JEE Main Practice Test- 14 - JEE MCQ

Suppose that f (0) = 0 and f ' (0) = 2, and let g (x) = f (- x + f (f (x))). The value of g ' (0) is equal to

The value of the definite integral,

A line L is perpendicular to the curve  at its point P and passes through (10, –1). The coordinates of the point P are

then the sum of the square of reciprocal of all the values of x where f(x) is non-differentiable, is equal to

h(x) = {x},k(x) = 5^{log₂ (x + 3)} then in [0, 1], Lagranges Mean Value Theorem is NOT applicable to
[Note : where [x] and {x} denote the greatest integer and fractional part function of x respectively]

If the function f (x) = ax e^–bx has a local maximum at the point (2, 10), then

then the value of x satisfying the equation f (x, 10) = f (x, 11), is

Number of integral solutions of the equation

[Note : where [x] denotes the greatest integer less than or equal to x and sgn x denotes signum function of x.]

The area bounded by the curve y = x² + 4x + 5 , the axes of co-ordinates & the minimum ordinate is

Number of roots of the equation x² –2x–log₂ |1 – x | = 3 is

Let F(x) be the primitive of w.r.t. x. If F(10) = 60 then the value of F(13), is

is continuous at x = 0, then
[Note : {x} denotes fractional part of x.]

[Note : where C is constant of integration.]

Point 'A' lies on the curve  and has the coordinate  where x > 0. Point B has the coordinates (x, 0). If 'O' is the origin then the maximum area of the triangle AOB is

Which one of the following statement is correct?

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)

If   then the value of must be

The sum of all the real roots of the equations
|x − 2|² + |x − 2| − 2 = 0 is …..

If P_n = cosⁿ x + sinⁿ x, then 2.P₆ - 3.P₄ + 1 = ..

If x = 2 + t³, y = 3t² and is a constant then the value of 343n must be

The value of 49A + 5B, where A = 1 - log₇2 and B = - log₅ 4 is

A transverse wave is travelling along a horizontal string. The first picture shows the shape of the string at an instant of time. This picture is superimposed on a coordinate system to help you make any necessary measurements. The second picture is a graph of the vertical displacement of one point along the string as a function of time. How far does this wave travel along the string in one second?

A cyclic process of an enclosed gas of constant mass is represented by volume (V) against absolute temperature (T) as shown. If P represents pressure, the graph representing the same process can be

A closed organ pipe is vibrating in its second overtone. The length of the pipe is 10cm and maximum amplitude of vibration of particles of the air in the pipe is 2mm. Then the amplitude of S.H.M. of the particles at 9cm from the open end is:

A sound source S and observers O₁, O₂ are placed as shown. S is always at rest and O₁, O₂ start moving with velocity v₀ at t = 0. At any later instant, let f₁ and f₂ represent apparent frequencies of sound received by O₁ and O₂, respectively. The ratio f₁/f₂ is

Equal masses of three liquids A, B and C have temperatures 10^oC, 25^oC and 40^oC respectively. If A and B are mixed, the mixture has a temperature of 15^oC. If B and C are mixed, the mixture has a temperature of 30^oC,. If A and C are mixed the mixture will have a temperature of

A steel rod is 4.000 cm in diameter at 30ºC. A brass ring has an interior diameter of 3.992 cm at 30ºC. In order that the ring just slides onto the steel rod, the common temperature of the two should be nearly (α_steel = 11 × 10^-6/ºC and α_brass = 19 × 10^-6/ºC)