Commerce (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

Show that the expansion of \[\left( x^2 + \frac{1}{x} \right)^{12}\]  does not contain any term involving x⁻¹.

Show that the statement
p : "If x is a real number such that x³ + x = 0, then x is 0"
is true by
(i) direct method
(ii) method of contrapositive
(iii) method of contradition.

Show that the following statement is true by the method of contrapositive
p : "If x is an integer and x² is odd, then x is also odd" 

Show that the following statement is true
"The integer n is even if an only if n² is even"

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola:

y² = 8x 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola 

4x² + y = 0 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas 

y² − 4y − 3x + 1 = 0 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y² − 4y + 4x = 0 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola 

 y² + 4x + 4y − 3 = 0 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y² = 8x + 8y 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y² = 8x + 8y

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola 

 4 (y − 1)² = − 7 (x − 3) 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola 

 y² = 5x − 4y − 9 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola 

x² + y = 6x − 14

For the parabola y² = 4px find the extremities of a double ordinate of length 8 p. Prove that the lines from the vertex to its extremities are at right angles. 

Find the length of the line segment joining the vertex of the parabola y² = 4ax and a point on the parabola where the line-segment makes an angle θ to the x-axis.  

Write the axis of symmetry of the parabola y² = x. 

Write the distance between the vertex and focus of the parabola y² + 6y + 2x + 5 = 0. 

Write the length of the chord of the parabola y² = 4ax which passes through the vertex and is inclined to the axis at \[\frac{\pi}{4}\]