If the sets \(A = \{3, 4, 5, 7\}\) and \(B = \{2, 3, 4, 9\}\),
Which of the sets \(A\) and \(B\) are overlapping or disjoint? Write it.[1]
Form any two proper subsets of set \(A\).[1]
If set \(C = \{2, 3, 4, 9\}\), then the set \(C\) is an improper subset of set \(B\). Give a reason.[1]
The marks obtained by \(12\) students of Grade Eight in the Annual Examination in Mathematics are given below:
\(22, 30, 25, 26, 24, 29, 27, 27, 28, 31, 33, 23\).
Sita said, “Mean divides the given data into two equal parts.” But Gita said, “Median divides the given data into two equal parts.” Whose statement is true?[1]
Find the mean from the above data.[2]
The monthly salary of Hari Rana is \(\text{Rs.}\,36{,}000\).
Write the amount in scientific notation.[1]
Express the number in the quinary number system.[2]
If Hari’s salary is twice as much as Suraj’s salary and Suraj’s salary is thrice as much as Shyam’s salary, find the annual salary of Shyam.[2]
Ram has a stationery shop at his house. He sells a calculator with a marked price \(\text{Rs.}\,450\) at a discount of \(12\%\), and he sells a ball at \(\text{Rs.}\,850\) after giving \(15\%\) discount.
If marked price (\(M\)) and discount (\(D\)) are given, then write the formula to find the price after discount.[1]
How much is the discount amount of the calculator? Find it.[1]
Find the marked price of the ball.[1]
By how much is the discount amount on the calculator more or less than the discount amount on the ball?[1]
Rina took a loan of \(\text{Rs.}\,50{,}000\) from Pawan at \(18\%\) per annum simple interest for \(3\) years.
How much simple interest is paid by Rina in \(3\) years? Find it.[1]
Find the total amount of principal and interest to be paid by Rina.[1]
If Rina took the loan at \(12\%\) per annum, then how much less interest would she have to pay?[2]
Bindu decided to exchange her square-shaped land of \(42\,\text{m}\) side with a rectangular land of equal area.
What was the area of her square-shaped land?[1]
If the length of the rectangular land to be exchanged is \(72\,\text{m}\), find the breadth of the land.[1]
What will be the length of wire required to fence the rectangular land three times?[2]
To fence the above square and rectangular land one round each, which land needs more wire and by how much?[1]
Express \(x^m \times x^n\) as a power of \(x\).[1]
Two equations are given below: \(2x - y = 5\) and \(x - y = 1\).
Write the degree of the given equations.[1]
Solve the above equations by using graphical method.[2]
Find the H.C.F. of: \(3x^3 - 15x^2\) and \(2x^3 - 50x\).[2]
Write a quadratic equation having roots \(4\) and \(5\) of \(x\).[2]
In the adjoining figure, \(TU\) intersects straight lines \(PQ\) and \(RS\) at points \(V\) and \(W\) respectively.
Write a pair of alternate angles from the figure.[1]
What type of triangle is \(\triangle VWX\) according to the angles of the triangle?[2]
At what value of \(\angle QVX\) will the given line segments \(PQ\) and \(RS\) be parallel?[1]
Construct a parallelogram \(ABCD\) with \(AB = 6\,\text{cm}\), \(BC = 4.5\,\text{cm}\), and \(\angle ABC = 45^\circ\).[3]
In the given figure, if \(\triangle ABC \sim \triangle DEF\), find the measurement of \(DF\).[2]
Write down the bearing of point \(A\) from point \(O\).[1]
\(L(0,-2)\), \(M(5,-4)\), and \(N(2,5)\) are the vertices of \(\triangle LMN\). Find the coordinates of the vertices of its image when it is reflected about the \(x\)-axis. Also, draw the graph of the reflection.[3]
If the centre of a circle is \(A(4,4)\) and \(B(7,4)\) is any point on its circumference, find the area of the circle.[2]
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