Question 1 :
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Question 2 :
Represent the following situation in the form of quadratic equations: Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Question 3 :
Represent the following situation in the form of a quadratic equation : The area of a rectangular plof is 528 $m^2$. The length of the plof (in metres) is one more than twice its breadth. We need to find the length and breadth of the plof.

Question 4 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 3x + 5 = 0$.

Question 6 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b61273b23058497998e.png' /> In the centre of a rectangular lawn of dimensions $50m×40m$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 $m^2$ in the above figure. Find the breadth of the pond.

Question 7 :
Find the roots of the following quadratic equation by factorisation: $2x^2 + x – 6 = 0$

Question 8 :
A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, original average speed of the train is?

Question 9 :
A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.

Question 10 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2+2\sqrt{2}x-6=0$

Question 11 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?

Question 12 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.

Question 13 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

Question 14 :
Find the sum of the first 40 positive integers divisible by 6.

Question 15 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.

Question 16 :
In an AP, given $d = 5, S_9 = 75$, find a and $a_9$.

Question 17 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?

Question 18 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.

Question 19 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.

Question 20 :
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum offirst n terms.