the area of the ellipse x2/a2 + y2/b2 = 1 is
The equation of the tangent to the curve (1 + x2)y = 2 - x where it crosses x-axis is
Find the value of
If is continuous at x = 0, then k =
The value of determinant ∆ of 3rd order is 9 then the value of ∆′2 where ∆′ is a determinant formed by cofactors of the element of ∆ is
The real part of is
at x = 2
The order of the differential equation x2+y2+2gx+2fy+c=0, is
The solution of the differential equation is
Integrating factor of differential equation cos x dy/dx+y sin x = 1 is
The solution of the differential equation x2 dy/dx-xy=1+cos y/x is
If , then find f′ 2
Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A into B is
If where n > 1 , then In − In−2
∫[(x+sinx)/(1+cosx)] dx =
If cos-1(x/a)+cos-1(y/b)=α, then (x2/a2)-(2xy/ab)cosα+(y2/b2)=
The statement "If x is divisible by 8, then it is divisible by 6" is false if x equals
A sentence in "If....then..." form is called an implication.
The only time when an implication is false is when the "If" part of the sentence is true and the "then" part of the sentence is false.
The number 32 makes the first part of the statement true and the second part of the statement false.
If the value of a determinants is 11, then the square of the determinant formed by its cofactor will be
If A is an 3x4 matrix and B is a matrix such that A'B and BA' both are defined, then size of B is
In a 12 storey building 3 persons enter a lift cabin. It is known that they will leave the lift at different storeys. In how many ways can they do so if the lift does not stop at the second storey.
There are 10 storeys for three persons for leaving the lift
(these are other than second storey and one at which they enter the lift).
So required number is 10 P 3 = 720
If A and B are such events that P(A)>0 and P(B)≠1, then P(A̅/B̅) is equal to
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
In ΔABC , r + r3 + r1 − r2 =
If the nth term of the geometric progression, 5, -5/2, 5/4, -5/8 is 5/1024, then the value of n is
If x and y are independent variables, then
The S.D. of 15 items is 6 and if each item is decreased by 1, then standard deviation will be
The one roots of the equation 2x5-14x4+31x3-64x2+19x+130=0 is
If one root of the equation a(b-c)x2+b(c-a)x+c(a-b)=0, is 1 then the other root is
The equation of the sphere concentric with the sphere x2 + y2 + z2 - 4x - 6y - 8z - 5 = 0 and which passes through the origin is
The number of st. lines that are equally inclined to three dimensional co-ordinate axes is
If tanθ+cotθ=2, then θ=
Two common tangents to the circle x2 + y2 = 2a2 and parabola y2= 8ax are
If the pairs of straigth lines x2 - 2pxy - y2 = 0 and x2 - 2qxy - y2 = 0 be such that each pair bisects the angle between the other pair, then
If makes an acute angle with , then is equal to
Let a, b and c be distributed non-vegetative numbers. If the vectors aî + aĵ + ck̂, î + k̂ and cî̂ + cĵ̂ + bk̂ lie in a plane, then c is