## [LATEST]\$type=sticky\$show=home\$rm=0\$va=0\$count=4\$va=0

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 x,1,z are in A.P. and x,2,z are in G.P., then x,4,z are in
•  A.P
•  G.P
•  H.P
•  None of the these
Solution
We have, ├ █(x,1,z are in AP⇒2=x+z@x,2,z are in GP⇒4=xz)} …(i) Since (i) does not satisfy 8=x+z and 16=xz. But, it satisfies the relation 4=(2 xz)/(x+2). Hence, x,4,z are in HP

Q2.The correct statement is
•  0.5+0.55+0.555+... to n terms =5n/9-5/81(1-10^(-n))
•  8+88+888+...+ to n terms=80/81 (10^n-1)-8n/9
•  1^2+(1^2+2^2 )+(1^2+2^2+3^2 )+...to n terms =(n(n+1)^2 (n+2))/12
•   All are correct
Solution
(d) We have, (a) 0.5+0.55+0.555+...=5/9 [0.9+0.99+0.999+...] =5/9[(1-0.1)+(1-0.01)+(1-0.001)+...to n terms] =5/9[(1+1+...to n terms)-├ (1/10+1/10^2 +1/10^3 +...+to n term)] =5/9 [n-(1/10 {1-1/10^n })/(1-1/10)] =5n/9-5/81 (1-10^(-n) ) (b) 8+88+888+...to n terms =8/9[9+99+999+...to n terms] =8/9[(10-1)+(10^2-1)+(10^3-1)+...to n terms] =8/9[(10+10^2+10^3+⋯+to n terms)-(1+1+1+…+to n terms)] =8/9 [10(10^n-1)/(10-1)-n] =80/81 (10^n-1)-8n/9 (c) the nth terms in the sequence is x_n=1^2+2^2+3^2+...+n^2 =(n(n+1)(2n+1))/6 =1/3 n^3+1/2 n^2+1/6 n ∴ The required sum =∑▒x_n =1/3 ∑▒〖n^3+1/2〗 ∑▒〖n^2+1/6〗 ∑▒n =1/3 [n(n+1)/2]^2+1/2.(n(n+1)(2n+1))/6+1/6.n(n+1)/2 =n(n+1)/12[(n+1)+(2n+1)+1 =n(n+1)/2 [n^2+3n+2] =n(n+1)/2(n+1)(n+2) =(n(n+1)^2 (n+2))/12

Q3.  The value of log_a⁡〖(log_b⁡x)〗/log_b⁡(log_a⁡b ) is
•   log_b⁡a
•  log_a⁡b
•   -log_a⁡b
•   -log_b⁡a
Solution
(c) We have, log_a⁡〖(log_b⁡a)〗/log_b⁡〖(log_a⁡b)〗 =log⁡〖(log_b⁡a)〗/log⁡a ×log⁡b/log⁡〖(log_a⁡b)〗 =log⁡(log⁡a/log⁡b )/log⁡a ×log⁡b/log⁡(log⁡b/log⁡a ) =log⁡〖(log⁡a )-log⁡〖(log⁡b)〗 〗/log⁡a ×log⁡b/log⁡〖(log⁡b )-log⁡〖(log⁡a)〗 〗 =-log⁡b/log⁡a =-log_a⁡b

Q4. If log_12⁡〖27=a,〗 then log_6⁡〖16=〗
•  (3-a)/(3+a)
•  4((3-a)/(3+a))
•  3((4-a)/(4+a))
•  3((4+a)/(4-a))
Solution
(b) We have, log_12⁡〖27=a〗 ⇒log_12⁡〖3^3=a〗 ⇒3 log_12⁡〖3=a〗 ⇒3/a=log_3⁡12 ⇒3/a=log_3⁡〖(2^2×3)=2 log_3⁡〖2+log_3⁡3 〗 〗 ⇒3/a=2 log_3⁡〖2+1〗 ⇒(3-a)/a=2 log_3⁡〖2⇒log_2⁡〖3=2a/(3-a)〗 〗 …(i) Now, log_6⁡〖16=log_6⁡〖2^4=4 log_6⁡〖2=4/log_2⁡6 〗 〗 〗 ⇒log_6⁡〖16=4/log_2⁡〖3+log_2⁡2 〗 〗=4/(2a/(3-a)+1) [Using (i)] ⇒log_6⁡〖16=4((3-a)/(3+a))〗

Q5.Let the sequence, a_1,a_2,a_3,…,a_2n, form an AP, then a_1^2-a_2^2+a_3^2-...+a_(2n-1)^2-a_2n^2 is equal to
•  n/(2n-1)(a_1^2-a_2n^2)
•  2n/(n-1)(a_2n^2-a_1^2)
•  n/(n+1)(a_1^2+a_2n^2)
•  None of these
Solution
Since, a_1,a_2,a_3,…,a_n form an AP. ∴ a_2-a_1=a_4-a_3=...=a_2n-a_(2n-1)=d Let S=a_1^2-a_2^2+a_3^2-a_4^2+...+a_(2n-1)^2-a_2n^2 =(a_1-a_2 )(a_1+a_2 )+(a_3-a_4 )(a_3+a_4 )+...+(a_(2n-1)-a_2n )(a_(2n-1)+a_2n) = -d(a_1+a_2+...+a_2n )=-d(2n/2 (a_1+a_2n )) …(i) Also, we know a_2n=a_1+(2n-1)d ⇒ d=(a_2n-a)/(2n-1) ⇒-d=(a_1-a_2n)/(2n-1) On putting the value of d in Eq, (i), we get S=(n(a_1-a_2n )(a_1+a_2n))/(2n-1)=n/(2n-1)(a_1^2-a_2n^2)

Q6. Which of the following statement is correct?
•  If each earn of an AP a number is added or subtracted, then the series so obtained is also an AP.
•  The nth term of geometric series whose first term is a and common ratio r,is ar^(n-1).
•  If each term of a GP be raised to the same power the resulting terms are in GP.
•  All of the above
Solution

Q7.If log⁡〖2,〗 log⁡〖(2^x-1)〗 and log⁡〖(2^x+3)〗 are in A.P., then 〖2,2〗^x-〖1,2〗^x+3 are in
•  A.P
•  H.P
•  G.P
•  None of these
Solution
We have, log⁡〖2,〗 log⁡〖(2^x-1),〗 log⁡〖(2^x+3)〗 are in A.P. ⇒〖2,2〗^x-〖1,2〗^x+3 are in G.P.

Q8.If x^18=y^21=z^28, then 3,3 log_y⁡〖x,3 log_z⁡〖y,7 log_x⁡z 〗 〗 are in
•  A.P
•  G.P
•  H.P
•  None of these
Solution
Let x^18=y^21=z^28=k Then, 18 log⁡〖x=21 log⁡〖y=28 log⁡〖z=log⁡k 〗 〗 〗 ⇒log_y⁡〖x=21/18,log_z⁡〖y=28/21,log_x⁡〖z=18/28〗 〗 〗 ⇒3 log_y⁡〖x=7/2,3 log_z⁡〖y=4,7 log_x⁡z=9/2〗 〗 ⇒3,3 log_y⁡〖z,3 log_z⁡〖y,7 log_x⁡z 〗 〗 are in A.P.

Q9.The sum of n terms of an A.P. is a n(n-1). The sum of the squares of these terms is
•  a^2 n^2 (n-1)^2
•  a^2/6 n(n-1)(2n-1)
•   (2a^2)/3 n(n-1)(2n-1)
•  (2a^2)/3 n(n+1)(2n+1)
Solution
Let A be the first term and D be the common difference of the AP. Then, S_n=an(n-1) ⇒n/2 {2 A+(n-1)D}=an (n-1) ⇒2A+(n-1)D=2 an-2 a ⇒2A-D=-2 a and D=2 a ⇒A=0,D=2 a The sum of the squares of the n terms of the sequence is S=A^2+(A+D)^2+(A+2D)^2+⋯+{A+(n-1)D}^2 ⇒S=D^2 {1^2+2^2+3^2+⋯+(n-1)^2} ⇒S=4 a^2 (n(n-1)(2n-1))/6=(2 a^2)/3 n(n-1)(2n-1)

Q10. A G.P. consists of an even number of terms. If terms sum of all the terms is 5 times the sum of the terms occupying odd places, the common ration will be equal to
•  2
•  3
•  4
•  5
Solution
Let there be 2n terms in the given G.P. with first term a and the common ratio r. Then, Sum of all terms =5 (Sum of odd terms) ⇒a_1+a_2+⋯+a_2n=5(a_1+a_3+⋯+a_(2n-1) ) ⇒a+ar+ar^2+⋯+ar^(2n-1)=5(a+ar^2+⋯+ar^(2n-2) ) ⇒a ((r^(2 n)-1))/((r-1))=5a ((r^(2 n)-1))/((r^2-1)) ⇒r+1=5 ⇒r=4 ## Want to know more

Please fill in the details below:

## Latest NEET Articles\$type=three\$c=3\$author=hide\$comment=hide\$rm=hide\$date=hide\$snippet=hide

Name

Admissions,1,Alternating Current,60,AP EAMCET 2020,1,Basic Maths,2,BCECE 2020,1,best books for iit jee,2,best coaching institute for iit,1,best coaching institute for iit jee preparation,1,best iit jee coaching delhi,1,best iit jee coaching in delhi,2,best study material for iit jee,4,BITSAT Registration 2020,1,Blog,62,books for jee preparation,1,books recommended by iit toppers,3,Capacitance,3,CBSE,1,CBSE accounts exam,1,CBSE boards,1,CBSE NEET,9,cbse neet 2019,3,CBSE NEET 2020,1,cbse neet nic,1,Centre of Mass,2,Chemistry,58,Class 12 Physics,15,coaching for jee advanced,1,coaching institute for iit jee,2,Collision,2,COMEDK UGET 2020 Application Form,1,COMEDK UGET 2020 Exam Form,1,COMEDK UGET news,1,CUCET 2020,2,Current Electricity,4,CVR college,1,Electromagnetic Induction,3,Electronics,1,Electrostatics,3,Energy,1,Engineering & Medical,1,Fluid Mechanics,4,Gravitation,2,GUJCET 2020 Application Form,1,Heat,4,iit admission,1,iit advanced,1,iit coaching centre,3,iit coaching centre in delhi,2,iit coaching classes,2,iit coaching in delhi,1,iit coaching institute in delhi,1,iit entrance exam,1,iit entrance exam syllabus,2,iit exam pattern,2,iit jee,5,iit jee 2019,3,iit jee advanced,2,iit jee books,3,iit jee coaching,2,iit jee exam,3,iit jee exam 2019,1,iit jee exam pattern,3,iit jee institute,1,iit jee main 2019,2,iit jee mains,3,iit jee mains syllabus,2,iit jee material,1,iit jee online test,3,iit jee practice test,3,iit jee preparation,6,iit jee preparation in delhi,2,iit jee preparation time,1,iit jee preparation tips by toppers,2,iit jee question paper,1,iit jee study material,3,iit jee study materials,2,iit jee syllabus,2,iit jee syllabus 2019,2,iit jee test,3,iit preparation,2,iit preparation books,5,iit preparation time table,2,iit preparation tips,2,iit syllabus,2,iit test series,3,IITJEE,100,IPU CET,1,JEE Advanced,83,jee advanced exam,2,jee advanced exam pattern,1,jee advanced paper,1,JEE Books,1,JEE Coaching Delhi,3,jee exam,3,jee exam 2019,6,JEE Exam Pattern,2,jee exam pattern 2019,1,jee exam preparation,1,JEE Main,85,jee main 2019,4,JEE Main 2020,1,JEE Main 2020 Application Form,2,JEE Main 2020 news,2,JEE Main 2020 Official Answer Key,1,JEE Main 2020 Registration,1,JEE Main 2020 Score,1,JEE Main application form,1,jee main coaching,1,JEE Main eligibility criteria,3,jee main exam,1,jee main exam 2019,3,jee main online question paper,1,jee main online test,3,JEE Main Paper-2 Result,1,jee main registration,2,jee main syllabus,2,JEE mains 2020,1,jee mains question bank,1,jee mains test papers,3,JEE Mock Test,2,jee notes,1,jee past papers,1,JEE Preparation,2,jee preparation in delhi,1,jee preparation material,4,JEE Study Material,1,jee syllabus,6,JEE Syllabus Chemistry,1,JEE Syllabus Maths,1,JEE Syllabus Physics,1,jee test series,3,KCET - 2020,1,Kinematics,1,Latest article,5,Latest Articles,61,Latest News,34,latest news about neet exam,1,Laws of Motion,2,Magnetic Effect of Current,3,Magnetism,3,MHT CET 2020,2,MHT CET 2020 exam schedule,1,Modern Physics,1,NCERT Solutions,15,neet,3,neet 2019,1,neet 2019 eligibility criteria,1,neet 2019 exam date,2,neet 2019 test series,2,NEET 2020,2,NEET 2020 Application Form,1,NEET 2020 Eligibility Criteria,1,NEET 2020 Registration,1,neet application form,1,neet application form 2019 last date,1,Neet Biology Syllabus,1,Neet Books,3,neet eligibility criteria,3,neet exam 2019,7,neet exam application,1,neet exam date,1,neet exam details,1,neet exam pattern,6,neet exam pattern 2019,2,neet examination,1,neet mock test 2019,1,Neet Notes,3,Neet Online Application Form,3,neet online test,2,neet past papers,1,neet physics syllabus,1,neet practice test,2,NEET preparation books,1,neet qualification marks,1,NEET question paper 2019,1,neet question papers,1,neet registration,1,Neet Study Material,3,neet syllabus,6,neet syllabus 2019,5,NEET Syllabus 2020,1,neet syllabus chemistry,1,neet syllabus for biology,1,neet syllabus for physics,1,neet test series,1,neet ug 2019,2,news,5,online study material for iit jee,1,Optical Instruments,1,Physics,110,physics books for iit jee,1,Power,1,Practical Physics,1,Quiz,5,Ray Optics,1,Rotational Motion,3,SHM,3,Simple Harmonic Motion,3,study materials for iit jee,1,Study Notes,110,study notes for iit jee,1,Thermodynamics,4,TS EAMCET Notification,2,Units and Dimensions,1,UPSEE 2020,1,UPSEE 2020 Application Form,2,UPSEE EXAM,1,Vectors,2,VITEE Application form,1,Wave Motion,3,Wave Optics,1,WBJEE 2020 Admit Card,1,WBJEE 2020 Answer Key,1,Work,1,
ltr
item
BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET, IIT JEE COACHING INSTITUTE: SEQUENCE AND SERIES QUIZ-8
SEQUENCE AND SERIES QUIZ-8