Question Paper. gat mains SECTION A (MATHEMATICS) Q.1. Solve the following questions. (2x10 = 20 marks).

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Roll No: Question Paper gat mains QTM-013 Class: 8 th M maximum Marks: 200 Total No. of Questions: 10 time allowed: 2:40 hrs. SECTION A (MATHEMATICS) Q.1. Solve the following questions.

1 Roll No: Question Paper gat mains QTM-013 Class: 8 th M maximum Marks: 200 Total No. of Questions: 10 time allowed: 2:40 hrs. SECTION A (MATHEMATICS) Q.1. Solve the following questions. (2x10 = 20 marks). (A) Find a rational number between 1 4 and 1. Also show the 2 resultant rational numbers on the number line. The denominator of rational number is greater than its numerator by 8. If the numerator is increased by 1, the number obtained is 3. Find the rational number. 2 (B) Factorize the expression a 2 2ab + b 2 c 2 Prove that the diagonals of a rectangle are of equal length. Q.2. Solve these questions (Any three) [3x6 = 18 marks] a. Find the smallest square number which is divisible by each of the numbers 6, 9 and 15. b. Find the number by which 1188 is divided so that the quotient is a perfect cube. c. Find the value of m for which 5 m 5 3 = 5 5 d. Subtract 3 pq (p q) from 2pq (p+q) Page No 1

2 e. Find measure of x in the given figure; 50 o 90 o x 110 o Q.3. Solve the questions [11x2 = 22 marks] i. Write the additive inverse of and 6. ii. Express 21 2 as the sum of two consecutive integers. iii. Identify the coefficient of each term in the expression ; x 2 y 2 10x 2 y + 5xy 2 20 iv. Show that (a b) 2 = a 2 + b 2 2ab v. 1 micron is equal to vi. Find the area of a rectangle with length 2 2 m & breadth 3 m 2. vii. viii. Find the square of 42 without actual multiplication. A square is also a, a, a and a ix. A decagon has sides. x. There are integers and rational numbers between 5 and 5. xi. Zero has reciprocals. Page No 2

3 SECTION B (general Science) LONG ANSWER TYPE QUESTIONS Q.4. Answer the following questions [2x10 = 20 marks] (A) Explain how do organisms like hydra and amoeba reproduce? With the help of a labeled diagram write the structure of the human eye? (B) What is combustion? What chemicals are used to make a match? Liquids conduct electricity ; write an experiment (activity) to prove the above statement. SHT ANSWER TYPE QUESTIONS Q.5. Answer these questions (Any three) [3x6 = 18 marks] a. Differentiate between protoplasm and cytoplasm. b. What are contact and non-contact forces? Give examples in support of your answer. c. What is static friction? What is the other name for sliding friction? d. Draw a diagram to show the position of endocrine glands in human body. e. Below are given the names of five metals found in Jammu and Kashmir. Write the name of at least one place against each metal they are dug out from. i. Chromite ii. Gold iii. Copper iv. Lead v. Uranium VERY SHT ANSWER TYPE QUESTIONS Q.6. Answer the given questions. [11x2 = 22 marks] i. Which bacteria causes the disease anthrax? ii. Who discovered the vaccine for small pox? Page No 3

4 iii. iv. Define metamorphism. What do you mean by term oviparous? v. What are ultrasounds? vi. vii. viii. ix. Frequency is measured in. Name some combustible substances. What is calorific value (in KJ/Kg) of LPG. Pure water is good conductor of electricity. (True/False) x. LED stands for. xi. Adrenalin is produced by which endocrine gland? SECTION C (SOCIAL STUDIES) LONG ANSWER TYPE QUESTIONS Q.7. Answer the following questions. [2x10 = 20 marks] (A) What do you understand by non-conventional source of energy? Give brief accounts about nuclear energy and geothermal energy. What is commercial farming? Mention its types and briefly explain the plantation. (B) What were the main causes of the failure of the revolt of 1857? What NAM stands for? List the factors that make NAM relevant even in present times. SHT ANSWER TYPE QUESTIONS Q.8. Answer these questions (Any three) [3x6 = 18 marks] a. Define socialism? Who were the founders of socialism? b. Write down the provisions of act of c. What are the locational factors of industries? Page No 4

5 d. Petroleum is reffered as black gold why? e. Write names of countries which constitute the SAARC group. VERY SHT ANSWER TYPE QUESTIONS Q.9. Answer the questions. [11x2 = 22 marks] i. In which year was league of nations formed. ii. iii. iv. What is the number of member countries of United Nations? When and where was 16 th SAARC summit held? In which year was the first railway line opened in India? v. Who was the founder of the Tata iron and steel company? vi. vii. viii. ix. What is resource conservation? Give three examples of non-renewable sources of energy. Name the country having the highest percentage of land under forest. An average urban Indian uses how many litres of water every day? x. What are ferrous minerals? xi. In how many agro-climatic zones is Jammu and Kashmir divided? SECTION D (ESSAY WRITING) Q.10. Write an essay of about words on the given topics. [1x20 = 20 marks] 1. Role of electricity in economic growth in J&K 2. Contribution of JK s Hydroelectric projects in economic development 3. Power fuels industrial growth J&K s hydroelectric potential, development Our resources, our capacites Page No 5

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Math 2 Variable Manipulation Part 2 Powers & Roots PROPERTIES OF EXPONENTS:

Math 2 Variable Manipulation Part 2 Powers & Roots PROPERTIES OF EXPONENTS: 1 EXPONENT REVIEW PROBLEMS: 2 1. 2x + x x + x + 5 =? 2. (x 2 + x) (x + 2) =?. The expression 8x (7x 6 x 5 ) is equivalent to?.