MCA Entrance Previous Year Question Bank

A student calculated mean and standard deviation of $100$ observations as $40$ and $5.1$ respectively. Later it was discovered that he had taken by mistake $50$ instead of $40$, then new standard deviation is:

If $P={\sin }^{20}\theta +{\cos }^{48}\theta$, then the inequality that holds for all values of $\theta$ is:

If the mean deviation of the numbers $1,1+d,1+2d,\dots ,1+100d$ from their mean is $255$, then the value of $d$ is:

Suppose values taken by a random variable $X$ are such that $a\le x_i\le b$, where $x_i$ denotes the value of $X$ in the $i^{th}$ case for $i=1,2,3,\dots ,n$, then:

The mean of first $n$ natural numbers is equal to $\frac{n+7}{3}$, then $n$ is equal to:

Two variables have least square regression lines $3x+2y=26$ and $6x+y=31$, then correlation between $x$ and $y$ is:

If the mean of the squares of first $n$ natural numbers be 11, then $n$ is equal to:

If ${\overline{X}}_1$ and ${\overline{X}}_2$ are the means of two distributions such that \overline{X}_1 < \overline{X}_2, and $\overline{X}$ is the mean of the combined distribution, then:

The mean deviation from the mean of the AP $a,a+d,a+2d,...,a+2nd$, is:

In a group of 200 students, the mean and the standard deviation of scores were found to be 40 and 15, respectively. Later on, it was found that the two scores 43 and 35 were misread as 34 and 53, respectively. The corrected mean of scores is: