Question 1 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $\frac{4}{3}x + 2y = 8 ; 2x + 3y = 12$
Question 2 :
A pair of linear equations is ______ if it has a unique solution.
Question 3 :
Solve the following pair of linear equations by the substitution and cross-multiplication methods : $8x + 5y = 9 ; 3x + 2y = 4$
Question 4 :
One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?
Question 5 :
The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number.
Question 6 :
A pair of linear equations in two variables, which has a solution, is called a _________________ pair of linear equations.
Question 7 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $\frac{3}{2}x + \frac{5}{3}y = 7 ; 9x – 10y = 14$
Question 8 :
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Question 9 :
The coach of a cricket team buys 3 bats and 6 balls for Rs. 3900. Later, she buys another bat and 3 more balls of the same kind for Rs. 1300. Which of these represent this situation algebraically?
Question 10 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{6}{x-1} - \frac{3}{y-2} = 1 ; \frac{5}{x-1} + \frac{1}{y-2} = 2$
Question 11 :
Solve, by substitution : $x + 2y – 4 =0 , 2x + 4y – 12 =0$
Question 12 :
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per km?
Question 13 :
The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Which of these represent the situation algebraically?
Question 14 :
A fraction becomes $\frac{9}{11}$, if 2 is added to both the numerator and the denominator.If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction.
Question 15 :
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. How much does a person have to pay for travelling a distance of 25 km?
Question 16 :
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bde273b230584979a32.JPG' />
In the above fig, ABCD is a cyclic quadrilateral. Find the values of x and y.
Question 19 :
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Question 20 :
2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
