Question 2 :
............. states that for any two positive integers $a$ and $b$ we can find two whole numbers $q$ and $r$ such that $a = b \times q + r$ where $0 \leq r < b .$
Question 3 :
Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion$\displaystyle \frac{7}{210}$
Question 4 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 6 :
Euclid's division lemma states that for two positive integers a and b, there exist unique integers q and r such that $a = bq + r$, where r must satisfy<br>
Question 7 :
Assem went to a stationary shop and purchased $3$ pens and $5$ pencils for $Rs.40$. His cousin Manik bought $4$ pencils and $5$ pens for $Rs. 58$. If cost of $1$ pen is $Rs.x$, then which of the following represents the situation algebraically?
Question 8 :
A choir is singing at a festival. On the first night $12$ choir members were absent so the choir stood in $5$ equal rows. On the second night only $1$ member was absent so the choir stood in $6$ equal rows. The same member of people stood in each row each night. How many members are in the choir?
Question 9 :
If the system of equation, ${a}^{2}x-ay=1-a$ & $bx+(3-2b)y=3+a$ possesses a unique solution $x=1$, $y=1$ then:
Question 10 :
What is the nature of the graphs of a system of linear equations with exactly one solution?
Question 11 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is
Question 12 :
What must be added to $x^3-3x^2-12x + 19$, so that the result is exactly divisible by $x^2 + x-6$?
Question 13 :
State whether the following statement is true or false.After dividing $ (9x^{4}+3x^{3}y + 16x^{2}y^{2}) + 24xy^{3} + 32y^{4}$ by $ (3x^{2}+5xy + 4y^{2})$ we get<br/>$3x^{2}-4xy + 8y^{2}$
Question 15 :
Find the Quotient and the Remainder when the first polynomial is divided by the second.$-6x^4 + 5x^2 + 111$ by $2x^2+1$
Question 16 :
Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.$49x^2-81$<br/>
Question 17 :
In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $
Question 18 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 19 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.
Question 20 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $a$ when $c=25 \ cm$ and $b=7 \ cm$.
Question 21 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$
Question 22 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>
Question 23 :
Find the value of $x$ if the distance between the points $(2, -11)$ and $(x, -3)$ is $10$ units.
Question 24 :
Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0
Question 25 :
A(2,6) and B(1,7) are two vertices of a triangle ABC and the centroid is (5,7) The coordinates of C are
Question 26 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 27 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is
Question 28 :
In what ratio, does $P(4, 6)$ divide the join of $A(-2, 3)$ and $B(6, 7)$
Question 29 :
Find the circumference of the circle with the following radius : 10 cm
Question 30 :
What is the length of arc AB making angle of $126^0$ at center of radius $8$?
Question 31 :
The radius of a circle whose area is equal to the sum of the areas of two circles where radii are 5 cm and 12 cm is
Question 32 :
If the area of a circle is $346.5 \displaystyle cm^{2}$. Its circumference is
Question 34 :
The probability of guessing the correct answer to a certain test is $\displaystyle\frac{x}{2}$. If the probability of not guessing the correct answer to this questions is $\displaystyle\frac{2}{3}$, then $x$ is equal to ______________.
Question 35 :
A biased coin with probability $p , 0 < p < 1 ,$ of heads is tossed until a head appears for thefirst time. If the probability that the number of tosses required is even, is $2 / 5 ,$ then $p$ equal to
Question 36 :
If $ \alpha \epsilon \left[ \frac { \pi  }{ 2 } ,\pi  \right] $ then the value of $\sqrt { 1+sin\alpha  } -\sqrt { 1-sin\alpha  } $ is equal to
Question 37 :
If $\displaystyle 5\tan \theta =4$, then find the value of $\displaystyle \frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }$. 
Question 40 :
The solution of $(2 cosx-1)(3+2 cosx)=0$ in the interval $0 \leq \theta \leq 2\pi$ is-