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

In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus is

If  \[A \cap B - B\] 

An investigator interviewed 100 students to determine the performance of three drinks: milk, coffee and tea. The investigator reported that 10 students take all three drinks milk, coffee and tea; 20 students take milk and coffee; 25 students take milk and tea; 12 students take milk only; 5 students take coffee only and 8 students take tea only. Then the number of students who did not take any of three drinks is 

For any two sets A and B, \[A \cap \left( A \cup B \right)'\]is equal to

The equation of the directrix of a hyperbola is x − y + 3 = 0. Its focus is (−1, 1) and eccentricity 3. Find the equation of the hyperbola.

Find the equation of the hyperbola whose focus is (1, 1), directrix is 3x + 4y + 8 = 0 and eccentricity = 2 .

Find the equation of the hyperbola whose focus is (1, 1) directrix is 2x + y = 1 and eccentricity = \[\sqrt{3}\].

Find the equation of the hyperbola whose focus is (2, −1), directrix is 2x + 3y = 1 and eccentricity = 2 .

Find the equation of the hyperbola whose focus is (a, 0), directrix is 2x − y + a = 0 and eccentricity = \[\frac{4}{3}\].

Find the equation of the hyperbola whose focus is (2, 2), directrix is x + y = 9 and eccentricity = 2.

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

9x² − 16y² = 144

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

16x² − 9y² = −144

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

 4x² − 3y² = 36

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

 3x² − y² = 4 

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

2x² − 3y² = 5.

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in  the distance between the foci = 16 and eccentricity = \[\sqrt{2}\].

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in  the  conjugate axis is 5 and the distance between foci = 13 .

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in  the conjugate axis is 7 and passes through the point (3, −2).

Find the equation of the hyperbola whose foci are (6, 4) and (−4, 4) and eccentricity is 2.

Find the equation of the hyperbola whose vertices are (−8, −1) and (16, −1) and focus is (17, −1).