Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions

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. 

The vertex of the parabola (y + a)² = 8a (x − a) is 

If the focus of a parabola is (−2, 1) and the directrix has the equation x + y = 3, then its vertex is 

The length of the latus-rectum of the parabola y² + 8x − 2y + 17 = 0 is 

The vertex of the parabola x² + 8x + 12y + 4 = 0 is

The length of the latus-rectum of the parabola 4y² + 2x − 20y + 17 = 0 is 

The length of the latus-rectum of the parabola x² − 4x − 8y + 12 = 0 is