Find six rational numbers between 3 and 4.

3

(a)

Write the following in decimal form and say what kind of decimal expansion each has:
\(\frac { 3 }{ 13 } \)

3

(a)

Express \(2.\overline { 93 } \) in the form of \(\frac { p }{ q } \), where p and q are integers, \(q\neq 0\)

3

(a)

Simplify: \((\sqrt{x})^{-\frac{2}{3}}\sqrt{y^{4}}\div\sqrt{(xy)^{-\frac{1}{2}}}\)

3

(a)

Simplify: \(\left( \sqrt { 3 } +1 \right) \left( 1-\sqrt { 12 } \right) +\frac { 9 }{ \left( \sqrt { 3 } +\sqrt { 12 } \right) } \)

3

(a)

Write the coefficients of x² in the following:
2 - x² + x³

3

(a)

Classify the following as linear, quadratic and cubic polynomials:
y + y² + 4

3

(a)

Verify whether the following are zeroes of the polynomial, indicated against them.
\(p(x)=3x+1,x=-\frac { 1 }{ 3 } \)

3

(a)

In which quadrant do the given points lie?(9,6)

3

(a)

Express the following linear equation in the form ax+by+c=0 and indicate the values of a, b and c in each case:
-2x+3y=6

3

(a)

Write three solutions of the equation 3x=y+3. Draw its graph and find the points where the graph intersects the axes.

3

(a)

In Figure ,PQ and RS are two mirrors placed parallel to each other An incident ray AB strikes the mirror PQ at B the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD.Prove that AB|| CD 

3

(a)

In figure, triangle ABC is right angles at A, AL is drawn perpendicular ro BC. Prove that \(\angle BAL=\angle ACB.\)

3

(a)

AD is an altitude of an isosceles triangle ABC in which AB = AC Show that
(i) AD bisects BC (ii) AD bisects \(\angle A\)

3

(a)

In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

3

(a)