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The area bounded by the parabola y2=4ax and the straight line y=2ax is
Let z₁ and z₂ be nth roots of unity which subtend a right angle at the origin. Then n must be of the form
The surface area of a cone including the base is 4π sq.ft., then the dimensions of the cone when the volume is maximum are
If the function f is defined by hen at what points is f differentiable
Which one of the following differential equations represents the system of circles touching y-axis at the origin ?
The order of differential equation (d2y/dx2)3=(1+dy/dx)1/2 is
If f, g : R → R, f(x) = (x + 1)2 g(x) = x2 + 1 then (fog) (-3) =
Negation of the conditional , ' if it rains , I shall go to school ' is
If A is a square matrix and I is the unit matrix of the same order 3 x 3 , then A .(adj A) is
Each coefficients in the equation ax2+bx+c=0 is determined by throwing an ordinary die. The probability that the equation will have equal roots is
A coin tossed until a head appears or until the coin has been tossed 5 times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times is
Sum of all terms of a G.P. is 5 times the sum of odd terms. The common ratio is
If the side of a triangle are 13, 14, 15, then the radius of the incircle is
If A and B are such events that P(A)>0 and P(B)≠1, then P(A̅/B̅) is equal to
There are five roads from a village to a town. In how many ways can a villager return after reaching the town?
Permutation : - A Permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.
For example, Suppose we have a set of three letters :A, B and C..... each possible arrangement would be an example of permutation.
Here in this question, there are 5roads leading to a town from a village.
He can go by 5 ways and can return by 4 ways
So the number of different ways in which a villager can go to the town and return back is 5×4=20
If B is a non-singular matrix and A is a square matrix, then det (B-1AB) =
If a,b are odd integers, the roots of the equation 2ax2+(2a+b)x+b=0, a≠0 are
A student obtain 75%, 80% and 85% in three subjects. If the marks of another subject are added, then his average cannot be less than
The equation of the plane which bisects the line joining (2,3,4) and (6,7,8) is
The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is
The equation of the sphere with centre (3, 6, -4) and touching the plane
2x - 2y - z - 10 = 0 is
As the required sphere touches the plane
2x - 2y - z - 10 = 0 .....(1)
∴ Radius of the required sphere = ⊥ from the center (3, 6, -4) of the required sphere to the plane (1)
∴ The required equation of the sphere is given by
(x - 3)2 + (y - 6)2 + (z + 4)2 = 16 (Central form)
⇒ x2 + 9 - 6x + y2 + 36 - 12y + z2 + 16 + 8z = 16
⇒ x2 + y2 + z2 - 6x - 12y + 8z + 45 = 0