Question 1 :
Which of the following is not the reciprocal of$$\displaystyle \left ( \frac{2}{3} \right )^{4}$$?

Question 3 :
The sum of the numbers $$2053$$ and $$412$$ which are in the scale of seven is

Question 5 :
For any two real number, an operation defined by $$a* b= 1 +ab$$ is.<br/>

Question 7 :
The minimum number of dimensions needed to construct a rectangle is

Question 8 :
State the following statement is true or false<br/>We can construct a quadrilateral if the measurement of four sides and one diagonal are given.

Question 10 :
If $$y = \dfrac{2}{\sin \theta + \sqrt{3}\cos \theta}$$, then the minimum value of $$y$$ that is greater than zero is<br/>

Question 11 :
Arrange the following steps in correct order in constructing a square whose one diagonal is $$5$$cm.<br/>Step 1 : Let PQ cut AC at O.<br/>Step 2 : Draw a diagonal AC = $$5$$cm.<br/>Step 3 : Join Ab, BC, CD and DA. Then ABCD is the required square.<br/>Step 4 : Draw PQ the perpendicular bisector of AC.<br/>Step 5 : With O as centre and OA radius draw a circle. Let the circle cut QP at points B and D.<br/>

Question 14 :
$$ABCD$$ is a square with centre $$O$$. If $$X$$ is on the side $$CD$$ such that $$DX=DO$$, find the ratio $$\angle DOX:\angle XOC$$

Question 15 :
If $$ABCD$$ is a rhombus whose diagonals cut at the origin $$O$$, then $$\vec{OA}+\vec{OB}+\vec{OC}+\vec{OD}$$ equals to

Question 16 :
Let ABCD be a parallelogram such that AB = q , AB = p, and $$\angle BAD $$ be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by

Question 17 :
A diagonal of a rectangle is inclined to one side of the rectangle at $$25^o$$. Find the acute angle between the diagonals.

Question 18 :
Solve for $$x$$:-<br/>$$\dfrac{{2x - 1}}{2}\,\,\, - \dfrac{{x + 3}}{3}\,\, = \dfrac{{x - 2}}{5}$$

Question 19 :
A number consists of two digits. The digit in the tens place exceeds the digit in the units place by $$4$$. The sum of the digits is&#160;$$\displaystyle \frac{1}{7}$$ of the number. The number is

Question 20 :
Solve the linear equation:$$\displaystyle \frac{5x + 1}{12} - 2 = \frac{3x - 1}{9}$$

Question 23 :
State true or false:The root of the equation $$\dfrac{y}{2}+6 = y$$ is $$\dfrac{1}{\sqrt{2}}$$.<br/>