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

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 equation of the line parallel to x-axis and having intercept − 2 on y-axis.

Draw the lines x = − 3, x = 2, y = − 2, y = 3 and write the coordinates of the vertices of the square so formed.

Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x-axis.

Find the equation of the straight line passing through (−2, 3) and inclined at an angle of 45° with the x-axis.

Find the equation of the line passing through (0, 0) with slope m.

Find the equation of the line passing through \[(2, 2\sqrt{3})\] and inclined with x-axis at an angle of 75°.