Arts (English Medium) इयत्ता ११ - CBSE Question Bank Solutions for Mathematics

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

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

\[\lim_{x \to \infty} \left\{ \frac{3 x^2 + 1}{4 x^2 - 1} \right\}^\frac{x^3}{1 + x}\]

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

Find the area of the triangle formed by the lines joining the vertex of the parabola \[x^2 = 12y\]  to the ends of its latus rectum.

Find the coordinates of the point of intersection of the axis and the directrix of the parabola whose focus is (3, 3) and directrix is 3x − 4y = 2. Find also the length of the latus-rectum. 

If b and c are lengths of the segments of any focal chord of the parabola y² = 4ax, then write the length of its latus-rectum. 

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

foci (± 4, 0), the latus-rectum = 12

If the parabola y² = 4ax passes through the point (3, 2), then find the length of its latus rectum.