Question 1 :
Solve the pair of equations: $\frac{2}{x} + \frac{3}{y} = 13 ; \frac{5}{x} - \frac{4}{y} = -2$

Question 2 :
Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions: $5x – 8y + 1 =0 ; 3x - \frac{24}{5}y + \frac{3}{5} = 0$

Question 3 :
The cost of 5 oranges and 3 apples is Rs. 35 and the cost of 2 oranges and 4 apples is Rs. 28. Let us find the cost of an orange and an apple.

Question 4 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdb273b230584979a2e.png' /> In the above fig, the lines represents ____________ lines.

Question 5 :
Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Question 6 :
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 7 :
Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Which of these represent this situation algebraically?

Question 8 :
Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $2x – 2y – 2 = 0 , 4x – 4y – 5 = 0$

Question 9 :
Solve the following pair of linear equations by the elimination method and the substitution method : $3x + 4y = 10 ~and ~2x – 2y = 2$

Question 10 :
The pair of equations 5x – 15y = 8 and $3x-9y=\frac{24}{5}$ has __________.

Question 11 :
If for some angle θ, cot 2θ = $\frac{1}{\sqrt{3}}$ then the value of sin3θ, where 2θ $\leq$ 90º is

Question 12 :
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where

Question 13 :
The number of zeroes, the polynomial p (x) = $(x – 2)^2 + 4$ can have, is

Question 14 :
A pair of linear equations $a_1x + b_1y + c_1 = 0$; $a_2x + b_2y + c_2 = 0$ is said to be inconsistent, if

Question 15 :
From each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in figure. The area of the remaining (shaded) portion is <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b67273b230584979997.PNG' />