Which of the following statements is true?

In 10², the exponent is

A perfect square number between 30 and 40 is

If x + y + z = 6 and z is an odd digit, then the 3-digit number xyz is

Find the smallest number by which the number 1296 must be divided to obtain a perfect cube.

Study the following frequency distribution table and answer the question given below:

The class with lowest frequency is 

Read the graph and answer the related question:

What was the difference of the number of labourers in the years 2002 and 2003?

The largest number of the three consecutive numbers is x + 1. Then, the smallest number is

The measure of each exterior angle of a regular polygon of 9 sides is

Which one of the following is a Pythagorian triplet?

In a school out of 340 students, 55% students are of Science. The remaining students are of Commerce. Find the number of students of Commerce.

Product of the monomials, -15p, -13q², pq is

We have 4 congruent equilateral triangles. What do we need more to make a pyramid?

The area of a trapezium is 40 cm² . Its parallel sides are 12 cm and 8 cm. The distance between the parallel sides is

The rent of 7 hectares is Rs.875. What is the rent of 16 hectares?

The factorisation of 6x² - 5x - 6 is

Is \((-4) \times [(-8) \times (-5)] = [(-4) \times (-8)] \times (-5)?\)

Simplify and write the answer in the exponential form: (-4)^-3 \(\times\) (-5)^-3 \(\times\) (5)³

Which of the following are not perfect squares? 33333

If the division N \(\div\) 2 leaves no remainder (i.e. zero remainder), what might be the one's digit of N?

Find the cube of 17.

Rohan and Shalu are playing with 5 cards as shown in the figure. What is the probability of Rohanpicking a card without seeing, that has the number 2 on it?

A courier-person cycles from a town to a neighbouring Suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph:

How far is the place of the merchant from the town?

Solve the following equations \(\frac { 2x }{ 3 } =18\)

Two regular polygons are such that the ratio between their number of sides is 1 : 3 and the ratio of measure of their interior angles is 4:7. Find the number of sides of each polygon.

We first drew BC. Instead, what could have been be the other starting points?

Given, P = Rs 40000 and R = 8% per annum compounded annually. Find the amount, if period is 2 yr.

Using (x + a) (x + b) = x² + (a + b)x + ab; find 5.1 x 5.2

Use a ruler to measure the distance in cm between the places joined by dotted lines. If the map has been drawn using the scale 1 cm 10 km, find the actual distances between House and School.

Four horses are tethered with equal ropes at 4 corners of a square field of side 70 m, so that they just can reach one another.Find the area left ungrazed by the horses.

Find the proportion between side of a square and its perimeter.

Factorise 19m²n³ - 57 mn²

Sorve the followings:
\(({-3\over7}\div{9\over14})\div({-5\over2})\)

If \(\frac{5^{m}\times5^{3}\times5{-2}}{5^{-5}}=5^{12}\)then find the value of m.

Find the least number by which we multiply to the 11760, so that we can get perfect number.

Check what the result would have been if Sundaram had chosen the number shown below: 39

Find the cube of \({4\over5}\) .

The following pie chart shows that the performance is an examination in a particular year for 360 students. Study the pie chart and answer the question given here.

(a) Find the number of students who passed with 1st division.
(b) Find the number of students who passed with 2nd division with more than those with 1st division.

The following data represent the expenditure on various items(named as A, B, ... ) of a family in a month. Represent the data in the form of a pie chart.

Find the root of the equation \(\frac { \left( 2+y \right) \left( 7-y \right) }{ \left( 5-y \right) \left( 4+y \right) } =1\)

Take identical cut-outs of congruent triangles of sides 3 cm, 4 cm and 5 cm. Arrange them as shown in the figure.

You get a trapezium. (Check it!) Which are the parallel sides here? Should the non-parallel sides be equal. You can get two more trapeziums using the same set of triangles. Find out them and discuss their shapes.

Construct the kite EASY, if AY = 8 cm, EY = 4 cm and SY = 6 cm in figure. Which properties of the kite did you use in the process?

Find the buying price of the following, when 5% sale tax is added on the purchase of two bars of soap at Rs 35 each.

Simplify (3x + 2y)² + (3x- 2y)².

What figure is formed, if only the height of a cube is increased or decreased?

Find the area of quadrilateral PQRS shown in the figure:

Find the values of x and y, if a and b are in inverse proportion.

Find the common factors of the given terms 14pq = 28 p²q²

Is there a number which is equal to its cube but not equal to its squares? If yes find it.

Present the following data in the form of a grouped frequency distribution table having 6 classes of equal size (one of the class being 40-48):

Solve the following linear equations:
m-\(\frac{m-1}{2}\)=1-\(\frac{m-2}{2}\)

Take a clock and fix its minute hand at 12.
Record the angle turned through by the minute hand from its original position and the time that has passed, in the following table:

What do you observe about T and A? Do they increase together? Is \(T\over A\) same every time?

Is the angle turned through by the minute hand directly proportional to the time that has passed? Yes; From the above table, you can also see
T₁ : T₂ = A₁ A₂, because
T₁ : T₂ = 15 30= 1 :2
A₁ : A₂ = 90 180 = 1 :2
Check if T₂: T₃ = A₂ A₃ and T₃ : T₄ = A₃ : A₄
You can repeat this activity by choosing your own time interval.

Use the distributivity of multiplication of rational numbers over addition to simplify:
\({-5\over4}\times[{8\over5}+{16\over15}]\)

Express the following numbers in standard form 5463

Find the value of \(\frac { \sqrt { 25.4016 } -\sqrt { 1.0609 } }{ \sqrt { 25.4016 } +\sqrt { 1.0609 } } \)

Find the values of the letters in each of the following and give reasons for the steps involved.\(\begin{matrix} \quad \quad A\ B \\ \quad \times \ \ \quad 3 \\ \_ \_ \_ \_ \_ \_ \_\_ \\ C\ A\ B \\ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

What is the smallest number by which 648 must be multiplied so that the product is a perfect cube?

Percentage wins in ODI by 8 top cricket teams.

The following table shows the colours preferred by students of a Class VIII :

Represent this data in the form of pie diagram (approx).

A man was engaged as typist for the month of February in 2009. He was paid Rs. 500 per day, but Rs.100 per day were deducted for the days he remained absent. He received Rs. 9200 as salary for the month. For how many days did he work?

The ratio between exterior angle and interior angle of a regular polygon is 1 : 3. Find the number of sides of the polygon. Also, find each of the interior and exterior angles.

Construct the following quadrilaterals. Quadrilateral PLAN PL = 4 cm, LA = 6.5 cm, \(\angle \)P = 90°, \(\angle \)A = 110°, \(\angle \)N = 85°

A milkman sold two of his buffaloes for Rs 20000 each. On one, he made a gain of 5% and on the other, a loss of 10%. Find his overall gain or loss. [Hint Find CP of each]

By using suitable identity, evaluate \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } ,if\ x+\frac { 1 }{ x } =5\quad \)

A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.

Find the length of the diagonal BD when, the area of the quadrilateral is 32 cm².

Observe the following tables and find, if x and y are directly proportional

if mean of some observations is (4x ²-9) and their sum is 16x⁴ -81. Then , find the number of observations