PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find: how many can speak Hindi only

In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find: 

how many can speak English only. 

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