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# JEE Mains 2019 Question Paper with Solutions- 9 Jan M1

If you want JEE Main solutions for free then you landed on right page. This blog contains quality solutions for JEE Mains 2019 9th January shift 1.

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Posted by Mahak Jain, 2/2/2021 Hesap Oluştur

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Attempting question papers is best way to practice. In this blog you have JEE Mains 2019 question paper with solutions for 9th January shift 1.

Before starting with JEE Mains 2019 question paper with solutions, let me tell you some tips to prepare better and score higher.

1. Know the syllabus and exam paper pattern. Click here to know the same.

2. One should be aware of previous year chapter wise weightage. Click here to know the chapter wise weightage of JEE Mains previous year paper.

3. Make a proper schedule. While planning out a schedule for JEE Mains preparation, it will be beneficial for you to have a properly structured schedule. Click here to read a short article on time management.

4. List down all equations and formulas. Best practice to remember and study Mathematics chapters is to list down all the equations and formulas that are used in that chapter. It is advisable to list down the equations and theories in a separate notebook, which you can refer to while solving questions.

5. Clear your concepts. Join with Kunduz private tutoring service to learn from best tutors. Read more about Kunduz private service here.

## JEE Mains 2019 Question Paper with Solutions- 9 January Shift 1

### Mathematics

#### Question 1

The area (in sq. units) bounded by the parabola y=x2-1, the tangent at the point (2,3) to it and y-axis is:

1. 14/3
2. 56/3
3. 8/3
4. 32/3

Question 2

The maximum volume (in cu.m) of the right circular cone having slant height 3 m is:

1. 3√3 π
2. 6 π
3. 2√3 π
4. 4/3 π

Question 3

For x2 ≠ nπ + 1, n∊N (the set of natural numbers), the integral is equal to:

(where c is a constant of integration)

Question 4

Let α and β be two roots of the equations x2+2x+2=0. Then, α1515 is equal to:

1. -256
2. 512
3. -512
4. 256

#### Question 5

If y=y(x) is the solution of the differential equation, xdy/dx + 2y = x2 satisfying y(1) =1, then y(1/2) is equal to

1. 7/64
2. 13/16
3. 49/16
4. 1/4

Question 6

Equation of a common tangent to the circle, x2+y2-6x=0 and the parabola y2=4x is:

1. 2√3 y = 12x + 1
2. √3 y = x + 3
3. 2√3 y = -x – 12
4. √3 y = 3x + 1

Question 7

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be members of the same team, is:

1. 200
2. 300
3. 500
4. 350

Question 8

Three circles of radii a,b,c (a<b<c) touch each other externally. If they have x-axis as a common tangent, then:

1. 1/√a = 1/√b + 1/√c
2. 1/√b = 1/√a + 1/√c
3. a,b,c are in AP
4. √a, √b, √c are in AP

Question 9

If the fractional part of the number 2403/3 is k/15. Then k is equal to:

1. 14
2. 6
3. 4
4. 8

#### Question 10

Axis of a parabola lies along the x-axis. It its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

1. (4,-4)
2. (5,2√6)
3. (8,6)
4. (6,4√2)

Question 11

The plane passing through the intersection of the planes x+y+z=0 and 2x+3y-z+4=0 and parallel to y axis also passes through the point:

1. (-3,0,-1)
2. (-3,1,1)
3. (3,3,-1)
4. (3,2,1)

Question 12

If a, b and c be three distinct real numbers in G.P and a+b+c=xb. Then x cannot be:

1. 4
2. -3
3. -2
4. 2

Question 13

Consider the set of all lines px+qy+r=0 such that 3p+2q+4r=0. Which one of the following statements is true?

1. The lines are all parallel
2. Each line passes through the origin.
3. The lines are not concurrent.
4. The lines concurrent at the point (0.75,0.5)

Question 14

The system of linear equations

x + y + z = 2

2x + 3y + 2z = 5

2x + 3y + (a2-1)z = a+1

1. has infinitely many solutions for a=4
2. is inconsistent when |a|=√3
3. is inconsistent when a=4
4. has a unique solution for |a|=√3

#### Question 15

Let a,b,c be vectors. Let a=i-j, b=i+j+k and c be the vector such that a✖c+b=0 and a.c=4. Then c2 is equal to

1. 19/2
2. 8
3. 17/2
4. 9

Question 16

Let a1, a2,………….., a30 be an AP,

and

If a5=27 and S-2T=75. Then a10 is equal to:

1. 57
2. 47
3. 42
4. 52

Question 17

5 students of a class have an average height of 150 cm and variance of 18cm2 . A new student whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is:

1. 22
2. 20
3. 16
4. 18

Question 18

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of the number of aces obtained in the two drawn cards. Then P(X=1) + P(X=2) equals:

1. 52/169
2. 25/169
3. 49/169
4. 24/169

Question 19

For x∊R-{0,1}, let f1(x)=1/x , f2(x)=1-x anf f3(x)=1/(1-x) be three given functions. If a function, J(x) satisfies (f2∘J∘f1)(x)=f3(x). Then J(x) is equal to

1. f3(x)

2. f1(x)

3. f2(x)

4. x-1f(x)

#### Question 20

Let

Then the sum of the elements in A is:

1. 5π/6
2. 2π/3
3. 3π/4
4. π

Question 21

If θ denotes the acute angle between the curves, y=10-x2 and y=2+x2 at a point of their intersection, then |tanθ| is equal to:

1. 4/9
2. 7/17
3. 8/17
4. 8/15

Question 22

If

, then the matrix A-50 when θ = π/12, is equal to:

Question 23

Let 0<θ<π/2. If the eccentricity of the hyperbola

is greater than 2, then the length of its latus rectum lies in the interval

1. (2,3]
2. (3,∞)
3. (3/2,2]
4. (1,3/2]

Question 24

The equation of the line passing through (-4,3,1), parallel to the plane x+2y-z=0 and intersecting the line (x+1)/-3 = (y-3)/2 = (z-2)/-1 is:

1. (x+4)/-1 = (y-3)/1 = (z-1)/1
2. (x+4)/3 = (y-3)/-1 = (z-1)/1
3. (x+4)/1 = (y-3)/1 = (z-1)/3
4. (x-4)/2 = (y+3)/1 = (z+1)/4

#### Question 25

For any θ ∈ (π/4, π/2), the expression 3(sinθ – cosθ)4 + 6(sinθ + cosθ)2 + sin6θ equals:

1. 13 – 4cos2θ + 6sin2θcos2θ

2. 13 – 4cos6θ

3. 13 – 4cos2θ + 6cos4θ

4. 13 – 4cos4θ + 2sin2θcos2θ

Question 26

If cos-1(2/(3x)) + cos-1(3/(4x))=π/2 (x > 3/4). Then x is equal to:

1. 1√145/12
2. 2√145/10
3. 3√146/12
4. 4√145/11

Question 27

The value of

is :

1. 2/3
2. 0
3. -4/3
4. 4/3

Question 28

If the Boolean expression (p⨁q) ∧ (~p⨀q) is equivalent to p∧q, where ⨁, ⨀ ∊ {∧, ∨}. Then the ordered pair (⨁, ⨀) is:

1. (∧, ∨)
2. (∨, ∨)
3. (∨, ∧)
4. (∧, ∧)

Question 29

1. exists and equals 1/4√2
2. does not exist
3. exists and equals 1/2√2
4. exists and equals 1/(4+2√2)

#### Question 30

Let f:R→R be a function defined as

then f is:

1. continuous if a=5 and b=5

2. continuous if a=-5 and b=10

3. continuous if a=0 and b=5

4. not continuous for any values of a and b

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