Question 1 :
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Question 2 :
Use elimination method to find all possible solutions of the following pair of linear equations :$2x + 3y =8 , 4x + 6y =7$

Question 3 :
Solve the following pair of equations by substitution method: $7x – 15y =2 ; x + 2y =3$

Question 4 :
What is the probability of an event which is sure (or certain) to occur?

Question 5 :
A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is red ?

Question 6 :
A die is thrown once. Find the probability of getting an odd number.

Question 9 :
Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder in the following : $p\left(x\right)$ = $x^4–3x^2+4x+5$, $g\left(x\right)$ = $x^2+1-x$

Question 11 :
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the express train.

Question 12 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $2x^2 + kx + 3 = 0$

Question 13 :
What are the LCM and HCF of 17, 23 and 29?

Question 14 :
What are the LCM and HCF (by prime factorisation method) of 6, 72 and 120?

Question 15 :
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?