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

Three long, straight and parallel wires carrying currents are arranged as shown in the figure. The wire C which carries a current of 5.0 amp is so placed that it experiences no force. The distance of wire C from wire D is then

A 100 turns coil shown in figure carries a current of 2 amp in a magnetic field . The torque acting on the coil is

Three long, straight and parallel wires carrying currents are arranged as shown in figure. The force experienced by 10 cm length of wire Q is

Four wires each of length 2.0 metres are bent into four loops P, Q, R and S and then suspended into uniform magnetic field. Same current is passed in each loop. Which statement is correct

A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to the one of the sides of the loop and is in the plane of the loop. If a steady current I is established in wire as shown in figure, the loop will