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Let ₁ and ₂ be the following straight lines.

Let 𝐿1 and 𝐿2 be the following straight lines. Suppose the straight line is Lies in the plane containing 𝐿1 and 𝐿2, and passes through the... View Article

Let x, and z be positive real numbers.

Let x, 𝑦 and z be positive real numbers. Suppose 𝑥, 𝑦 and z are the lengths of the sides of a triangle opposite to its angles 𝑋, 𝑌 and Z,... View Article

Let S be the set of all complex numbers z satisfying

Let S be the set of all complex numbers z satisfying | 2 + + 1| = 1. Then which of the following statements is/are TRUE? Answer: b, c... View Article

Let M be a 3 × 3 invertible matrix with real entries

Let M be a 3 × 3 invertible matrix with real entries and let I denote the 3 × 3 identity matrix. If −1 = adj (adj ), then... View Article

Let the function : R → R be defined by ( ) = ³− ²+ ( − 1) sin

Let the function : R → R be defined by ( ) = 3 − 2 + ( − 1) sin and let : R → R be an arbitrary function. Let g : R... View Article

Consider all rectangles lying in the region

Consider all rectangles lying in the region and having one side on the x-axis. The area of the rectangle which has the maximum perimeter among... View Article

Let C₁ and C₂ be two biased coins such that

Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are , respectively. Suppose α is the... View Article

Let , and λ be positive real numbers.

Let , and λ be positive real numbers. Suppose P is an end point of the latus rectum of the parabola 2 = 4λ , and suppose the... View Article

Let the functions: R ⟶ R and g : R ⟶ R be defined by

Let the functions: R ⟶ R and g : R ⟶ R be defined by Then, the area of the region in the first quadrant bounded by the curves = ( ), = g( )... View Article

If the function : R ⟶ R is defined by ( ) = | | ( – sin ),

If the function : R ⟶ R is defined by ( ) = | | ( – sin ), then which of the following statements is TRUE? a) is one-one, but NOT onto... View Article

Suppose a, b denote the distinct real roots of the quadratic polynomial

Suppose , denote the distinct real roots of the quadratic polynomial 2 + 20 − 2020 and suppose , denote the distinct complex roots... View Article

Let the function f: (0, π) → R be defined by f(θ) = (sin θ + cos θ)² + (sinθ – cos θ)⁴ .

Let the function f: (0, π) → R be defined by f(θ) = (sin θ + cos θ)2 + (sinθ - cos θ)4 . Suppose, the... View Article

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

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