The topic 'linear equations' deals with how to solve simultaneous equations, how to solve equations by introducing dummy variables etc. The practice questions given below come with detailed explanations and video solutions.

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Instructions

For the following questions answer them individually

Question 1

In a two digit number the difference of digits is 4 and 10 times the number is equal to 14 times the sum of the digits of the number and the number formed by reversing the digits. Find the number

Question 2

If the cost of buying 7 apples, 12 bananas and 17 oranges is equal to Rs 219 and the cost of buying 3 apples, 5 bananas and 7 oranges is 91, then find the cost of buying 1 apple, 1 banana and 1 orange.

Question 3

Aradhna is analysing the different investment opportunities available to her. She can invest Rs 1 lakh in the following schemes.

- Investing in fixed deposit at 10% p.a.
- Investing in stock market where she will get 20% if the market rises and will lose 5% if it falls
- Put options on the stock market which will rise 15% in value if the market tanks and fall by 10% if the market rises.

What is Aradhna's maximum guaranteed return?

Question 4

Amit is reconciling the day's trades at the end of the day in his record book. He realizes that while recording the number of maree biscuits sold, he reversed the digits of the two digit number. If the number recorded was more than 10 but 72 fewer than the actual number, how many maree biscuits were sold?

Question 5

In CAT 2014, a student gets 3 marks for every right answer and -1 for every wrong answer. There are 120 questions in all and Ajay attempted all of them and got a score of 188. How many did he get right?

Question 6

The cost of 4 pencils, 2 erasers, and a sharpener together is Rs 80 whereas the cost of 1 pencil, 2 erasers, and a sharpener together is Rs 35. Find the cost of 2 pencils, 2 erasers and 1 sharpener together.

Question 7

Which of the following values can ‘a’ not take if the following set of equations has a unique solution:

ax + 3y + 4z = -5

4x + 2y - z = 2

7x - ay + 5z = 10

Question 8

The currency of the land of the Mayans was the Tyka and three type of coins were defined: 1 Tyka, 10 Tyka and 100 Tyka. In how many ways could a Mayan pay 255 Tykas?

Question 9

What is the equation of the line that is parallel to the line 3x + 4y + 6 =0 and at a distance of 1 unit to it and closer to the origin?

Question 10

What is the total number of natural number solutions to 3X+2Y = 50 if X < Y?

Question 11

X is an even three digit number such that Y-X=198 where Y is the number formed by reversing the digits of X. If the middle digit of X is the sum of the first and third digit, then find X

Question 12

Sunil goes to buy two mangoes, five bananas and three pineapples and realizes he has Rs 7 less than what is required. He then removes three bananas from his basket and can buy the remaining fruits with Rs 2 left over. If he had tried buying a mango and three pineapples he would have Rs 17 remaining, then what is the maximum number of pineapples that could have been bought by Sunil?

Question 13

A, B and C are three successive multiples of 7. If 5 times the largest number is 14 less than 8 times the smallest number, what is the average of the three numbers?

Question 14

A box contains 3 apples, 5 oranges and 13 pineapples. Atleast how many fruits should one pick to have atleast 6 fruits of the same kind?

Question 15

In olden days, there were only 4 paisa, 7 paisa and 11 paisa coins. What is the maximum amount you can't exactly pay using just the three sets of coins?

Question 16

Which condition will a,b,c satisfy if the set of equations 3x + 4y + z = a, 2x + 6y + 4z = b and x - y - 2z = c has atleast 1 solution ? Also a + b + c $$\neq$$ 0.

Question 17

The quantity of cholesterol in the body is linearly dependent on the number of cigarettes smoked as well as the weight of a person. Raju weighs 100 kilos and smokes 100 cigarettes a month. He got his cholesterol checked and got a high reading of 1200 mg/mL. In order to reduce the cholesterol levels, he tried to control the risk factors. He failed to lose any weight but cut his smoking to half (50 cigarettes a month). He checked his cholesterol, it showed to be 1000 mg/mL

Excited he further cut his smoking to 33 cigarettes a month. How much will his cholesterol show this month?

Question 18

The speed of an elevator varies linearly with the square-root of the number of people in it. When 9 people are there in the lift, it can go from 1st floor to the 3rd floor, which are 100 m apart, in 10 sec. When there are 4 people in the lift, it can move from 5th floor to the 12th floor, which are 700 m apart, in 35 seconds. How many people should present in the lift so that it stops moving?

Question 19

What is the integral value from which all the integers can be expressed from expression 43x+37y such that both x and y are integers.

Question 20

F(x) = $$a_0 + a_1x + a_2x^2 + ... + a_nx^n$$ , where $$a_0, a_1, ..., a_n$$ are non-negative integers. If F(1) = 4 and F(F(1)) = 82, find the value of F(5)

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