Algebraic Identities

Branches of Algebra

  1. Elementary Algebra.
  2. Advanced Algebra.
  3. Abstract Algebra.
  4. Communicative Algebra
  5. Linear Algebra.

For UPSC Prelims CSAT exam only elementary algebra and linear algebra are important.

Polynomial: In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7.

Degree of polynomial: Degree of Polynomials 1 Polynomial in One Variable. The degree of polynomials in one variable is the highest power of the variable in the algebraic expression. 2 Browse more Topics Under Polynomials 3 Multivariable polynomial. For a multivariable polynomial, it the highest sum of powers of different variables in any of the terms in the expression.

Practice Questions:

1. The cost of two tables and three chairs is ₹705. If the table costs ₹40 more than the chair, find the cost of the table and the chair.
a. 125 & 165
b. 155 & 165
c. 150 & 180
d. 140 & 150

2. A sum of Rs. 13.50 is made by 38 coins which are either 50 paise or 25 paise. Find the number of 25 paise coins?
a. 16
b. 24
c. 18
d. 22

3. In an examination consisting of 60 questions, three marks are given for every correct answer and one mark is deducted for every wrong answer. A student attempts all the questions and gets 120 marks.
a. 45
b. 42
c. 15
d. 18

4. If the price of a book is reduced by rupees 5 a person can buy 5 more books for rupees 300 find the original list price of the book.
a. Rs 15
b. Rs 20
c. Rs 25
d. Rs 30

5. A two-digit number is such that the ten's digit exceeds twice the units digit by 2 and the number obtained by interchanging the digits is 5 more than 3 times the sum of the digits. Find the two-digit number.
a. 86
b. 83
c. 89
d. 80

6. If the present ages of Nandu and Shobhit are 20 and 24 years respectively, then find the ratio between the ages of Nandu (before 4years) and Shobhit (after 4 years)
a. 5:9
b. 4:7
c. 2:3
d. 5:6

7. At present, the ratio between the ages of Arun and Deepak is 4: 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
a. 19 ½ years
b. 15 years
c. 12 years
d. 21 years

8. The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double of the sum of the ages of his sons. The father's present age is?
a. 40 years
b. 48 years
c. 45 years
d. 55 years

9. In 1930, a person's age was 8 times that of his son. In 1938, the father's age became 10 times that of his son's age in 1930. The ages of the son and father in 1940 were.
a. 16 years 58 years
b. 15 years 50 years
c. 14 years 42 years
d. 13 years 34 years

10. A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father's and mother's age is 51 years. What is the age of the son?
a. 7 years
b. 5 years
c. 4 years
d. 3 years

11. A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?
a. 60%
b. 45.5%
c. 40%
d. 37.5%

12. In 2002, Meena’s age was one-third of the age of Meera, whereas in 2010, Meena’s age was half the age of Meera. What is Meena’s year of birth?
a. 1992
b. 1994
c. 1996
d. 1998

13. Ena was born 4 years after her parents' marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena's father get married?
a. 22 years
b. 23 years
c. 24 years
d. 25 years

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