Question 1 :
The degree of the polynomials  $p(y) = y^{3}, q(y) = (1-y^{4})$  are<br/>
Question 4 :
$p(y) = 5y^3 - 2y^2 + y + 10$ is a polynomial in $y$ of degree
Question 5 :
If one of the zeros of a quadratic polynomial of the form $x^2 + ax + b$ is the negative of the other, then it<br>
Question 6 :
If $\alpha$,$\beta$ are zero of quadratic polynomial $\displaystyle kx^2 + 6x + 6 $, then find the value of k such that $ \displaystyle ( \alpha + \beta )^2 2\alpha \beta = 24 $
Question 7 :
The degree of the expression<br>$(1+x)(1+{ x }^{ 6 })(1+{ x }^{ 11 })........(1+{ x }^{ 101 })$<br>is
Question 9 :
Firs term of an arithmetic progression is $2$. If the sum of its first five terms is equal to one-fourth of the sum of the next five terms, then the sum of its first $30$ terms is
Question 10 :
Find the sum of the first $25$ terms of an A.P whose $n$th term is given by ${a}_{n}=8-3n$
Question 11 :
A man arranges to pay off a debt of Rs. 3600 in 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid he dies leaving one-third of the debt unpaid. Find the value of the first instalment. 
Question 12 :
I<span>f the sum of an AP is the same for $p$ terms as for the $q$ terms , Find the sum for $(p+q)$ terms</span>
Question 13 :
How many terms of the $ AP -5, \frac{-9}{2}, -4, $ .... will give the sum $0$?
Question 14 :
How many terms of the AP 6, 12, 18, 24,.... must be take to make the sum 816?
Question 15 :
Solve for $x$ and $y$ by using method of substitution :<br>$0.2x+0.3y=1.3$; $0.4x+0.5y=2.3$
Question 16 :
The cost of 9 chairs and 3 tables is Rs. 306, while the cost of 6 chairs and 3 tables is Rs. 246. Then the cost of 6 chairs and 1 table is
Question 18 :
The difference between two numbers is $ 7$  and their sum is $35$. What will be their product?
Question 19 :
Using substitution method find the value of x and y:<br><span>$x - 9y = 18$ and $-x + 3y = -15$<br></span>
Question 20 :
<span>Based on equations reducible to linear equations</span><br/><span>Solve for x and y: </span><span>$\dfrac {24}{2x+y}-\dfrac {13}{3x+2y}=2; \dfrac {26}{3x+2y}+\dfrac {8}{2x+y}=3$</span>
Question 21 :
The cost of an article $A$ is $15$% less than that of article $B.$ If their total cost is $2,775\:Rs\:;$ find the cost of each article$.$ <br>
Question 22 :
If the same photograph is printed in different sizes, then we say both the photographs are<span><br/></span>
Question 23 :
If the corresponding sides of two triangles are proportional, then the two triangles are similar by which test
Question 26 :
If $\triangle ABC\sim \triangle  PQR,$  $ \cfrac{ar(ABC)}{ar(PQR)}=\cfrac{9}{4}$,  $AB=18$ $cm$ and $BC=15$ $cm$, then $QR$ is equal to:
Question 27 :
Let $WXYZ$ be a square. Let $P,Q,R$ be the mid points of $WX, XY$ and $ZW$ respectively and $K,L$ be the mid-points of $PQ$ and $PR$ respectively. What is the value of $\cfrac { area\quad of\quad triangle\quad PKL }{ area\quad of\quad square\quad WXYZ } $?
Question 28 : Match the column.<br/><table class="wysiwyg-table"><tbody><tr><td>1. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$<br/></td><td>(a) AA similarity criterion </td></tr><tr><td>2. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,<br/>$\displaystyle \angle A=\angle P,\angle B=\angle Q$<br/><br/></td><td>(b) SAS similarity criterion </td></tr><tr><td>3. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$<br/>$\angle A=\angle P$<br/></td><td>(c) SSS similarity criterion </td></tr><tr><td>4. In $\displaystyle \Delta ACB,DE||BC$<br/>$\displaystyle \Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$<br/></td><td>(d) BPT</td></tr></tbody></table>
Question 29 : <div><span>One card is drawn from a well-shuffled deck of $52$ cards. Find the probability of getting a spade.</span></div>
Question 30 : <div><span>When a die is thrown, list the outcomes of an event of getting:</span><br/></div>I. A prime number,<br/>II. Not a prime number.<br/>
Question 31 : There are $50$ students in a class and their results is below:<span class="wysiwyg-font-size-medium"> </span><span class="wysiwyg-font-size-medium"><br/></span><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">Result (Pass/Fail)</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">Pass</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">Fail</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">No. of students</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$35$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$15$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr></tbody></table><p>If a student chosen at random out of the class (i.e., without any bias), find the probability that the student is not failing (i.e., the student passed the examination).</p>
Question 32 :
A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a spade or a king ?
Question 33 :
A pair of dies is thrown, find the probability of getting a total of numbers is more than $10$.
Question 34 :
<span>Two dices are thrown simultaneously. What is the probability of getting two numbers whose product is even?</span>
Question 35 :
<span>A box contains $20$ cards marked with the numbers $ 1 $ to $20$. One card is drawn from this box at random. What is the probability that number on the card is a multiple of $5$?</span>
Question 37 : <span>Calculate mode for the following data shows the number of colour pencils the students have in a class.<br/></span><table class="wysiwyg-table"><tbody><tr><td>Colour Pencils</td><td>$0-5$</td><td>$5-10$</td><td>$10-15$</td><td>$15-20$</td><td>$20-25$</td><td>$25-30$</td></tr><tr><td>Number of students</td><td>$14$</td><td>$16$</td><td>$17$</td><td>$13$</td><td>$8$</td><td>$12$</td></tr></tbody></table>
Question 38 :
<span>The marks obtained by $20$ students in maths are $35,  40,  78,  30,  50,  78,  36,  65,  78,  40,  30,  65,  50,  35,  80,  95,  80,  36,  95,  35$. Find the Arithmetic mean of the students by direct method.</span>
Question 39 : Consider the following data:<br><table class="wysiwyg-table"><tbody><tr><td>$X$</td><td>$1$</td><td>$2$</td><td>$3$</td><td>$4$</td><td>$5$</td></tr><tr><td>$f$</td><td>$3$</td><td>$5$</td><td>$9$</td><td>-</td><td>$2$</td></tr></tbody></table>The arithmetic mean of the above distribution is $2.96$. What is the missing frequency?
Question 40 : The mode of the following series is 36. Find the missing frequency in it<br/><table class="wysiwyg-table"><tbody><tr><td>Class interval</td><td>0-10</td><td>10-20</td><td>20-30</td><td>30-40</td><td>40-50</td><td>50-60</td><td>60-70</td></tr><tr><td>Frequency</td><td>8</td><td>10</td><td>......</td><td>16</td><td>12</td><td>6</td><td>7</td></tr></tbody></table>
Question 41 :
Find the positive value of x if the distance between the points (x, -1) and (3, 2) is 5.
Question 42 :
Find $a$ if the distance between $(a , 2)$ and $(3 , 4)$  is $8 $.
Question 46 :
$\triangle ABC$ has vertices $A(-11, 4), B(-3, 8)$, and $C(3, -10)$. The coordinates of the center of the circle circumscribed about $\triangle ABC$ are
Question 47 :
The mid point of the segment joining $(2a, 4)$ and $(-2, 2b)$ is $(1, 2a+1)$, then value of b is
