Multiple Choice QuestionsThe 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
C.
9/2
To find value of 'k' of the given lines L1 and L2 are intersecting each other.
Let 
⇒ Any point P on line L1 is of type
P(2p+1), 3p-1, 4p+1) and any point Q on line L2 is of type Q (q+3, 2q+k, q).
Since, L1 and L2 are intersecting each other, hence, both points P and Q should coincide at the point of intersection, i.e, corresponding coordinates of P and Q should be same.
2p+1 =q +3,
3p-1 =2q +k
4p+1 = q
solving these we get value of p and q as
p = -3/2 and q = -5
Substituting the values of p and q in the third equation
3p-1 = 2q+k, we get
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
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