Category: Mathematics Mcqs

If the ratio of boys to girls in class is 3:2 and there are 15 boys, how many girls are there?

A. 10
B. 12
C. 15
D. 20

Answer

Correct Answer: A. 10

Detail about MCQs

To find the number of girls in the class, we use the given ratio and the number of boys.
Step 1: Understand the ratio
The ratio of boys to girls is 3:2. This means that for every 3 boys, there are 2 girls.
Step 2: Represent the ratio
Let the number of boys be 3x and the number of girls be 2x, where x is a scaling factor.
Step 3: Substitute the given value
It is given that there are 15 boys. Thus:
3x=15
Step 4: Solve for x
Divide both sides by 3:
x= 15/3 = 5
Step 5: Calculate the number of girls
The number of girls is 2x
2x =2 ×5 =10
Step 6: Match with the options
The correct answer is: A. 10

Find the value of x in the inequality 3x-5>7

A. X>4
B. X<4
C. X>3
D. X<3

Answer

Correct Answer: A. X>4

Detail about MCQs

Solution: 3x−5>7
Eliminate the constant term −5
To simplify, add 5 to both sides of the inequality. This removes −5 from the left-hand side:
3x −5 +5 >7 +5
3x >12
: Isolate xxx
Now, divide both sides of the inequality by 3to solve for x. Since we are dividing by a positive number, the direction of the inequality remains unchanged
x> 12/3
x>4

If the arithmetic mean of seventy five numbers is 35. If each number is increased by 5, then mean of new number is ____?

A. 30
B. 40
C. 70
D. 90

Answer

Correct Answer: B. 40

Detail about MCQs

To find the new mean after increasing each number by 5, you can follow these steps:
1. Original mean: 35
2. Number of values: 75
When each number is increased by 5, the new mean will be:
New Mean=Original Mean+5
New Mean=35+5=40
So the correct answer is B. 40.

Binary number 10101 is equivalent to its decimal equivalent ___?

A. 10
B. 20
C. 21
D. 111

Answer

Correct Answer: C. 21

Detail about MCQs

To convert the binary number 10101 to its decimal equivalent, you can use the positional notation system. Each digit in a binary number represents a power of 2, starting from the rightmost digit as 2^0, then increasing by one power for each subsequent digit to the left.

So, 10101 in binary is calculated as:

1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 16 + 0 + 4 + 0 + 1 = 21

Therefore, the correct answer is:

C. 21

If 20% of an electricity bill is deducted, then Rs. 100 is till to be paid. How much was the original bill?

A. Rs. 115
B. Rs. 110
C. Rs. 125
D. None of these

Answer

Correct Answer: C. Rs. 125

Detail about MCQs

To solve this problem, let’s denote the original electricity bill amount as .

If 20% of the bill is deducted, the remaining amount to be paid is 100. This means 80% of the bill remains.

We can set up the equation as follows:
0.80×x=100
Now, let’s solve for :
x=100​/0.80=125

So, the original electricity bill was Rs. 125.

Therefore, the correct answer is C. Rs. 125.

A shopkeeper earns 15% profit on a shirt even after allowing 31% discount on the list price. If list price is Rs125, then cost price of shirt is?

A. 87
B. 80
C. 75
D. None of these

Answer

Correct Answer: C. 75

Detail about MCQs

Let’s break down the problem step by step:

  1. The shopkeeper earns a 15% profit on the shirt.
  2. The shopkeeper offers a 31% discount on the list price.

First, let’s find out the selling price (SP) after applying the discount: Discount = 31% of the list price = 0.31 * 125 = Rs 38.75 So, the selling price after the discount = List price – Discount = Rs 125 – Rs 38.75 = Rs 86.25

Now, we know that the shopkeeper earns a 15% profit on the selling price. Let’s represent the cost price (CP) as x.

The selling price (SP) after profit = Cost price (CP) + Profit So, SP = CP + 15% of CP = CP + 0.15 * CP = 1.15 * CP

Given that SP = Rs 86.25, we can write the equation as: 1.15 * CP = 86.25

Now, we can solve for the cost price (CP): CP = 86.25 / 1.15 = Rs 75

So, the cost price of the shirt is Rs 75.

Therefore, the correct answer is C. 75.

How many numbers up to 450 are divisible by 4, 6 and 8 together?

A. 19
B. 18
C. 17
D. None of these

Answer

Correct Answer: B. 18

Detail about MCQs

To find the numbers up to 450 that are divisible by 4, 6, and 8 together, we need to find the numbers that are divisible by the least common multiple (LCM) of 4, 6, and 8.

The LCM of 4, 6, and 8 is the smallest number that is divisible by all three numbers, which can be found by calculating the prime factorization of each number:

  • 4 = 2^2
  • 6 = 2 * 3
  • 8 = 2^3

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers: 2^3 * 3 = 24.

So, any number that is divisible by 24 is also divisible by 4, 6, and 8.

Now, to find how many numbers up to 450 are divisible by 24, we divide 450 by 24:

450 ÷ 24 = 18 with a remainder of 18.

So, there are 18 whole multiples of 24 up to 450.

Therefore, the correct answer is B. 18.

If the roots of the equation are -7/4 , 4/7 then the equation will be?

A. 28x^2+43x-28=0
B. 28x^2-43x-28=0
C. 28x^2+49x-16=0
D. 28x^2-33x-28=0

Answer

Correct Answer: C. 28x^2 + 49x -16 = 0


Solution

If the roots of the equation are -7/4 and 4/7, then the equation can be written as:

(x + 7/4)(x – 4/7) = 0

Multiplying out the terms gives:

x^2 + (7/4)x – (4/7)x – 7/4 * 4/7 = 0
x^2 + (49x – 16)/28 = 0

Multiplying both sides by 28 to get rid of the denominator, we get:

28x^2 + 49x – 16 = 0

Therefore, the equation with roots -7/4 and 4/7 is 28x^2 + 49x - 16 = 0.

If S=the sum of the roots of the equation and P= Product of the roots of the equation, then their equation can be written as:

A. x^2+Sx+P=0
B. x^2+Sx-P=0
C. x^2-Sx-P=0
D. x^2-Sx+P=0

Answer

Correct Answer: D. x^2-Sx+P=0


Solution

If we have a quadratic equation of the form ax^2 + bx + c = 0, the sum of its roots is given by:

S = -b/a

and the product of its roots is given by:

P = c/a

To see why these formulas are true, we can use Vieta’s formulas, which state that for a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term, and the product of the roots is equal to the constant term divided by the coefficient of the quadratic term.

So, we can write the quadratic equation as:

a(x – r1)(x – r2) = 0

where r1 and r2 are the roots of the equation. Expanding the product and comparing the coefficients with the equation ax^2 + bx + c = 0, we get:
a(x^2 – (r1 + r2)x + r1r2) = 0
Equating the coefficients of corresponding powers of x, we get:
r1 + r2 = -b/a
r1r2 = c/a

Therefore, we have:

S = -b/a
P = c/a
Thus, if S is the sum of the roots of the equation and P is the product of the roots of the equation, we can write the equation as:
x^2 – Sx + P = 0

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