Question 1 :
State whether the statement is True or False.Expand: $(2x-\dfrac{1}{2x})^2 $ is equal to $4x^2-2+\dfrac{1}{4x^2} $.<br/>
Question 2 :
State whether the statement is True or False.Evaluate: $(1.6x+0.7y)(1.6x-0.7y)$ is equal to $2.56x^2-0.49y^2$.<br/>
Question 6 :
Which of the following rational numbers lies between $0$ and $-1$?
Question 7 :
The value of $8\times 2\dfrac {4}{5} + 8\times 3\dfrac {1}{5}$ is
Question 8 :
Which of the following rational numbers is in the standard form?
Question 9 :
Find whether the following statement are true or false.<br>In a rational number of the form $\cfrac { p }{ q } ,q$ must be a non zero integer.
Question 10 :
For any two real number, an operation defined by $a* b= 1 +ab$ is.<br/>
Question 12 :
A computer is programmed to add $3$ to the number $N$, multiply the result by $3$, subtract $3$, and divide this result by $3$. The computer answer will be
Question 14 :
The numerator of a fraction is $5$ less than its denominator. If $3$ is added to the numerator and denominator both, the fraction becomes $\dfrac{4}{5}$. Find the original fraction.
Question 15 :
Solve the following linear equations. If $\cfrac{3t-2}{4}-\cfrac{2t+3}{3} = \cfrac{2}{3}-t$, then $t  $ is equal to<br/>
Question 16 :
In a school for midday meal food is sufficient for 250 students for 33 days, if each student is given 125 gm meals. 80 more students joined the school.If same amount of meal is given to each student, then the food will last for
Question 18 :
There is a number, the second digit of which is smaller than its first digit by $4$ and if the number was divided by the digits sum, the quotient would be $7$. Can you find the number ?
Question 19 :
Find the value of $\dfrac {4}{y} + 4$ given that $\dfrac {4}{y} + 4 = \dfrac {20}{y} + 20$
Question 20 :
If $\displaystyle \frac{x^2\, -\, (x\, +\, 1)(x\, +\, 2)}{5x\, +\, 1}\, =\, 6$, then $x$ is equal to
Question 21 :
Find the value of $x$ , which makes the two expressions$\left ( x+1 \right ) \: \left ( x+2 \right )$ and $x\left ( x+7 \right )-6$ equal to each other.
Question 22 :
Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?<br/>
Question 23 :
Find the value of<br>${ \left( \sqrt { { x }^{ 2 }-{ a }^{ 2 } } +x \right) }^{ 5 }-{ \left( \sqrt { { x }^{ 2 }-{ a }^{ 2 } } -x \right) }^{ 5 }$
Question 24 :
Two numbers are in the ratio $\displaystyle 1\frac {1}{2} : 2\frac{2}{3}$.When each one of these is increased by $15$, their ratio becomes $\displaystyle 1\frac{1}{2} : 2\frac{1}{2}$. The larger of the numbers is
Question 25 :
The four consecutive numbers add up to $74$. What are these integers?
Question 26 :
Half of a herd of buffaloes are going in to the field and three fourths of the remaining are playing nearby. The rest $9$ are drinking water from pond. Find total number of buffaloes in the herd.
Question 27 :
The number of solution of $ \left| \left[ x \right] -2x \right| =4$, where $[x]$ denotes the greatest integer less than $x$ is<br/>
Question 29 :
The volume of a cylinder of height 4 cm and total surface area 484$\displaystyle cm^{2}$ is
Question 30 :
Water in a canal, $30\space dm$ wide and $12\space dm$ deep, is flowing with a speed of $10\space km/hour$. How much area will it irrigate in $30$ minutes, if $8\space cm$ of standing water is required for irrigation.
Question 31 :
The side of a cube is 10 cm. What is its volume ?
Question 32 :
The volume of a cube whose diagonal is $ \displaystyle \sqrt{3}  $ m will be
Question 33 :
Calculate the volume of a dice with the dimession $13$ m $\times$ $13$ m $\times 13$ m
Question 34 :
If the surface area of a cube is $384$ sq.m, then its volume is
Question 35 :
If the volume of right cylinder with radius $2$ cm is $\displaystyle 100\pi\  { cm }^{ 3 }$, then the height of cylinder (in cm) is
Question 37 :
The number of cubes of side 3 cm that can be cut from a cube of side 6 cm is
Question 38 :
Choose the correct answer from the given four options:<br>The usual form of $5.658 \times 10^5$ is<br><br>
Question 41 :
$\left \{\left (\dfrac {1}{3}\right )^{-3} -\left (\dfrac {1}{2}\right )^{-3}\right \} \div \left (\dfrac {1}{4}\right )^{-3} = ?$
Question 42 :
Choose the correct answer from the given four options:<br>Which of the following numbers in the standard form?<br><br>
Question 49 :
If $9^n = 27^{n+1}$, then calculate the value of $2^n $.
Question 50 :
Take $6$ less than a number $n$. If you raise this result to the $5th$ power, it is equal to $32$. Calculate the value of $n$.
Question 51 :
The inverse of the function $f : R \rightarrow {x \in R : x < 1}$ given by $f(x)=\dfrac{e^{x}-e^{-x}}{e^{x}+e^{-x}},$ is 
Question 55 :
If $5^{k^2}(25^{2k})(625) = 25\sqrt{5}$ and $k < -1$, find the value of $k$.
