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1. The sum of numbers divisible by 7 between 50 and 100 ?
2. A bag contains red, green and blue balls. The total number of balls is 80. If 60% of the total balls are blue, what is the probability of taking a blue ball?
3. Square root of 2 is
4. The distance between A to B is 5 cm, B to C is 6 cm, C to D is 9 cm, D to E is 12 cm, E to F is 6.5 cm and F to G is 4.8 cm. Then,what is the distance between B to F?
5. The greatest common factor of x ² y ² z ²,x ² y z ² and x y z ² is
6. The sum of a number and its square is 90. Find the required numbers.
7. In how many ways can five people sit in a round table?
8. If two dice are rolled, what is the probability of getting same number on both the dies?
9. Compare 4/5 and 5/6
10. The value of 25 factorial times 24 factorial is
Explanation for question No 1 |
Numbers which are divisible by 7 between 50 and 100 are 56,63,70,77,84,91,98.
Now we have to find the sum of these numbers For that we have to add these numbers 56 + 63 + 70 + 77 + 84 + 91 + 98 = 539 So the correct answer for this question is 539 option A |
Explanation for question No 2 |
Total number of balls n (S)= 80
60% of the total balls are blue Number of blue balls = 60% of 80 = (60/100)x80 = (4800/100) = 48 Let "A" be the event of getting blue balls n (A) = 48 Probability of getting blue balls = n(A)/n(S) = 48/80 = 3/5 So the correct answer for this question is 3/5 option A |
Explanation for question No 3 |
Let √2 be rational
Since √2 is rational we shall write it as fraction √2 = a/b taking squares on both sides = 2 = a^{2}/b^{2} 2b^{2} = a^{2} 2 divides a^{2} 2 divides a let a = 2 c 2b^{2} = (2c)^{2} 2b^{2} = 4c^{2} c^{2} = 2b^{2}/4 c^{2} = b^{2}/2 2 divides b from this we come to know that and b are having common factor 2 other than 1. So we shall decide that a/b is not rational number.It is irrational. √2 is irrational So the correct answer for this question is irrational option B |
Explanation for question No 4 |
Let us draw a picture for the above information
From this we need to find the distance between the points B and F BF = BC + CD + DE + EF BC = 6 cm CD = 9 cm DE = 12 cm EF = 6.5 cm BF = 6 + 9 + 12 + 6.5 BF = 33.5 cm So the correct answer for this question is 33.5 option B |
Explanation for question No 5 |
x^{2} y^{2} z^{2},x^{2} y z ^{2}, x y z ^{2}
To find GCF, we have to select the common terms only GCF = x y z^{2} So the correct answer for this question is x y z^{2} option C |
Explanation for question No 6 |
Let x be the required number and x^{2} be its square
x + x ^{2} = 90 x + x ^{2} - 90 = 0 (x + 10) (x - 9) = 0 x + 10 = 0 x - 9 = 0 x = -10 x = 9 Therefore the required numbers are 9 and 81 So the correct answer for this question is 9 and 81 option A |
Explanation for question No 7 |
Let A,B,C,D and E are the names of the seats in the round table
So the arrangements will be in the form ABCDE,BCDEA,CDEAB,............. Total number of ways = 5 ! 5! = 5 x 4 x 3 x 2 x 1 = 120 To find the number if ways So the correct answer for this question is 120 option C |
Explanation for question No 8 |
Sample space S = {{1,1)(1,2)(1,3)(1,4)(1,5) (1,6)
= {2,1)(2,2)(2,3)(2,4)(2,5) (2,6) = {3,1)(3,2)(3,3)(3,4)(3,5) (3,6) = {4,1)(4,2)(4,3)(4,4)(4,5) (4,6) = {5,1)(5,2)(5,3)(5,4)(5,5) (5,6) = {6,1)(6,2)(6,3)(6,4)(6,5) (6,6)} n(S) = 36 Let A be the event of getting the same number on both the dies A = {(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)} n(A) = 6 probability of getting the same number on both dies = n(A)/n(S) = 6/36 = 1/6 So the correct answer for this question is 1/6 option C |
Explanation for question No 9 |
To compare these fractions,first we have to consider the denominators.
Since the denominators are not same,first we have to make the denominators same. L.C.M of 5 and 6 = 30 = (4/5)x (6/6) = (24/30) = (5/6)x (5/5) = (25/30) Therefore 4/5 is less than 5/6 So the correct answer for this question is (5/6) > (4/5) option B |
Explanation for question No 10 |
We shall write 25 ! as 25 x 24 x 23 x 22 x 21 x .........x 1
Instead of writing 25 x 24 x 23 x ........x 1 as 25 x 24 ! = 25(24!)^{2} So the correct answer for this question is 25(24!)^{2} option B |