Question 1 :
Check whether the following is a quadratic equation: $(x + 1)^2 = 2(x – 3)$

Question 2 :
Sum of the areas of two squares is $468 m^2$. If the difference of their perimeters is 24 m, find the sides of the two squares.

Question 4 :
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

Question 5 :
State True or False whether the following quadratic equation has two distinct real roots: $\sqrt{2}x^2-\frac{3}{\sqrt{2}}x+\frac{1}{\sqrt{2}}=0$

Question 6 :
If sinθ = $\frac{1}{3}$,then the value of ($9 cot^{2}θ + 9$) is

Question 7 :
If in the following figure, ∆ ABC ~ ∆ QPR, then the measure of ∠Q is <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b62273b230584979990.PNG' />

Question 8 :
The number of zeroes lying between –2 to 2 of the polynomial f (x), whose graph is given below, is <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b61273b23058497998f.PNG' />

Question 9 :
Two coins are tossed simultaneously. The probability of getting at most one head is

Question 10 :
The largest number which divides 318 and 739 leaving remainders 3 and 4, respectively is

Question 11 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc8273b230584979a15.JPG' /> In the above fig. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

Question 12 :
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

Question 14 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc7273b230584979a14.JPG' /> In the above fig. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?

Question 16 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.

Question 17 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?

Question 18 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.

Question 19 :
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day, etc., the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

Question 20 :
In an AP, given $a_{12} = 37, d = 3$, find a and $S_{12}$.