Question 1 :
State whether true or false :<br>$ 8 + ab $ is a binomial
Question 2 :
If $a=\displaystyle \frac{9}{3-b},b=\frac{9}{3-c}$ then the value of $c$ in terms of $a$ is
Question 4 :
Find the value of polynomial $q(z) = 5z^{3} - 4z + \sqrt {2}$ at $z = 2(\sqrt2 = 1.41)$
Question 6 :
By how much is x$^4$ + 4x$^2$y$^2$ + y$^4$ more than x$^4$ - 8x$^2$y$^2$ + y$^4$ ?
Question 8 :
Find the value of the polynomial $4x^{2} - 5x + 3$, when $x = 2$
Question 9 :
Find the sum of the following polynomials and write the degree of the sum so obtained.<br/><br/>$5m^2+3m+8\, ; \, m^3-6m^2+4m\, ; \, m^3-m^2-m+5$
Question 11 :
Three cubes of metal whose edges are 6 cm 8 cm and 10 cm respectively are melted and a single cube is formed What is the length (in cm) of the diagonal of the newly formed cube?
Question 12 :
if $\,x = 3 + 2\sqrt 2 ,\,$ then find the vlaue of$\,{x^{\dfrac{1}{2}}}\, - {x^{\dfrac{1}{2}}}$
Question 13 :
If $a\times b=\dfrac { a }{ b } -\dfrac { b }{ a } $, find $\dfrac { 5\times 6 }{ 6\times 5 } $.
Question 14 :
Rahul's monthly salary is Rs. $2p^2+p-3$. His annual expenditure is Rs. $14p^2+6p-10.$ Find his annual saving.
Question 15 :
${\left( {1 + x} \right)^m}{\left( {1 - x} \right)^n}$ ${x^2}$ $-6$ .Find absolute value at $x=0$
Question 16 :
Coefficient of $x$ in $-9x{ y }^{ 2 }{ z }$ is
Question 17 :
Solve the following equations :<br>$x\left( x+y+z \right) ={ a }^{ 2 },\ y\left( x+y+z \right) ={ b }^{ 2 },\ z\left( x+y+z \right) ={ c }^{ 2 }.$
Question 18 :
If $\displaystyle \frac{1}{x+1}+\frac{2}{y+z}+ \frac{2006}{2006}=1$, find the value of $\displaystyle \frac{x^2}{x^2+x}+\frac{y^2}{y^2+y} + \frac{z^2}{z^2+2006z}$
Question 20 :
A floor which measures $15m\, \times\, 8m$ is to be laid with tiles measuring $50cm\, \times\, 25cm$. Find the number of tiles required.<br/>Further, if a carpet is laid on the floor so that a space of 1 m exists between its edges and the edges of the floor, what fraction of the floor is uncovered.
Question 21 :
The area of a semi circle is  circle is $\displaystyle \dfrac{\pi}{4}$ then the perimeter <br/>
Question 22 :
From a circle of radius 7 cm the largest possible square is cut and removed Find the area of the remaining portion (in cm$\displaystyle ^{2}$)
Question 23 :
The produce of a square field when sold at therate of Rs. 1.50 per 100 sq. metres fetchesRs. 1350. What will be the cost of putting afence all round the field at the rate of 50 paiseper metre?
Question 24 :
Find the area of a circular park whose circumference is $22$m.
Question 25 :
The length of a rectangle is $\left( \cfrac { 6 }{ 5 } \right) $th of its breadth. It its perimeter is $132m$, its area will be ______ .
Question 26 :
The ratio of the areas of the in circle and circumcircle of square is:
Question 27 :
A horse is placed for grazing inside a square field 12 cm long and is tethered to one corner by a rope 8 cm long. The area it can graze is
Question 28 :
A drinking glass is in the shape of a frusturm of a cone of height 14 cm. The diameter of its two circular ends are 4 cm and 2 cm then the capacity glass is -
Question 29 :
The diameters of two wheels are $10$ in. and $14$ in. The smaller makes $50$ more revolutions than the larger in going a certain distance. This distance, in inches, is
Question 30 :
The cost of fencing a circular field at the rate of Rs 12 per meter is Rs 1320 The field is to be ploughed at Rs 2 per $\displaystyle m^{2}$ then of ploughing is $\displaystyle \left ( \pi =\frac{22}{7} \right )$<br/>
Question 31 :
Find the area of the circle if the area of an isosceles right triangle inscribed in it is 18 $\displaystyle cm^{2}$
Question 32 :
A boy walks diagonally across a square lot. What percent does he save by not walking along the edges(approximately)?
Question 34 :
If $x$ and $n$ are both positive integers, such that $\displaystyle { 4 }^{ x }\times{ n }^{ 2 }={ 4 }^{ x+1 }$, then what is the value of $n$?
Question 36 :
In the $5$th term of $(x+y)^n$, the exponent of y is $4$, then the exponent of y in the $8$th term is
Question 38 :
The value of $ \left\{ \sqrt[4] { \left( \dfrac{1}{x} \right) }^{-12} \right\}^{- \frac{2}{3}} , $ when $x=9$ is :
Question 39 :
If $4^{2x + 2} = 64$, then calculate the value of $x $.
Question 40 :
Find the value of $ \left ( 2^{\tfrac{1}{4}}-1 \right )\left ( 2^{\tfrac{3}{4}}+2^{\tfrac{1}{2}}+2^{\tfrac{1}{4}}+1 \right )$
Question 44 :
$\dfrac{2^{n + 4} - 2 \times 2^n}{2 \times 2^{n + 3}} + 2^{-3} = $ ?
