If are in A.P., where a, b, c are sides of the triangle ABC, then are in

Statement1: If a line intersects a hyperbola at (2, 6) and (4, 4) and one of the asymptotes at (1, 2) then the centre of the hyperbola is (1, 2) because
Statement2: Mid point of the chord intercepted by hyperbola is same as midpoint of the chord intercepted between
asymptotes

lf , then the value of a and c is

lf then is equal to

lf , then

The gradient of the curve y=f(x) at P is slope of the tangent line at P i.e.,

PM = length of the tangent
PR = length of the normal to the curve y=f(x)
Area of triangle formed by the positive x-axis and the normal and the tangent to at is

The partial pressures of CH₃0H, CO and H₂ in the equilibrium mixture for the reaction, at 427C are 2.0, 1.0 and 0.1 atm respectively The value of K_p for the decomposition of CH₃0H into CO and H₂ is:

At 500 K, the equilibrium constant for reaction c is 0.6At the same temperature, the equilibrium constant for the reaction  , will be:

For the reaction, KC 1.8 10^-6 at 185C The value of Kc at 185C for the reaction;

In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and third terms is 35, then the first term of this geometric progression is

Statements-1: = (2n + (a) cost (0 t)
Statements-2:
and if f(a + x) = f(x)

If x enotes the rounded off value of x  and the area bounded by the two curves defined by y =  and . In the interval 0 x 1 is equal to 2 square units, The value of the constant is

Statement-1: then
Statement-2 : is the reflection of

If ln 2 then the value of the definite integral equals

Let the unit vectors  and  be perpendicular and the unit vector  be inclined at an angle θ to both  and  If  then

We should know how to take dot product of two vectors.

A random variable X has the probability distribution

For the events is prime number} and , the probability of is