PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

Write the number of terms in the expansion of \[\left( 2 + \sqrt{3}x \right)^{10} + \left( 2 - \sqrt{3}x \right)^{10}\] . 

Write the number of terms in the expansion of \[\left( 2 + \sqrt{3}x \right)^{10} + \left( 2 - \sqrt{3}x \right)^{10}\] . 

Write the number of terms in the expansion of \[\left( 1 - 3x + 3 x^2 - x^3 \right)^8\]

Which term is independent of x, in the expansion of \[\left( x - \frac{1}{3 x^2} \right)^9 ?\]

Write the number of terms in the expansion of  \[\left[ \left( 2x + y^3 \right)^4 \right]^7\] .

Find the number of terms in the expansion of\[\left( a + b + c \right)^n\]

If rth term in the expansion of \[\left( 2 x^2 - \frac{1}{x} \right)^{12}\]  is without x, then r is equal to

If the fifth term of the expansion  \[\left( a^{2/3} + a^{- 1} \right)^n\]  does not contain 'a'. Then n is equal to

The coefficient of \[x^{- 3}\]  in the expansion of \[\left( x - \frac{m}{x} \right)^{11}\]  is

The coefficient of the term independent of x in the expansion of \[\left( ax + \frac{b}{x} \right)^{14}\] is 

If the coefficients of the (n + 1)^th term and the (n + 3)^th term in the expansion of (1 + x)²⁰are equal, then the value of n is

If the coefficients of 2nd, 3rd and 4th terms in the expansion of \[\left( 1 + x \right)^n , n \in N\]  are in A.P., then n =

Constant term in the expansion of \[\left( x - \frac{1}{x} \right)^{10}\]  is

Calculate the mean deviation from the median of the following frequency distribution:

The number of telephone calls received at an exchange in 245 successive one-minute intervals are shown in the following frequency distribution:

Compute the mean deviation about median.

Calculate the mean deviation about the median of the following frequency distribution:

While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

Calculate the mean, variance and standard deviation of the following frequency distribution. 

The perpendicular from the origin to the line y = mx + c meets it at the point (−1, 2). Find the values of m and c.

Find the equation of the straight line which cuts off intercepts on x-axis twice that on y-axis and is at a unit distance from the origin.