Difficult Questions

Calculate: (-7/3) × (6/5) × (-14/9)

Calculate: 3/7 + 6/11 + 8/21 + 5/22 using properties efficiently

Evaluate: (-4/5) × (3/7) × (15/16) × (-14/9)

Using distributivity, solve: 2/5 × 3/7 - 1/14 - 3/7 × 3/5

Why is the equation x/5 + 7 = 0 important in understanding rational numbers?

Which number system is the smallest that contains solutions to all linear equations of the form ax + b = c?

When we say 'rational numbers are dense,' we mean:

If we define a new operation * such that a * b = ab + a + b, is this operation commutative for rational numbers?

How does the concept of identity elements relate to solving equations?

How do the properties of rational numbers connect to the properties of real numbers?

How do rational numbers prepare students for understanding irrational numbers?

Solve: $\frac{2x+1}{3} = \frac{x-1}{2}$

If $x = 3$ is the solution to $ax + 5 = 2x + 11$, what is the value of $a$?

Solve: $\frac{3x-1}{4} = \frac{2x+3}{5}$

Solve: $5(x-1) - 3(x+2) = 2$

Solve: $2x + 3(x-1) = 4(x+2) - 1$

Solve: $\frac{x+1}{2} - \frac{x-1}{3} = 1$

Solve: $\frac{3x}{4} = \frac{2x-1}{3}$

In the equation $ax + b = cx + d$, the solution is:

What is the solution to $\frac{2x+3}{5} = \frac{x-2}{2}$?

Solve: $\frac{2x-1}{3} + \frac{x+2}{2} = 4$

The equation $px + 5 = qx + 3$ has solution $x = 2$. If $p = 4$, what is $q$?

Solve: $\frac{3x+1}{2} = \frac{2x-1}{3} + 1$

If each interior angle of a regular polygon is 135°, how many sides does it have?

In square PQRS, if the length of diagonal PR is 8√2 cm, what is the side length?

What type of quadrilateral has perpendicular diagonals that bisect each other?

In a kite ABCD where AB = AD and CB = CD, which angles are equal?

Which statement about regular polygons is FALSE?

Which quadrilateral can have exactly one line of symmetry?

If ABCD is a parallelogram and ∠A : ∠B = 2 : 3, find ∠A.

Which quadrilateral has opposite angles that are supplementary?

In kite ABCD with AB = AD = 5 cm and BC = CD = 8 cm, which diagonal is longer?

In which situation would you use a bar graph instead of a pie chart?

If you conduct a coin toss experiment 100 times and get 60 heads, what can you conclude?

What is the theoretical probability of getting exactly 50 heads in 100 coin tosses?

How does sample size affect the reliability of experimental probability?

Using prime factorization, find $\sqrt{324}$.

Which number should be subtracted from 1000 to make it a perfect square?

Generate a Pythagorean triplet using $m = 4$ in the formula $(2m, m^2 - 1, m^2 + 1)$.

Which of the following is true about the square root of an irrational number?

In a right triangle, if two sides are 5 and 12, what is the third side?

What is the smallest perfect square that is divisible by 2, 3, and 5?

Express 1024 as a power of 2 and find its square root.

If the area of a square field is 6400 square meters, what is the cost of fencing it at ₹25 per meter?

Using triangular numbers, what is $6^2$?

What is the square root of the largest 4-digit perfect square?

A farmer has a square plot of land. If he increases each side by 10 meters, the area increases by 1000 square meters. What was the original side length?

What is the digital root pattern for perfect squares?

If a number is both a perfect square and a perfect cube, what can we say about it?

Using prime factorization, find $\sqrt[3]{8000}$.

What is the smallest number by which 392 must be multiplied to make it a perfect cube?

Using the consecutive odd number pattern, what odd numbers sum to $4^3$?

Find $\sqrt[3]{13824}$ using prime factorization.

What is the next Hardy-Ramanujan number after 1729?

What is $\sqrt[3]{0.008}$?

Which number should be multiplied to 500 to make it a perfect cube?

In a cube, if the surface area is 294 cm², what is the volume?

What is the cube root of the largest 4-digit perfect cube?

Using the sum pattern, which consecutive odd numbers sum to $5^3$?

If a cuboid has dimensions 5 cm × 2 cm × 5 cm, how many such cuboids are needed to form a cube?