There are three inlet taps whose diameters are 1 cm, 3 cm and 5 cm respectively. The rate of flow of the water is directly proportional to the square of the diameter. It takes 7 minutes for the smallest pipe to fill an empty tank. Find the time taken to fill an empty tank when all the three taps are opened.

(a) 13 sec

(b) 15 sec

(c) 12 sec

(d) 10 sec

Given triangles with sides T₁ : 3, 4, 5; T₂ : 5, 12, 13; T₃ : 6, 8, 10; T₄ : 4, 7, 9 and a relation R in set of triangles defined as R = {(Δ₁, Δ₂) : Δ₁ is similar to Δ₂}. Which triangles belong to the same equivalence class?
(a) T₁ and T₂
(b) T₂ and T₃
(c) T₁ and T₃
(d) T₁ and T₄

Let R be a relation on the set L of lines defined by l₁ R l₂ if l₁ is perpendicular to l₂, then relation R is
(a) reflexive and symmetric
(b) symmetric and transitive
(c) equivalence relation
(d) symmetric

Given set A ={1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be
(a) reflexive if (1, 1) is added
(b) symmetric if (2, 3) is added
(c) transitive if (1, 1) is added
(d) symmetric if (3, 2) is added

Given set A = {a, b, c). An identity relation in set A is
(a) R = {(a, b), (a, c)}
(b) R = {(a, a), (b, b), (c, c)}
(c) R = {(a, a), (b, b), (c, c), (a, c)}
(d) R= {(c, a), (b, a), (a, a)}

A relation S in the set of real numbers is defined as xSy ⇒  x – y+ √3 is an irrational number, then relation S is
(a) reflexive
(b) reflexive and symmetric
(c) transitive
(d) symmetric and transitive

Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is
(a) 144
(b) 12
(c) 24
(d) 64

Given a function lf as f(x) = 5x + 4, x ∈ R. If g : R → R is inverse of function ‘f then
(a) g(x) = 4x + 5
(b) g(x) = 54𝑥−5
(c) g(x) = 𝑥−45
(d) g(x) = 5x – 4

If A = [a_ij] is a 2 × 3 matrix, such that  a_ij= (−𝑖+2𝑗)25.then a₂₃ is

Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is
(a) 6
(b) 36
(c) 32
(d) 64

If |𝑎⃗| = 4 and -3 ≤ λ ≤ 2 then the range of |𝜆𝑎⃗| is
(a) [0, 8]
(b) [-12, 8]
(c) [0, 12]
(d) [8, 12]