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Let f:R → R be a differentiable function such that its derivative

Let f:R → R be a differentiable function such that its derivative f’ is continuous and f(π) = -6. If F: [0, π ] → R is... View Article

Let the function f: [0, 1] → R be defined by f(x) = 4^x/(4^x + 2).

Let the function f: [0, 1] → R be defined by f(x) = 4x/(4x + 2). Then the value of f(1/40) + f(2/40) + f(3/40) + …+ f(39/40) –... View Article

Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6

Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6, are rolled together and the sum of the numbers on the faces is observed. This... View Article

In a hotel, four rooms are available.

In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at... View Article

An engineer is required to visit a factory for exactly four days

An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits... View Article

For non-negative integers s and r, let

For non-negative integers s and r, let Then which of the following statements is/are TRUE? a) (m, n) = (n, m) for all positive integers m, n... View Article

Let a and b be positive real numbers.

Let a and b be positive real numbers. Suppose and if the area of the parallelogram is 8, then which of the following statements is/are TRUE?... View Article

Let α, β, γ, δ be real numbers such that α ² + β ² + γ ² ≠ 0 and α + γ = 1.

Let α, β, γ, δ be real numbers such that α 2 + β 2 + γ 2 ≠ 0 and α + γ = 1. Suppose the... View Article

Let f: R → R and g: R → R be functions satisfying f(x + y) = f(x) + f(y) + f(x)f(y)

Let f: R → R and g: R → R be functions satisfying f(x + y) = f(x) + f(y) + f(x)f(y) and f(x) = xg(x) For all x, y ∈ R. If... View Article

Let a and b be positive real numbers such that a > 1 and b < a.

Let a and b be positive real numbers such that a > 1 and b < . Let P be a point in the first quadrant that lies on the hyperbola .... View Article

Let b be a nonzero real number.

Let b be a nonzero real number. Suppose f = R → R is a differentiable function such that f(0) = 1. If the derivative f' of f satisfies the... View Article

The value of the limit

The value of the limit Answer: 8 Solution: Using transformation and submultiple angle formula in denominator... View Article

Let the functions f: (−1,1) → R and g: (−1, 1) → (−1, 1) be defined by f(x) = |2x − 1| + |2x + 1|and g (x) = x − [x]

Let the functions f: (−1,1) → R and g: (−1, 1) → (−1, 1) be defined by f(x) = |2x − 1| + |2x + 1|and g (x) = x... View Article

The trace of a square matrix is defined to be the sum of its diagonal entries.

The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 x 2 matrix such that the trace of A is 3 and the trace... View Article

Let O be the centre of the circle x² + y² = r², where r > √5/2 .

Let O be the centre of the circle x2 + y2 = r2, where r > √5/2 . Suppose PQ is a chord of this circle and the equation of the line... View Article

The probability that a missile hits a target successfully is 0.75.

The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are... View Article

For a complex number z, let Re(z) denote the real part of z.

For a complex number z, let Re(𝑧) denote the real part of z. Let S be the set of all complex numbers z satisfying 𝑧4 − |𝑧|4 = 4 𝑖𝑧2, where... View Article

Let A(1,0), B(6,2), C(3/2, 6) be the vertices of a triangle ABC.

Let A(1,0), B(6,2), C(3/2, 6) be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangle APC, APB and BPC... View Article

Let S be the set of points where the function

Let S be the set of points where the function, (𝑥) = |2 − |𝑥 − 3||, 𝑥 ∈ 𝐑, is not differentiable. Then, the value of... View Article

If the sum of the coefficients of all even powers of x

If the sum of the coefficients of all even powers of in the product (1 + x + x2 + x3 … . +x2 )(1 − x + x2 − x3 … . +... View Article

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