Question 3 :
Sum of two negative integers always gives a numbersmaller than both the integers.

Question 4 :
Let n> 2 be an integer and $\displaystyle f:P\rightarrow R$ a function defined on the set of points in the plane, with the property that for any regular n-gon $\displaystyle A_{1}A_{2}... A_{n},$ $\displaystyle f\left ( A_{1} \right )+f\left ( A_{2} \right )+ ... +F\left ( A_{n} \right )= 0.$ Prove that f is the zero function. 

Question 5 :
The difference between the greatest and the smallest 4-digit numbers that can be formed by the digits $5,3,0\ and\ 8$ such that 5 is always at the ones place and no digits are repeated is

Question 6 :
If n  is an integer between 0  to 25, then the minimum value of $n!\left( {25 - n} \right)!$  is 

Question 7 :
If the range of $15,14,x,25,30,35$ is $23$, then the least possible value of $x$ is<br>

Question 8 :
Let $ x,y,z$ be three observations. The mean of these observation is&#160;

Question 10 :
<p class="wysiwyg-text-align-left">By which congruency are the following pair of triangles congruent:<br/></p><p class="wysiwyg-text-align-left">In $\Delta\,ABC$ and $\Delta \,DEF$, $\angle\,B = \angle\,E = 90\,^{\circ}, AC = DF$ and $BC = EF.$</p>

Question 11 :
In $\displaystyle \Delta DEF, \angle D={ 87 }^{ o }$ and $ \angle F={ 43 }^{ o }$ . If&#160;$\displaystyle \Delta DEF\cong \Delta BAC$,&#160;then find the measure of $\displaystyle \angle A$.

Question 12 :
In $\bigtriangleup ABC and&#160;\bigtriangleup QRP, AB =QR,\angle B=\angle R\:and \: \angle C=\angle P.$ By A.S.A, $\triangle ABC$ and $\triangle QRP$ are similar

Question 13 :
Multiplication of the numbers $\displaystyle 1\frac{1}{3} \times&#160;\displaystyle 3\frac{1}{4} \times&#160;\displaystyle \frac{7}{8}$ gives ____ .

Question 15 :
Construct an isosceles$\triangle ABC,$ where base $AB=7\ cm$ and $\angle ABC=50^{o}$. Also, find the measure of $\angle ACB$.

Question 16 :
The sides $A B , B C , C A$ of a triangle $A B C$ have $3,4$ and $5$ interior points respectively on them. Thenumber of triangles that can be constructed using these points as vertices is

Question 17 :
Find the value of following polynomial by taking $x = 1$ and $a = 2$:<br/>$3x^4-ax^3+5x-3$

Question 18 :
The counter example of the statement, "The roots of $x^2-6x-112=0$are natural numbers"?

Question 19 :
The area of a rectangle whose length is $5$ units more than twice its width is $75$ square units. What is its width?

Question 20 :
An article is sold at $20\%$ profit. If is cost price is increased by Rs. $50$ and at the same time if its selling price is also increases by Rs. $30$ ,&#160;the percentage of profit decrease by $\dfrac {10}{3}\%$. Find the cost price approximately.

Question 21 :
Two&#160;partners invest Rs. $12,500$ and Rs. $8,500$ respectively in their business and&#160;arrange that $60$% of the profit should be divided equally between them and the&#160;remaining profit treated as interest on the capital. If one partners share is Rs. $300$ more than that of the other, find the whole amount of the profit.

Question 22 :
By selling a certain number of goods for Rs.&#160;<span class="MathJax_Preview"><span class="MathJax"><span class="math"><span class="mrow"><span class="mn">5<span class="mo">,<span class="mn">500<span class="MJX_Assistive_MathML">5,500, a shopkeeper loses equal to one-tenth of their selling price. Find the loss&#160;percent.

Question 23 :
Simple interest on a certain amount is&#160;$\displaystyle \frac{9}{16}$ of the principal. If the number representing the rate of interest in percent and time in year be equal then the time is-

Question 24 :
The ratio of the number of sides of a square and the number of edges of a cube is

Question 26 :
State whether the statement are true (T) or false (F).<br>If an isosceles triangle has more than one line of symmetry, then it need not be an equilateral triangle.

Question 27 :
Fill in the blanks.<br/>Rotation turns an object about a&#160; <u>&#160;&#160;</u><u>P&#160; </u>&#160;point. The fixed point is the centre of <u>&#160;&#160;</u><u>Q&#160; &#160;</u><u></u>. The angle by which the object rotates is the&#160; <u></u><u>&#160;&#160;</u><u>R&#160; </u>.<br/>Then, P&#160; &#160;Q&#160; &#160;R is:

Question 30 :
Reena’s mother said, to make idlis, you must take two parts rice and one part urad dal. What percentage of such a mixture would be urad dal?