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.

**Q1.**If e

^{cosx}-e

^{-cosx }=4, then the value of cosx is

(d) Let e

^{cosx}=y.

^{cosx}-e

^{(-cosx )}=4

^{2}-4y-1=0

^{cosx}=2+√5⇒cosx=log

_{e}(2+√5)

_{e}(2+√5)>1 and cosx≤1

**Q2.**If the sum of the squares of the roots of the equation x

^{2}-(sinÎ±-2)x-(1+sinÎ± )=0 is least, then Î±=

(c) Let p,q be the roots of the given equation.

^{2}+q

^{2}=(p+q)

^{2}-2pq

^{2}+q

^{2}=(sinÎ±-2 )

^{2}+2(1+sinÎ±)

^{2}+q

^{2}=sin

^{2}Î±-2 sinÎ±+6=(sinÎ±-1 )

^{2}+5

^{2}+q

^{2}is last when sinÎ±-1=0

**Q3.**Number of real roots of the equation (6-x)

^{4}+(8-x)

^{4}=16 is

(b) Put (6-x+8-x)/2=y

^{4}+(y+1)

^{4}=16

^{4}+6y

^{2}+1=8 ⇒y

^{4}+6y

^{2}-7=0

^{2}=1,-7 ⇒y

^{2}=1 (∵y

^{2}=-7 is not possible)

**Q4.**If x

^{2}+ax+10=0 and x

^{2}+bx-10=0 have a common root, then a

^{2}-b

^{2}is equal to

(d) Let Î± be a common root of the equations x

^{2}+ax+10=0 and x

^{2}+bx-10=0.

^{2}+a Î±+10=10 and, Î±

^{2}+b Î±-10=0

^{2}+Î±(a+b)=0 and (a-b)Î±+20=0 ⇒Î±=-(a+b)/2 and Î±=-20/(a-b) ⇒-(a+b)/2=-20/(a-b)⇒a

^{2}-b

^{2}=40

**Q5.**If a and b are the non-zero distinct roots of x

^{2}+ax+b=0, then the least value of x

^{2}+ax+b is

(c) Since a,b are roots of x

^{2}+ax+b=0.

^{2}+a

^{2}+b=0 and, b

^{2}+ab+b=0

^{2}and b+a+1=0

^{2}+a+1=0

^{2}-a-1=0

^{2}+ax+b is -((a

^{2}-4b)/4)=-((1+8)/4)=-9/4

**Q6.**For a≠b, if the equation x

^{2}+ax+b=0 and x

^{2}+bx+a=0 have a common root, then the value of a+b equals

(a) Let Î± be the common root for both the equations x

^{2}+ax+b=0 and x

^{2}+bx+a=0, then Î±

^{2}+aÎ±+b=0 And Î±

^{2}+bÎ±+a=0 ⇒ Î±

^{2}/((a

^{2}-b

^{2}))=Î±/(b-a)=1/(b-a) ∴ Î±

^{2}=-(a+b) and Î±=1 Hence, a+b=-1

**Q7.**The expression tan{i log((a-ib)/(a+ib)) } reduces to

(b) We have, log((a-ib)/(a+ib)) =log(a-ib)-log(a+ib) =[log√(a

^{2}+b

^{2})+i tan

^{-1}((-b)/a) ]-[log√(a

^{2}+b

^{2})+i tan

^{-1}(b/a) ] =-2i tan

^{-1}(b/a) ∴i log((a-ib)/(a+ib))=2 tan

^{-1}(b/a)=tan

^{-1}((2 b/a)/(1-b

^{2}/a

^{2}))=tan

^{-1}((2 ab)/(a

^{2}-b

^{2})) ⇒tan{i log((a-ib)/(a+ib)) }=tan{tan

^{-1}((2 ab)/(a

^{2}-b

^{2})) }=(2 ab)/(a

^{2}-b

^{2})

**Q8.**7

^{(2 log75 )}is equal to

(c) 7

^{(2 log75 )}=7

^{(log7(52) )}=(5)

^{2}=25 [∵a

^{logax}=x;x>0,x≠0,1]

**Q9.**The value of expression 2(1+Ï‰)(1+Ï‰

^{2})+3(2+Ï‰)(2+Ï‰

^{2})+4(3+Ï‰)(3+Ï‰

^{2})+⋯+(n+1)(n+Ï‰)(n+Ï‰

^{2}), where Ï‰ is an imaginary cube root of unity is

(c) {n(n+1)/2}

^{2}+n

**Q10.**If cosÎ±+2 cosÎ²+3 cosÎ³=sinÎ±+ 2sinÎ²+ 3sinÎ³=0, then the value of sin3 Î±+ 8sin 3 Î²+ 27sin 3 Î³ is

(c) Let Î±=cosÎ±+i sinÎ±,b=cosÎ²+i sinÎ² and, c=cosÎ³+i sinÎ³

^{3}+8 b

^{3}+27 c

^{3}=18 abc