As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

(b) √(2+√5-√(6-3√5+√(14-6√5) ) )

^{2})) )

^{2}))

**Q2.**If Î±≠Î² and Î±

^{2}=5Î±-3,Î²

^{2}=5Î²-3, then the equation having Î±/Î² and Î²/Î± as its roots is

(b) Given, Î±

^{2}-5Î±+3=0 and Î²

^{2}-5Î²+3=0

^{2}+Î²

^{2}=(50+26)/4=19

^{2}-x(Î±/Î²+Î²/Î±)+Î±Î²/Î±Î²=0

^{2}-x((Î±

^{2}+Î²

^{2})/Î±Î²)+1=0

^{2}-19x+3=0

**Q3.**For the equation 1/(x+a)-1/(x+b)=1/(x+c), if the product of the roots is zero, then the sum of the roots is

(d) Since, (b-a)/(x

^{2}+(a+b)x+ab)=1/(x+c)

^{2}+2ax+ab+ca-bc=0

**Q4.**If the equation x

^{3}-3x+a=0 has distinct roots between 0 and 1, then the value of a is

(d) Let f(x)=x

^{3}-3x+a

^{2}-3=0

**Q5.**Let [x] denote the greatest integer less than or equal to x. Then, in [0,3] the number of solutions of the equation x

^{2}-3x+[x]=0, is

(c) We have the following cases:

^{2}-3x+[x]=0

^{2}-3x=0

^{3}-3x+[x]=0

^{2}-3x+1=0

^{2}-3x+[x]=0

^{2}-3x+2=0

**Q6.**If the equations ax

^{2}+bc+c=0 and 2x

^{2}+3x+4=0 have a common root, then a∶b∶c

(a) The equation 2x

^{2}+3x+4=0 has complex roots which always occur in pairs.

**Q7.**If Î± and Î² are the solutions of the quadratic equation ax

^{2}+bx+c=0 such that Î²=Î±

^{(1/3)}, then

**Q8.**If Î± and Î² are roots of the quadratic equation x

^{2}+4x+3=0, then the equation whose roots are 2Î±+Î² and Î±+2Î² is

(d) Given, Î±,Î² are the roots of equation x

^{2}+4x+3=0

^{2}+4Î±Î²+Î±Î²+2Î²

^{2}=2(Î±+Î²)

^{2}+Î±Î² =2(-4)

^{2}+3=35

^{2}-(sum of roots)x+(product of roots)=0

^{2}+12x+35=0

**Q9.**The number of real solution of the equation (9/10)=-3+x-x

^{2}is

(a) Let f(x)=-3+x-x

^{2}

^{2}-4(3)=-11<0

^{2}<0

**Q10.**If the roots of the equation 8x

^{3}-14x

^{2}+7x-1=0 are in GP, then the roots are

(a) Since, the roots of the equation 8x

^{3}-14x

^{2}+7x-1=0 are in GP.

^{3}=1/8⇒Î±=1/2 and hence,Î²=1/2. So, roots are 1, 1/2,1/4.