PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is

The standard deviation of first 10 natural numbers is

The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is 

Let x₁, x₂, ..., x_n be n observations. Let  \[y_i = a x_i + b\]  for i = 1, 2, 3, ..., n, where a and b are constants. If the mean of \[x_i 's\]  is 48 and their standard deviation is 12, the mean of \[y_i 's\]  is 55 and standard deviation of \[y_i 's\]  is 15, the values of a and b are 

The standard deviation of the observations 6, 5, 9, 13, 12, 8, 10 is

\[\lim_{x \to 0} \left\{ \frac{e^x + e^{- x} - 2}{x^2} \right\}^{1/ x^2}\]

\[\lim_{x \to a} \left\{ \frac{\sin x}{\sin a} \right\}^\frac{1}{x - a}\]

\[\lim_{x \to 0} \frac{\sin x}{\sqrt{1 + x} - 1} .\] 

Write the value of \[\lim_{x \to - \infty} \left( 3x + \sqrt{9 x^2 - x} \right) .\]

Write the value of \[\lim_{n \to \infty} \frac{n! + \left( n + 1 \right)!}{\left( n + 1 \right)! + \left( n + 2 \right)!} .\]

Write the value of \[\lim_{x \to \pi/2} \frac{2x - \pi}{\cos x} .\] 

Write the value of \[\lim_{n \to \infty} \frac{1 + 2 + 3 + . . . + n}{n^2} .\]

(vii)  find the equation of the hyperbola satisfying the given condition:

foci (± 4, 0), the latus-rectum = 12

Find the general solution of the following equation:

Find the general solution of the following equation:

Find the general solution of the following equation:

Find the general solution of the following equation:

Find the general solution of the following equation:

Find the general solution of the following equation:

Find the general solution of the following equation: