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Find the approximate value of $\sqrt{30}$ using perfect square method.

The sum of two numbers is 12. When three times the first number is added to 5 times the second number, the resultant number is 44. The two numbers are: .

If $x+\frac{1}{x}=3$, calculate $x^2+\frac{1}{x^2},x^3+\frac{1}{x^3}$ and $x^4+\frac{1}{x^4}$

Choose the option that gives the side view of the below given solid.

For the figure given below, which of the following is/are correct?

Compute the value of x in each of the following figures:

${1400}^n$ is NOT divisible by which of the following, if n is a natural number:

If y = 2x + 3, then what is the value of y at x = 5?

Question 45

Sate weather the given statement is true or false.

When the distance is kept fixed, speed and time vary directly with each other.

Find the square roots of 121 and 169 by the method of repeated subtraction.

If $(a^2+b^2)=1\frac{1+b+ia}{(1+b-ia)}$

Simplify the expression and choose the correct option

$\sqrt[2]{28}$$\times$$\sqrt[3]{312}$$\times$$\sqrt[6]{69}$

Find the value of $\frac{x^{a(b-c)}}{x^{b(a-c)}}÷(\frac{x^b}{x^a}{)}^c$

The sides of a rectangular park are in the ratio 4:3. If the area is 1728 m², find the cost of fencing it at the rate of Rs. 2.50/m.

Is a rational number? If so, how do you write it in a form conforming to the definition of a rational number (that is, the denominator as a positive integer)?

The height of the cuboid whose volume and base area are 275 cm3 and 25 cm2 respectively is ______ .

Select the sequence which is not an arithmetic sequence.

At what rate percent will a sum of Rs. 1000 amount to Rs. 1102.50 in 2 years at compound interest?

Find a number whose double is $45$ greater than its half.

A and B can do a work in 8 days; B and C in 12 days, and A and C in 16 days. In what time could they do it, all working together?

Question 2 (i)
Without doing any calculation, find the numbers which are surely not perfect squares:
153

A train takes 30 s to cross a pole while traveling at a speed of 120 km/h. How much time will it take to cross the pole if its speed is increased by 30 km/h?

Question 52

In the following question, fill in the blanks to make the statements true.

$3^5÷3^{-6}$ can be simplified as ___ .

A cuboidal box is 5 cm by 5cm by 4cm. Find its surface area.

All the letters of the word $\text{NUMBER}$ are arranged in different possible ways. What are the number of arrangements possible so that no two words are repeated?

Use factor theorem to factorise completely: ³ + ² – 4 – 4.

Find the total surface area and volume of a cube whose length is 12 cm.