Important Mathematics formula pdf for competitive exam 2025. Maths Formulas and Tricks for SSC, IBPS, UPSC and RRB exam 2025.
Mathematics Formula PDF for Competitive Exam
Properties of Set Operations:
For any three sets A B, and C, the following hold.
(i) Commutative Property
(a) A B , , = B A (set union is commutative)
(b) A B + + = B A (set intersection is commutative)
(ii) Associative Property
(a) A B , , ^ h C = ^ h A B , , C (set union is associative)
(b) A B + + ^ h C = ^ h A B + + C (set intersection is associative)
(iii) Distributive Property
(a) A B + , ^ h C = ^ h A B + , ( ) A C + (intersection distributes over union)
(b) A B , + ^ h C = ^ h A B , + ( ) A C , (union distributes over intersection)
Mostly we shall verify these properties with the given sets. Instead of verifying the above properties with examples, it is always better to give a mathematical proof. But this is beyond the scope of this book. However, to understand and appreciate a rigorous mathematical proof, let us take one property and give the proof.
De Morgan’s Laws :
De Morgan’s father (a British national) was in the service of East India Company, India. Augustus De Morgan (1806-1871) was born in Madurai, Tamilnadu, India. His family moved to England when he was seven months old. He had his education at Trinity college, Cambridge, England. De Morgan’s laws relate the three basic set operations Union, Intersection and Complementation.
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Maths Objective Type Questions
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1. The average age of boys and girls in a class is 10.5 years, that of the boys is 10.6 years, and that of the girls is 10.1 yr. If there are 60 boys in the class, how many girls are there in the class? (A) 15 (B) 20 (C) 22 (D) 25 Answer: A |
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2. x is a whole number. If the only common factors of x and x2 are 1 and x, then x is (A) 1 (B) a perfect square (C) An odd number (D) a prime number Answer : D |
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3. A sum of Rs. 1,000 is borrowed at a certain rate of interest. After 4 months, Rs 500 is again borrowed, but this time at a rate of interest that is thrice the original rate. At the end of the year, the total interest on both amounts is Rs. 100. What is the original rate per annum? (A) 3.33% (B) 5% (C) 8% (D) 10% Answer: B |
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4. If a person drives at a speed which is 3/2 of his usual speed. It takes him 4/5 hours less time than the normal time. Find his original times. (A) 4 (B) 5 (C) 6 (D) 7 Answer: C |
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5. A tank can be filled by one tap in 10 min and by another in 30 min. Both taps are kept open for 5 min, and then the first one is shut off. In how many more minutes is the tank completely filled? (A) 5 (B) 7.5 (C) 10 (D) 12 Answer: C |
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6. The rate of simple interest on a sum of money is 6 per cent per annum for the first 3 years, 8 per cent per annum for the next 5 years and 10 per cent per annum for the period beyond 8 years. If the simple interest accrued by the sum for a total period of 10 years is Rs 1,560, what is the sum? (A) Rs. 1,500 (B) Rs. 3,000 (C) Rs. 2000 (D) Data Inadequate Answer: C |
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7. Line AB is 24 m in length and is tangent to the inner one of the two concentric circles at point C. Points A and B lie on the circumference of the outer circle. The distance of the chord from the centre is 5 cm. The radius of the outer circle is (A) 13m (B) 5m (C) 7m (D) 4m Answer: A |
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8. Divide Rs 1,000 into two parts so that if the two parts are invested at 4% and 5% simple interest, the total yearly income may be Rs 46.50. (A)Rs 350 at 4% and Rs 650 at 5% (B)Rs 650 at 4% and Rs 350 at 5% (C)Rs 400 at 4% and Rs 600 at 5% (D)Rs 600 at 4% and Rs 400 at 5% Answer: A |
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9. A large cube is formed from the material obtained by melting three cubes, 3cm, 4cm and 5cm, respectively. Find the ratio of the total surface area of the smaller cubes to the larger cube. (A) 2:1 (B) 3:2 (C) 25:18 (D) 27:20 Answer: C |
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10. A can do a certain work in 12 days. B is 60% more efficient than A. How many days will B and A together take to do the same job? (A) 80/13 (B) 70/13 (C) 75/13 (D) 60/13 Answer : D |