Question 1 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be
Question 2 :
Solve the following simultaneous equations by the method of equating coefficients.$\displaystyle \frac{x}{2}+3y=11; \, \, x+5y=20$
Question 4 :
The greatest number which divides $134$ and $167$ leaving $2$ as remainder in each case is
Question 5 :
When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder is 4. The remainder is z when x+y is divided by 5. The value of $\dfrac { 2z-5 }{ 3 } $ is
Question 6 :
$\alpha $ and $\beta $ are zeroes of polynomial $x^{2}-2x+1,$ then product of zeroes of a polynomial having zeroes $\dfrac{1}{\alpha }$  and    $\dfrac{1}{\beta }$ is
Question 8 :
Divide $\displaystyle x\left( x+1 \right) \left( x+2 \right) \left( x+3 \right)$ by $\left( x+3 \right) \left( x+2 \right) $
Question 10 :
The probability of choosing randomly a number c from the set $\{1, 2, 3, ..........9\} $ such that the quadratic equation $x^2+ 4x +c=0$ has real roots is:
Question 11 :
If $\displaystyle r_{1}\:$ and $ r_{2}$ are the roots of $\displaystyle x^{2}+bx+c=0$ and $\displaystyle S_{0}=r_{1}^{0}+r_{2}^{0}$, $\displaystyle S_{1}=r_{1}+r_{2}$ and $\displaystyle S_{2}=r_{1}^{2}+r_{2}^{2}$, then the value of $\displaystyle S_{2}+bS_{1}+cS_{0}$ is
Question 12 :
If A(x,0), B(-4,6), and C(14, -2) form an isosceles triangle with AB=AC, then x=
Question 14 :
The coordinates of the point of intersection of X-axis and Y-axis is( 0,0)<br/>State true or false.<br/>
Question 15 :
The point lying on common tangent to the circle $x^2+y^2=4$ and $x^2+y^2+6x+8y-24=0$ is
Question 16 :
There cannot be more than two tangents to a circle parallel to a given secant.
Question 17 :
There is a Pythagorean triplet whose one member is $6$ and other member is $10$
Question 18 :
In a right triangle, the square of the hypotenuse is $x$ times the sum of the squares of the other two sides. The value of $x$ is:<br/>
Question 19 :
$\tan \theta$ increases as $\theta$ increases.<br/>If true then enter $1$ and if false then enter $0$.<br/>
Question 20 :
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 21 :
Maximum value of the expression $\begin{vmatrix} 1+{\sin}^{2}x & {\cos}^{2}x & 4\sin2x \\ {\sin}^{2}x & 1+{\cos}^{2}x & 4\sin2x \\ {\sin}^{2}x & {\cos}^{2}x & 1+4\sin2x \end{vmatrix}=$
Question 22 :
The perimeters of two similar triangles is in the ratio $3 : 4$. The sum of their areas is $75$ sq. cm. Find the area of each triangle in sq. cm.
Question 23 :
If the diameter of a circle is increased by 200% then its area is increased by<br>
Question 24 :
Area of a circle with diameter 'm' radius 'n' and circumference 'p' is
Question 26 :
If a right circular cone and a cylinder have equal circles as their base and have equal heights, then the ratio of their volumes is 2 : 3.<br>
Question 27 :
Find the volume of the frustum cone whose base and topradius is 20 ft and 10 ft respectively. The height of the cone is 300 ft. (Use $\pi$= 3).
Question 28 :
If the events $A$ and $B$ mutually exclusive events such that $P(A)=\dfrac {1}{3}(3x+1)$ and $P(B)=\dfrac {1}{4}(1-x)$, then the aet of possible values of $x$ lies in the interval:
Question 29 :
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 ______________.
