List of top Questions asked in CBSE Class X

12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

Five cards--the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. 
(i) What is the probability that the card is the queen? 
(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

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 (see Fig. 5.6).

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?

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 (see Fig. 5.5). In how many rows are the 200 logs placed and how many logs are in the top row?

In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

Check whether the following are quadratic equations : 
(i) $(x + 1)^2 = 2(x – 3)$                      (ii) $x^2 – 2x = (–2) (3 – x)$
(iii) $(x – 2)(x + 1) = (x – 1)(x + 3)$     (iv) $(x – 3)(2x +1) = x(x + 5)$
(v) $(2x – 1)(x – 3) = (x + 5)(x – 1)$       (vi) $x^2 + 3x + 1 = (x – 2)^2$
(vii) $(x + 2)^3 = 2x (x^2 – 1)$               (viii) $x^3 – 4x^2 – x + 1 = (x – 2)^3$

A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.

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.

A die is thrown once. Find the probability of getting 
(i) a prime number; 
(ii) a number lying between 2 and 6;
(iii) an odd number.

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the given figure), and these are equally likely outcomes. What is the probability that it will point at
(i) 8?
(ii) an odd number? 
(iii) a number greater than 2?
(iv) a number less than 9?

How many terms of the AP : 9, 17, 25, ..... must be taken to give a sum of 636?

Find the sum of the odd numbers between 0 and 50.

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see the given figure).What is the probability that the fish taken out is a male fish?

Find the sum of the first 15 multiples of 8.

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

If the sum of the first n terms of an AP is $4n – n^2$, what is the first term (that is $S_1$)? What is the sum of first two terms? What is the second term? Similarly, find the $3^{rd}$, the $10^{th}$ and the $n^{th}$ terms.

A box contains 5 red marbles,8 white marbles and 4 green marbles.One marble is taken out of the box at random.What is the probability that the marble taken out will be
(i) red?  (ii) white?  (iii) not green?

Show that $a_1, a_2, . . ., a_n, .....$ form an AP where an is defined as below:

1. $a_n = 3 + 4n$
2. $a_n = 9 – 5n$

Also find the sum of the first 15 terms in each case.

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

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 (i)red?(ii)not red?

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

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Find the sum of first 22 terms of an AP in which d = 7 and 22^nd term is 149.

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction? 
(ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu? 
(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number. 
(iv) Meena went to bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received. 
(v) 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.