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

In a survey it was found that 21 persons liked product P₁, 26 liked product P₂ and 29 liked product P₃. If 14 persons liked products P₁ and P₂; 12 persons liked product P₃ and P₁ ; 14 persons liked products P₂ and P₃ and 8 liked all the three products. Find how many liked product P₃ only.

Let A and B be two sets in the same universal set. Then,\[A - B =\]

Let U be the universal set containing 700 elements. If A, B are sub-sets of U such that \[n \left( A \right) = 200, n \left( B \right) = 300 \text{ and } \left( A \cap B \right) = 100\].Then \[n \left( A' \cap B' \right) =\] 

Let A and B be two sets that \[n \left( A \right) = 16, n \left( B \right) = 14, n \left( A \cup B \right) = 25\] Then, \[n \left( A \cap B \right)\] 

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.