Question 1

The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second larges…

Accepted Answer

Given the angles of a quadrilateral are in the ratio of 2:4:7:5 Let the angles of a quadrilateral are 2x, 4x, 7x, 5x But we know that sum of the angles = 360 degrees. => 2x + 4x + 7x + 5x = 360 => x = 20 Therfore, the smallest angle of the quadrilateral = 2x = 2x20 = 40 degrees. One of the angle of the triangle = 2 x 40 = 80 degrees The other angle is 180 - (40 + 80) = 60 degrees. Hence the second largest angle of the triangle is 60 degrees.

Question 2

If V = 12R / (r + R) , then R =

Accepted Answer

We have to rearrange the equation to make R the subject. Start by cross multiplying by (r + R); V (r + R) = 12R Multiply out the bracket Vr + VR = 12R

Question 3

If x is a whole number, then x²(x² - 1) is always divisible by ?

Accepted Answer

we can do this by trial and error method. Putting x = 2,we get 2²(2² - 1) = 12. checking with other integers, the above equation always gives a value which is a multiple of 12, So, x²(x² - 1) is always divisible by 12.

Question 4

Find the number of factors of 9321 ?

Accepted Answer

9321 = 3 x 13 x 239 = 31 x 13 1 x 239 1 ; add one to all the powers ie., (1+1) x (1+1) x (1+1)= 8 ; we get eight factors.

Question 5

The product of a number and its multiplicative inverse is

Accepted Answer

The mutiplicative inverse of a number is nothing but a reciprocal of a number. Now, the product of a number and its multiplicative inverse is always equal to 1. For example : Let the number be 15 Multiplicative inverse of 15 = 1/15 The product of a number and its multiplicative inverse is = 15 x 1/15 = 1.

Question 6

3131×31-27 =?

Accepted Answer

We know that a m × a n = a m + n ∴ 31 31 - 27 = 31 4 = 961 x 961.

Question 7

What is the remainder when 1523+2323 is divided by 19 ?

Accepted Answer

15 23 + 23 23 = 19 - 4 23 + 19 + 4 23 The remainder on dividing by 19 will be - 4 23 + 4 23 = 0.

Question 8

Find the next number in the series 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 20,...

Accepted Answer

The pattern is three consecutive numbers and then three consecutive numbers missing.Then four consecutive numbers and then four consecutive numbers missing.Then five consecutive numbers and then five consecutive numbers missing. The next number=20+6=26

Question 9

Find the next number in the series 141,137,146,130,155,119,...

Accepted Answer

The pattern is -4, +9,-16, +25, -36 The next number=119+49=168

Question 10

In a triangle ABC, angle 'a' is the smallest one & A+7B = 112. Find the range of value 'c' ?

Accepted Answer

A+7B=112 it is clear that A = 14, then it becomes A>=B, but A is smallest angle) given so, range of A is 0.0001 to 13.9999 ( I am taking upto 4 decimal places) so, range of B becomes 14 to 16 ( after rounding off to 4 decimal places) so, range of C becomes 152 to 164 ( after rounding off to 4 decimal places)

Question 11

Which expression is equivalent to i233 ?

Accepted Answer

We know that, i 2 = - 1 i 3 = i 2 x i = - 1 x i = - i i 4 = i 2 x i 2 = - 1 x - 1 = 1 Hence , i 233 = i 4 x 58 + 1 = i 232 x i 1 = 1 x i = i

Question 12

If n is natural number , then 6n2+6n is always divisible by :

Accepted Answer

6 n 2 + 6 n = 6 n n + 1 , which is always divisible by 6 and 12 both, since n(n+1) is always even.

Question 13

Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.55 ?

Accepted Answer

The weight will be 250g plus (1.55 - 0.65)/0.10 units of 100g 250 + 900 = 1150 This is the maximum weight that can be sent at that price. But, weights exceeding 250 + 800 will also get charged this amount (that is what the ‘part thereof’ implies). Hence a package weighing 1145 will be charged $1145

Question 14

A number divided by 296 leaves the remainder 75. If the same number is divided by 37, what will be the remainder ?

Accepted Answer

1

Question 15

The sum of the digits of a two-digits number is 10,while when the digits are reversed, the number decreases by 54. Find the changed number ?

Accepted Answer

Let the original number is 82 i.e 8 + 2 = 10 and when the digits are reversed i.e 28 The difference is 82 - 28 = 54 i.e, the number is decreased by 54.

Question 16

What is the value of 4 in 475?

Accepted Answer

The value of 4 in 475 means the place value of 4 in 475 and not its face value. Face value means the digit itself though it is at any place in the given number. But place value means the value of digit in its place in the given number. Here the place value of 4 in 475 can be determined by as 4 is in 100's place in 475. Hence, the place value of 4 in 475 is 4x100 = 400.

Question 17

3x + y = 19 and x + 3y = 1. Find the value of 2x + 2y

Accepted Answer

To solve a pair of simultaneous equations such as those given we can add or subtract them. Adding we get 4x + 4y = 20 Therefore 2x + 2y = 10

Question 18

How many numbers with distinct digits are possible product of whose digits is 18?

Accepted Answer

Two digit numbers: The two digits can be 2 and 9: Two possibilities 29 and 92. Three-digit numbers: The three digits can be 1, 2 and 9 => 3! Or 6 possibilities. We cannot have three digits as (3, 3, 2) as the digits have to be distinct. We cannot have numbers with 4 digits or more without repeating the digits. So, there are totally 8 numbers.

Question 19

Find the remainder when 1234 x 1235 x 1237 is divided by 8.

Accepted Answer

When we divide 1234 by 8, remainder is 2 When we divide 1235 by 8, remainder is 3 When we divide 1237 by 8, remainder is 5 ---> 2 x 3 x 5 = 30 As 30 will not be the remainder because it is greater than 8, when 30 divided by 8, remainder = 6.

Question 20

A teacher multiplies 987 by a certain number and obtains 556781 as her answer. If in the answer, both 6 and 7 are wrong but the other digits are correct, then the correct answer will be

Accepted Answer

Given number is 987 = 3 x 7 x 47. So, required number must be divisible by each one of 3, 7, 47. None of the numbers in 553681 and 555181 are divisible by 3. While 556581 is not divisible by 7. Correct answer is 555681.

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