The area bounded between the parabolas x²=y/4 and x² = 9y, and the straight line y = 2 is

If the line  and  intersect, then k is equal to

• -1

• 2/9

• 9/2

• 9/2

13.

Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is

• 3/8

• 1/5

• 1/4

• 1/4

If z ≠ 1 and  is real, then the point represented by the complex number z lies

• either on the real axis or on a circle passing through the origin

• on a circle with centre at the origin

• either on the real axis or on a circle not passing through the origin

• either on the real axis or on a circle not passing through the origin

The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

• 10/3

• 3/5

• 6/5

• 6/5

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty, is

• 5²

• 3⁵

• 2⁵

• 2⁵

An ellipse is drawn by taking a diameter of the circle (x–1)² + y² = 1 as its semiminor axis and a diameter of the circle x² + (y – 2)² = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

• 4x²+ y² = 4

• x² +4y² =8

• 4x² +y² =8

• 4x² +y² =8

A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

• -1/4

• -4

• -2

• -2

A spherical balloon is filled with 4500π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is

• 9/7

• 7/9

• 2/9

• 2/9

Let A = . If u₁ and u₂ are column matrices such that Au1 =  and Au2 = , then u₁ +u₂ is equal to