{"id":194007,"date":"2022-06-16T12:49:48","date_gmt":"2022-06-16T07:19:48","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?p=194007"},"modified":"2023-04-09T17:11:21","modified_gmt":"2023-04-09T11:41:21","slug":"jee-main-mathematics-chapter-wise-important-questions","status":"publish","type":"post","link":"https:\/\/www.aakash.ac.in\/blog\/jee-main-mathematics-chapter-wise-important-questions\/","title":{"rendered":"JEE Main 2023 Mathematics Chapter-wise Important Questions"},"content":{"rendered":"

\"jee<\/a><\/p>\n

Practice and conceptual knowledge are simple ways to command <\/span>Mathematics<\/span> for the JEE Mains exam. <\/span>JEE Mains exam<\/span> comprises <\/span>Physics<\/span>, <\/span>Chemistry<\/span>, and Mathematics with equal weightage. Although the <\/span>syllabus<\/span> is vast and time is tight, hard work and smart learning techniques always let you stand ahead.<\/span><\/p>\n

This article will help you understand the difficulty level of Mathematics questions in JEE Mains<\/a>.<\/span><\/p>\n

Also See:\u00a0JEE Main 2022 Exam Live Updates<\/a><\/p>\n

Chapter-wise Important Questions for JEE Mains<\/b><\/h4>\n

Chapter 1: Sets, Relations, and Functions<\/b><\/p>\n

1. If log2x+logx2 = 52 = log2y + logy2 and xy, then find the value of x+y-2.<\/p>\n

log<\/span>2<\/span>x<\/span>+<\/span>log<\/span>x<\/span>2<\/span> = <\/span>5<\/span>2<\/span> = <\/span>log<\/span>2<\/span>y<\/span> + <\/span>log<\/span>y<\/span>2<\/span><\/p>\n

t + <\/span>1<\/span>t<\/span> = <\/span>5<\/span>2<\/span>, s + <\/span>1<\/span>s<\/span> = <\/span>5<\/span>2<\/span>; where t = <\/span>log<\/span>2<\/span>x<\/span>, s = <\/span>log<\/span>2<\/span>y<\/span><\/p>\n

t = 2, <\/span>1<\/span>2<\/span> and s = 2, <\/span>1<\/span>2<\/span> (as <\/span>t<\/span>s<\/span>, <\/span>x<\/span>y<\/span>)<\/span><\/p>\n

t = 2, s = <\/span>1<\/span>2<\/span>\u00a0 and t = <\/span>1<\/span>2<\/span> , s = 2<\/span><\/p>\n

log<\/span>2<\/span>x<\/span> = 2 and <\/span>log<\/span>2<\/span>y<\/span> = <\/span>1<\/span>2<\/span><\/p>\n

x = 4 and y = <\/span>2<\/span><\/p>\n

Hence, <\/span>x+y-<\/span>2<\/span> = 4 + <\/span>2<\/span> –<\/span>2<\/span> = 4.<\/span><\/p>\n

2. What is the range of sin-1(x\u00b2+1x\u00b2+2)?<\/p>\n

Here, <\/span>x\u00b2+1<\/span>x\u00b2+2<\/span> = <\/span>1-<\/span>1<\/span>x\u00b2+2<\/span><\/p>\n

Now, 2 <\/span> x<\/span>2<\/span> + 2 < <\/span> for all x <\/span> R<\/span><\/p>\n

1<\/span>2 <\/span>1<\/span>x\u00b2+2<\/span>>0<\/span><\/p>\n

–<\/span>1<\/span>2 <\/span>–<\/span>1<\/span>x\u00b2+2<\/span><0 <\/span><\/p>\n

1<\/span>2 <\/span>1-<\/span>1<\/span>x\u00b2+2<\/span><1<\/span><\/p>\n

6<\/span>sin<\/span>-1<\/span>(1-<\/span>1<\/span>x\u00b2+2<\/span>)<<\/span>2<\/span><\/p>\n

Hence, Range is [<\/span>6<\/span>,<\/span>2<\/span>).<\/span><\/p>\n

Chapter 2: Complex Numbers and Quadratic Equations<\/b><\/p>\n

1. The addition of all positive integral values of \u2018a\u2019, a [1, 500] for which the equation [x]\u00b3 + x – a = 0 has a solution. Find it.<\/p>\n

a is integer then x must be an integer, i.e., [x] = x.<\/span><\/p>\n

[x]\u00b3 + x – a = 0<\/span><\/p>\n

[x]\u00b3 + x = a<\/span><\/p>\n

1<\/span>a<\/span>500<\/span><\/p>\n

1<\/span>x<\/span>7<\/span>, x <\/span> 1<\/span><\/p>\n

a<\/span>i<\/span>=<\/span>x=1<\/span>7<\/span>(<\/span>x<\/span>3<\/span>+x)<\/span> = 812<\/span><\/p>\n

2. Find the least integral value of \u2018a\u2019 if (a – 3)x2 + 12x + (a + 6) >0 x R.<\/p>\n

ax<\/span>2<\/span>+bx+c>0 <\/span> x <\/span> R<\/span><\/p>\n

a > 0, D < 0<\/span><\/p>\n

(a – 3) > 0 and (a +9)(a – 6), a > 6<\/span><\/p>\n

Hence, least integral value of a = 7.<\/span><\/p>\n

Chapter 3: Matrices and Determinants<\/b><\/p>\n

1.Find the value of |a|, if the system of equations x + ay = 0, az + y = 0, ax + z = 0 has an infinite solution.<\/p>\n

x + ay = 0 <\/span> x = – ay<\/span><\/p>\n

ax + z = 0 <\/span> -a<\/span>2<\/span>y+z=0<\/span><\/p>\n

az + y = 0 <\/span> a<\/span>3<\/span>y+y=0<\/span><\/p>\n

a<\/span>3<\/span> = -1 <\/span> a = -1<\/span><\/p>\n

Hence, |a| = 1.<\/span><\/p>\n

2. A square matrix A is said to be nilpotent of index m. If Am=0, now, if for this A<\/p>\n

(1 – A)<\/span>n<\/span>=1+A+<\/span>A<\/span>2<\/span>+…+<\/span>A<\/span>m-1<\/span>, then find the value of n.<\/span><\/p>\n

Let B = <\/span>1+A+<\/span>A<\/span>2<\/span>+…+<\/span>A<\/span>m-1<\/span><\/p>\n

B <\/span>(1 – A)<\/span>n<\/span>= <\/span>(1 – A)<\/span>n<\/span>(<\/span>1+A+<\/span>A<\/span>2<\/span>+…+<\/span>A<\/span>m-1<\/span>)<\/span><\/p>\n

B <\/span>(1 – A)<\/span>n<\/span> = 1 – <\/span>A<\/span>m<\/span><\/p>\n

B (1 – A)<\/span>n<\/span> = 1, (as <\/span>A<\/span>m<\/span>=0<\/span>)<\/span><\/p>\n

B = <\/span>(1 – A)<\/span>-n<\/span><\/p>\n

n = -1<\/span><\/p>\n

Check our visual story on 5 Reasons Why You Must Attempt JEE Main Mock Tests<\/strong><\/p>\n

5 Reasons Why You Must Attempt JEE Main Mock Tests<\/a><\/p><\/blockquote>\n