Question 1 :
Choose the correct answer from the given four options in the question: If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ________ .
Question 2 :
The prime factorisation of a ___________ is unique, except for the order of its factors.
Question 4 :
The cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r. Is it True or False?
Question 6 :
If x and y are both odd positive integers, then $x^2+ y^2$ is even but not divisible by 4. Is it true?
Question 7 :
Every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer. TRUE or FALSE ?
Question 9 :
Any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. TRUE or FALSE ?
Question 10 :
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 lof. Determine the probability that the pen taken out is a good one.
Question 11 :
A trial is made to answer a true-false question. The answer is right or wrong. Does this statement has equally likely outcome or not?
Question 12 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf4273b230584979a4b.PNG' />
A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two thrones then what is the probability that the total score is 6?
Question 13 :
A piggy bank contains hundred 50p coins, fifty Rs.1 coins, twenty Rs.2 coins and ten Rs.5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be will not be a Rs.5 coin?
Question 14 :
Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is less than or equal to 12?
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bef273b230584979a47.PNG' />
In the above image, suppose you drop a die at random on the rectangular region shown. What is the probability that it will land inside the circle with diameter 1m?
Question 16 :
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a number divisible by 5.
Question 17 :
What is the probability of an event which is impossible to occur ?
Question 18 :
Savita and Hamida are friends. What is the probability that both will have different birthdays (ignoring a leap year)?
Question 19 :
Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on the different days?
Question 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a59273b230584979928.PNG' />
In the above image, 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. What is the probability that the fish taken out is a male fish?
Question 21 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bee273b230584979a45.PNG' />
A child has a die whose six faces show the letters as given above. The die is thrown once. What is the probability of getting A?
Question 22 :
In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half-minute after starting?
Question 23 :
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 not green?
Question 24 :
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 not red?
Question 25 :
State true or false:
$b^2 – 4ac$ is called the discriminant of the quadratic equation $ax^2 + bx + c = 0$.
Question 26 :
Check whether the following is quadratic equation : $x^3 - 4x^2 - x + 1 = (x-2)^3$
Question 27 :
Find the roots of the following quadratic equation (by the factorisation method): $3x^2+5\sqrt{5}x-10=0$
Question 28 :
Does the following equation has the sum of its roots as 3? $3x^2-3x+3=0$
Question 29 :
Check whether the following is a quadratic equation: $(x + 2)^3 = 2x (x^2 – 1)$
Question 30 :
Check whether the following is a quadratic equation: $(x + 1)^2 = 2(x – 3)$
Question 31 :
Represent the following situation in the form of a quadratic equation : The product of two consecutive positive integers is 306. We need to find the integers.
Question 32 :
Find the roots of the following quadratic equation by factorisation: $100x^2 – 20x + 1 = 0$
Question 35 :
Justify why the following quadratic equation has no two distinct real roots: $x^2-3x+4=0$
Question 38 :
Find two consecutive odd positive integers, sum of whose squares is 290.
Question 39 :
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 40 :
State True or False whether the following quadratic equation has two distinct real roots: $x\left(1-x\right)-2=0$
Question 41 :
Which constant must be added and subtracted to solve the quadratic equation $9x^2+\frac{3}{4}x-\sqrt{2}=0$ by the method of completing the square?
Question 42 :
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the cost of each article?
Question 43 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2-3\sqrt{5}x+10=0$
