Multiple Choice QuestionsThe area bounded between the parabolas x2=y/4 and x2 = 9y, and the straight line y = 2 is
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
B.
35
Y ⊆ X, Z ⊆ X
Let a ∈ X, then we have following chances that
(1) a ∈ Y, a ∈ Z
(2) a ∉ Y, a ∈ Z
(3) a ∈ Y, a ∉ Z
(4) a ∉ Y, a ∉ Z
We require Y ∩ Z = φ
Hence (2), (3), (4) are chances for ‘a’ to satisfy Y ∩ Z = φ.
∴ Y ∩ Z = φ has 3 chances for a.
Hence for five elements of X, the number of required chance isÂ
3 × 3 × 3 × 3 × 3 = 35
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 4500Ï€ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72Ï€ 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 =Â 
. If u1 and u2 are column matrices such that Au1 =Â 
 and Au2 = 
, then u1 +u2 is equal to
 and 
 intersect, then k is equal to
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