Mock 14 – Mixed Practice (Part 3)

Which one of the following is not a basic solution of the system of linear equations x₁ + 2x₂ + x₃ = 4, 2x₁ + x₂ + 5x₃ = 5?

Match List I (law) with List II (axiom). List I: A. Absorption law, B. Bounded law, C. Identity law, D. Distributive law. List II: I. a + 1 = 1; II. a + 0 = a; III. a·(b + c) = (a·b) + (a·c); IV. a + (a·b) = a.

Which of the following statements about sets are true? A. 0 ∈ ∅ B. ∅ ∈ {0} C. ∅ ∈ {∅} D. {∅} ∈ {∅} E. {∅} ⊂ {∅, {∅}}

If f(n) = 5f(n/2) + 3 and f(1) = 7, where n = 2ᴷ and K is a positive integer, then f(2ᴷ) =

The chairs of an auditorium are to be labelled with a letter followed by a positive two digits integer where labelling is starting with A01. How many maximum possible chairs could be labelled in this way?

Which of the following is not the most common property in social network ?

Match List I with List II. List I: (A) ∅ ∩ {∅} = (B) {∅} ∩ {∅} = (C) {∅, {∅}} − ∅ = (D) ∅ ∪ {{∅}} =. List II: (I) ∅ (II) {∅} (III) {{∅}} (IV) {∅, {∅}}

Which of the following are quantities (in grams) of food X and Y respectively when the cost of food is minimum:

Let R = {x ∈ N : x is a multiple of 3 and x ≤ 100} and S = {x ∈ N : x is a multiple of 5 and x < 100}. What is the number of elements in (R ∩ S) × (S ∩ R)?

How many integral solutions are there to x + y + z + w = 29, where x ≥ 1, y ≥ 2, z ≥ 3 and w ≥ 0?

Find the sum of all four digit numbers formed using the digits 1,2,4 and 6 .

Four persons: P, Q, R and S are in police custody and one of them has committed a crime. They confess as follows:

A. Person P: Q did it.

B. Person Q: S did it.

C. Person R: I did not do it.

D. Person S: Q lied. If exactly one of the statements is false, which of the following is the guilty person.

A warehouse has 50 aisles, 85 horizontal locations in each aisle, and 5 shelves. Storage bins are specified by aisle, location and shelf. What is the least number of products so that at least two must be stored in the same bin?

Match List I (identity) with List II (name). List I: A. x + x = x, B. x + 0 = x, C. x + 1 = 1, D. x + xy = x. List II: I. Identity law, II. Absorption law, III. Idempotent law, IV. Domination law.

The number of positive integers not exceeding 100 that are either odd or the square of an integer is ____

Let R1 = {(1,1), (2,2), (3,3)} and R2 = {(1,1), (1,2), (1,3), (1,4)}. Match List I with List II. List I: A. R1 ∪ R2, B. R1 − R2, C. R1 ∩ R2, D. R2 − R1. List II: I. {(1,1), (1,2), (1,3), (1,4), (2,2), (3,3)}, II. {(1,1)}, III. {(1,2), (1,3), (1,4)}, IV. {(2,2), (3,3)}.

Find the lexicographic ordering of the bit strings 0 < 1 given below based on the ordering .

(A) 001

(B) 010

(C) 011

(D) 0001

(E) 0101

Choose the correct answer from the options given below:

A survey has been conducted on methods of commuter travel. Each respondent was asked to check Bus, Train or Automobile as a major method of travelling to work. More than one answer was permitted. The results reported were as follows : Bus 30 people; Train 35 people; Automobile 100 people; Bus and Train 15 people; Bus and Automobile 15 people, Train and Automobile 20 people; and all the three methods 5 people. How many people completed the survey form?

If Aᵢ = {−i, …, −2, −1, 0, 1, 2, …, i}, then ⋃ᵢ₌₁^∞ Aᵢ is