents and so on. What is the number of his ancestors during the $5^{\text{th}}$ generation preceding his own?
For a symmetrical distribution:
The standard deviation of a distribution is 5. If each observation is increased by 2, then the new standard deviation will be:
The range of the data 12, 25, 15, 18, 35, 11, 45, 33, 22, 10 is:
If the mode of a distribution is 18 and the mean is 24, then the median is:
If \(P(A)=0.8\), \(P(B)=0.5\) and \(P(B|A)=0.4\), then the value of \(P(A|B)\) is:
An experiment succeeds twice as often as it fails. The probability of success in the next trial is:
If an event cannot occur, then its probability is:
The relation between mean, median and mode for a moderately asymmetrical distribution is:
The average of squared deviations from mean is called:
If the first quartile is 142 and the semi-interquartile range is 18, then the third quartile is:
The algebraic sum of the deviations of a set of \(n\) values from their arithmetic mean is:
The arithmetic mean of \(1,2,3,\ldots,n\) is:

If the mean of the distribution is \(5\), then the value of \(P\) is:

\[ \begin{array}{|c|c|c|c|c|c|} \hline x_i & 2 & 4 & 6 & P & 10 \\ \hline f_i & 3 & 2 & 1 & 4 & 2 \\ \hline \end{array} \]
 

The average of 5 numbers is 27. If one number is excluded, the average becomes 25. The excluded number is:
Two dice are thrown and the sum of the numbers which come up on the dice is noted. Among the following events:
• A: The sum is even.
• B: The sum is a multiple of 3.
• C: The sum is less than 4.
• D: The sum is greater than 11. Which pair of events are mutually exclusive?
\[ \tan^{-1}(1)+\cos^{-1}\left(-\frac12\right)+\sin^{-1}\left(-\frac12\right) = \]
In a right angled isosceles triangle \(\Delta ABC\), right angle at \(C\), if side \(a=2\), then sides \(b\) and \(c\) are respectively
The general solution of \[ 2\cos\theta-\sqrt3=0 \] is

Match List-I with List-II. 

The Boolean expressions \[ (AB)' = A' + B' \] and \[ (A+B)' = A'B' \] represent
A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man?