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Find the product:

$\left(i\right)x+y-10and12xy$.

$\left(ii\right)\left(\frac{4}{6}\right)aband\left(\frac{-3}{10}\right)x^{2}y$

$\left(iii\right)(x+y+z+p)andxyzp$

$\left(iv\right)2x^2+6xy-24and3ab$ [4 MARKS]

A circle centered at O and of radius 4 cm is divided into six equal parts as shown in the figure below.

If we join alternate points starting from A, then the 2D shape so obtained is

In the given figure, $\Delta AEC$ and $\Delta DBF$ are equilateral. Prove that all the other triangles are also equilateral. (Given that bases of the triangles are parallel). [4 MARKS]

Question 2(ii)

Simplify and express the result in power notation with positive exponent:

${\left(\frac{1}{2^3}\right)}^2$

Question 3 (i)
Explain how a square is:

(i) A quadrilateral

Question 1(ii)
Using laws of exponents, simplify and write the answer in exponential form:
(ii) $6^{15}÷6^{10}$

If a racing car covers 200 km in 2 hours then find its speed.

If P is the interoir point of parallelogram ABCD, prove that the sum of area of ΔPAB and ΔPDC is as equal to half of the area of parallelogram ABCD [2 MARKS]

Q. शिक्षा प्रबंधन में वैश्विक गठबंधन (GEC) निम्नलिखित में से किस संस्थान की एक पहल है?

Five boys go to a store and each buys a notebook, an eraser, and a pen. Find an expression for the total cost (in dollars) if the price of a notebook is $\$x$, an eraser is $\$y$, and a pen is $\$z.$

Question 1

Write the correct answer from the given four options.

196 is the square of

a) 11

b) 12

c) 14

d) 16

Solve the following.

If 25 labourers harvest 20 acres of maize crop in a day, then how many acres do 35 labourers harvest during the same period?

Consider the figure:

If BC = AC, x = 2y, and angle ∠ACB = 60^o, then the value of ∠B + y (in degrees) is

The picnic spot is 55 km away from the school. The first stop is taken at 22 km from the school. What percentage of the distance is remaining to reach the destination?

Choose the correct equivalent of 140 from the given pairs:

In figure, if QT is perpendicular to PR, $\angle TQR={40}^{\circ }$ and $\angle SPR={30}^{\circ }$ , find x and y. [4 MARKS]

Arrange the values of the following expressions in increasing order from bottom to top.

Convert the decimal 0.25 in to fraction

Question 101

The strength of a school is 2000. If 40 % of the students are girls, then how many boys are there in the school?

Fill in the following blanks:

[Are
these equivalent ratios?]

If the following solid is cut vertically then the 2D shape is:

Find the size of the class interval in the following:

(a) 11 − 20

(b) 31 − 35

(c) 41 − 49

Solve the following.

There are 60 students in VII std. class. 30% of them are girls. Find the strength of boys.

What is the perimeter of a rectangle of length $7\text{cm}$ and breadth $4\text{cm}$?

Question 2: In the given diagram, name the point(s):



On $\angle EOF$

₹ 4000 - ₹ 1500 = ₹ ___

Given line 'm' is parallel to line 'l'. Find x?

Which of the following combination of measurements can be used to make right-angled triangle?



Dimensions are given in same length unit.

Question 146(ii)

The given table shows the crop production of a state in the year 2008 and 2009. Observe the table given below and answer the given questions.

$\begin{array}{ccc}Crop& 2008Harvest\left(Hectare\right)& Increase/Decrease\left(Hectare\right)in2009\\ Bajra& 1.4\times {10}^3& -100\\ Jowar& 1.7\times {10}^6& -440000\\ Rice& 3.7\times {10}^3& -100\\ Wheat& 5.1\times {10}^5& +190000\end{array}$

Write the production of all the crops in 2009 in their standard form.

Take nine numbers forming a square in a calendar and mark the four numbers at the corners. Then the difference between the squares of the diagonal pairs is always ____.