Question 1 :
If $\displaystyle x^{2}+y^{2}-2x+6y+10=0,$ and x-3y=10, then the value of $\displaystyle x^{2}+y^{2}$ is
Question 3 :
Before Robert Norman worked on 'Dip and Field Concept', his predecessor thought that the tendency of the magnetic needle to swing towards the poles was due to a point attractive. However, Norman showed with the help of experiment that nothing like point attractive exists. Instead, he argued that magnetic power lies is lodestone. Which one of the following is the problem on which Norman and others worked?
Question 5 :
For the expression $ax^2 + 7x + 2$ to be quadratic, the necessary condition is<br>
Question 6 :
<div><span>Check whether the following is a quadratic equation.</span></div><div><span>$(x - 3) (2x + 1) = x (x + 5)$</span><br/></div>
Question 8 :
<span>Check whether the given equation is a quadratic equation or not.</span><br/>${ x }^{ 2 }+2\sqrt { x } -3$
Question 9 :
The difference of two natural numbers is $4$ and the difference of their reciprocals is $\dfrac{1}{3}$. Find the numbers.
Question 11 :
Hugo lies on top of a building, throwing pennies straight down to the street below. The formula for the height $H$, that a penny falls is $H=Vt+5{t}^{2}$, where $V$ is the original velocity of the penny (how fast Hugo throws it when it leaves his hand) and $t$ is equal to the time it takes to hit the ground. The building is $60$ metres high, and Hugo throws the penny down at an initial speed of $20$ meters per second. How long does it take for the penny to hit the ground,
Question 12 :
The sum of two numbers is $12$ and their product is $20$. Find the numbers.<br/>
Question 13 :
If $s = a + 2\; and \;t =a- 2$, which of the following represents the product of s and t <span>for every number $a$ ?</span>
Question 14 :
The difference between a two-digit number and the number obtained by interchanging the position of the digits is $45$. What is the difference between the digits of that number?
Question 15 :
If $\left (a + \dfrac {1}{a}\right )^{2} = 3$, then the value of $a^{6} - \dfrac {1}{a^{6}}$ will be
Question 16 :
Sum of a number and its reciprocal is $5\dfrac { 1 }{ 5 } $. Then the required equation is
Question 18 :
The quadratic equation $ax^2+bx+c=0$ will have real and distinct roots if :
Question 20 :
If $a + b + c = 2s$, then the value of $(s - a)^{2} + (s - b)^{2} + (s - c)^{2}$ will be
Question 22 :
If $\alpha, \beta$ are the roots of the equation $2x^{2} - 3x - 6 = 0$, then the equation whose roots are $\alpha^{2} + 2$ and $\beta^{2} + 2$ is
Question 23 :
If $x = 3t, y = 1/ 2(t + 1)$, then the value of $t$ for which $x = 2y$ is
Question 24 :
The rectangular fence is enclosed with an area $16$cm$^{2}$. The width of the field is $6$ cm longer than the length of the fields. What are the dimensions of the field?<br/>
Question 25 :
If $|2x + 3|\le 9$ and $2x + 3 < 0$, then