Calculate the decimal which represents the fraction \(\frac{7}{8}\)

Factorize: 20x²-9x+1.

What does a theorem require?

Calculate the value of x in the figure given below.

If a transversal intersects two parallel lines, then which of the pairs of angles is equal.

\(\triangle ABC\cong \triangle PQR,\) AB=PQ. Which statement has been followed in this?

In \(\Delta\)ABC, E is the mid-point of median AD, then the ratio of area of \(\Delta\)BED to the area \(\Delta\)ABC is _______________

The points scored by a basketball team in a series of matches are as follows: 17,2,7,17,25,514,18,10. Find range.

Find three rational numbers between 3/7 and 5/11.How many rational numbers can be determined lying between these numbers?

Simplify the product:(4√3+3√2)x(4√3-3√2)

Evaluate 105 x106 without direct-multiplying.

Factorize: 12(x²+7)²-8(x²+7)(2x-1)-15(2x-1)².

Plot the following points A(5,0), B(-1,2), C(2,-2), D(0,4), E(-3,-3), F(0,-1)

Write the following equation in the form ax+by+c=0 and find values of a, b and c: 4=3x-5y. Check whether (1, -1) and (3, 1) are solutions of this equation or not.

Solve 4x - 7 = 9. Represent the solution
(i) on the number line
(ii) in the Cartesian plane.

Find six rational numbers between 3 and 4.

Simplify: \(\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } } -\frac { 2 }{ \sqrt { 5 } -\sqrt { 3 } } -\frac { 3 }{ \sqrt { 2 } +\sqrt { 5 } } \)

If f(x) = x³-3x²+3x-4, find f(2)+f(-2)+f(0).

The perpendicular distance of a point from the x-axis is 4 units and the perpendicular distance from the y-axis is 5 units.Write the coordinates of such a point if it lies in the
(a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant

Write four solutions for each of the following equations:
\(\pi x+y=9\)

If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.

Express y in terms of x in the equation 5x-4y+20=0.Draw the graph and find the points where the lines represented by this equation cuts x-axis and y-axis

When 5 times the larger of the two numbers is divided by the smaller, the quotient and remainder are 2 and 9 respectively. Form a linear equation in two variables. Write it in standard form.

Find your rational numbers between \(\frac { 1 }{ 5 } \) and \(\frac { 1 }{ 6 } \)  

\(\frac { \sqrt { 147 } }{ \sqrt { 75 } } \) is not a rational number as \(\sqrt { 147 } \) and \(\sqrt { 75 } \) are not rational.State whether it is true or false.Justify your answer. 

Arrange in descending order \(\sqrt [ 3 ]{ 2 } ,\sqrt [ 4 ]{ 5 } ,\sqrt [ 6 ]{ 7 } \) and \(\sqrt[12]{3}\) .

The polynomial \(p(x)=kx^3+9x^2+4x-8\) when divided by (x+3) leaves a remainder 10 (1-k). Find the value of k.

Factorise: \((ax+by)^2+(ay-bx)^2\)

If a+b+c=6 and ab+bc+ca=11, find the value of a³+b³+c³-3abc.

Geetha told her classmate Radha that "\(\sqrt { \frac { \left( \sqrt { 2 } -1 \right) }{ \left( \sqrt { 2 } +1 \right) } } \) is an irrational number." Radha replied that "you are wrong" and further claimed that "If there is a number 'x' such that x³ is an irrational number, then x⁵ is also irrational". Geetha said, "No Radha, you are wrong". Radha took some time and after verification accepted her mistakes and thanked Geetha for pointing out these mistakes. 
(i) Justify both the statements.
(ii) What value is depicted from this question?