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Let ₁ and ₂ be the following straight lines.

Let 𝐿1 and 𝐿2 be the following straight lines. \(\begin{array}{l}L_{1}:\frac{x-1}{1} = \frac{y}{1} = \frac{z-1}{3}\end{array} \) and \(\begin{array}{l}L_{2}:\frac{x-1}{-3} = \frac{y}{-1} =... 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... 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... 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... 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)... View Article

Consider all rectangles lying in the region

Consider all rectangles lying in the region \(\begin{array}{l}\left \{ (x,y)\epsilon R\times R:0 \leq x\leq \frac{\pi }{2}\: and\: 0\leq y\leq 2sin(2x)\right... 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\(\begin{array}{l}\frac{2}{3}... 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... 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 \(\begin{array}{l}f(x) = e^{x-1} – e^{-\left... View Article

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

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

Let a and b be positive real numbers.

Let a and b be positive real numbers. Suppose \(\begin{array}{l}\vec{PQ} = a \hat{i} + b \hat{j}\end{array} \) and \(\begin{array}{l}\vec{PS} =... 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... View Article

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