Govt. Exams
Entrance Exams
Odd numbers between 10 and 50: 11, 13, 15, ..., 49.
This is an AP with first term 11, last term 49, and common difference 2.
Number of terms = (49-11)/2 + 1 = 19 + 1 = 20.
∛512 = ∛(8³) = 8, since 8 × 8 × 8 = 512.
12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. LCM = 2³ × 3² = 8 × 9 = 72.
36 = 2² × 3².
Number of factors = (2+1)(2+1) = 3 × 3 = 9.
The factors are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
51 = 3 × 17 (not prime), 53 is prime (only divisible by 1 and 53), 55 = 5 × 11 (not prime), 57 = 3 × 19 (not prime).
Therefore, 53 is the smallest prime greater than 50.
Using dividend = divisor × quotient + remainder: Number = 11 × 9 + 5 = 99 + 5 = 104
To find the remainder when a number is divided by another, use the division algorithm: \(\text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder}\)
Step 1: Set up the division
We need to express 527 in the form:
where \(q\) is the quotient and \(r\) is the remainder with \(0 \leq r < 15\).
Step 2: Divide 527 by 15
Perform the division:
The quotient is \(q = 35\).
Step 3: Calculate the product
Step 4: Find the remainder
Subtract the product from the dividend:
Since \(0 \leq 2 < 15\), this is a valid remainder.
Verification:
To find the remainder when 527 is divided by 15:
15×35=525
Now subtract:
527−525=2
Therefore, the remainder is 2.
Answer: The remainder is \(2\) (Option A)
This question asks us to find the average value of the numbers 1 through 15.
The first 15 natural numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.
Use the formula for sum of first n natural numbers: \[\text{Sum} = \frac{n(n+1)}{2}\]
Average is the sum divided by the count of numbers.
The average of the first 15 natural numbers is 8.
This question asks us to find an unknown number based on a sequence of arithmetic operations performed on it.
Let the unknown number be x. According to the problem, when x is multiplied by 8 and then 15 is subtracted, the result is 49.
Add 15 to both sides of the equation to move the constant to the right side.
Divide both sides by 8 to find the value of x.
The number is 8, which corresponds to answer choice (B).
Largest 3-digit number = 999, Smallest 3-digit number = 100.
Difference = 999 - 100 = 899
