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JEE Mains 2019 Question Paper with Solutions- 9 Jan M1

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Posted by Mahak Jain, 2/2/2021
JEE Mains 2019 Question Paper with Solutions- 9 Jan M1

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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.

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

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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.

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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

Correct answer: 3

JEE Mains 2019 Question Paper with Solutions 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

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

Correct answer: 3

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

Question 3

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

\int x\sqrt{\frac{2\sin(x^2-1) - \sin2(x^2 -1)}{2\sin(x^2-1) + \sin2(x^2 -1)}}dx is equal to:

(where c is a constant of integration)

1.  \log_e |\frac{1}{2}\sec^2(x^2 -1)| +c
2.
\frac{1}{2}\log_e |\sec^2(x^2 -1)| +c
3.\frac{1}{2}\log_e \left |\sec^2\left (\frac{x^2 -1}{2} \right )\right | +c
4.\log_e \left |\sec^2\left (\frac{x^2 -1}{2} \right )\right | +c

Correct answer: 1

For x2 ≠ nπ + 1, n∊N (the set of natural numbers), the integral JEE Mains 2019 Question Paper with Solutions

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

Correct answer: 1

Let α and β be two roots of the equations x2+2x+2=0. Then, α15+β15 is equal to

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

Correct answer: 3

JEE Mains 2019 Question Paper with Solutions 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

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

Correct answer: 2

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

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

Correct answer: 2

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 JEE Mains 2019 Question Paper with Solutions

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

Correct answer: 1

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

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

Correct answer: 4

If the fractional part of the number 240/3 is k/15. Then k is equal to JEE Mains 2019 Question Paper with Solutions

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)

Correct answer: 3

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

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)

Correct answer: 4

JEE Mains 2019 Question Paper with Solutions 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

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

Correct answer: 4

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

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)

Correct answer: 4

Consider the set of all lines px+qy+r=0 such that 3p+2q+4r=0. Which one of the following statements is true JEE Mains 2019 Question Paper with Solutions

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

Correct answer: 2

The system of linear equations x + y + z = 2 2x + 3y + 2z = 5 2x + 3y + (a2-1)z = a+1

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

Correct answer: 1

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 JEE Mains 2019 Question Paper with Solutions

Question 16

Let a1, a2,………….., a30 be an AP,

S = \sum_{i = 1}^{30}a_i

 and  

T = \sum_{i = 1}^{15}a_{(2i-1)}

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

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

Correct answer: 4

Let a1, a2,.............., a30 be an AP, If a5=27 and S-2T=75. Then a10 is equal to

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

Correct answer: 2

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 JEE Mains 2019 Question Paper with Solutions

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

Correct answer: 2

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

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)

Correct answer: 1

JEE Mains 2019 Question Paper with Solutions 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

Question 20

Let 

A = \left\{ \theta \in \left (-\frac{\pi}{2}, \pi \right ): \frac{3+2 i\sin\theta}{1-2i\sin\theta} \textup{\;is\;purely\;imaginary}\right \}

 Then the sum of the elements in A is:

  1. 5π/6
  2. 2π/3
  3. 3π/4
  4. π

Correct answer: 2

Then the sum of the elements in A is

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

Correct answer: 4

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 JEE Mains 2019 Question Paper with Solutions

Question 22

If 

A = \begin{bmatrix} \cos\theta & \sin\theta\\ \sin\theta & \cos\theta \end{bmatrix}

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

1.\begin{bmatrix} \frac{\sqrt3}{2} &\frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt3}{2} \end{bmatrix}
2.\begin{bmatrix} \frac{1}{2} &\frac{\sqrt3}{2} \\ -\frac{\sqrt3}{2} & \frac{1}{2} \end{bmatrix}
3.\begin{bmatrix} \frac{1}{2} &-\frac{\sqrt3}{2} \\ \frac{\sqrt3}{2} & \frac{1}{2} \end{bmatrix}
4.\begin{bmatrix} \frac{\sqrt3}{2} &\frac{1}{2} \\ \frac{1}{2} & \frac{\sqrt3}{2} \end{bmatrix}

Correct answer: 1

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 

\frac{x}{\cos^2\theta} - \frac{y}{\sin^2\theta} = 1

 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]

Correct answer: 2

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 JEE Mains 2019 Question Paper with Solutions

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

Correct answer: 2

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

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

Correct answer: 2

JEE Mains 2019 Question Paper with Solutions For any θ ∈ (π/4, π/2), the expression 3(sinθ - cosθ)4 + 6(sinθ + cosθ)2 + sin6θ equals

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

Correct answer: 1

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

Question 27

The value of 

\int_{0}^{\pi}|\cos x|^3dx

 is :

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

Correct answer:

JEE Mains 2019 Question Paper with Solutions The value of cos cube x is

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. (∧, ∧)

Correct answer: 1

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

Question 29

\lim_{y\rightarrow 0} \frac{\sqrt{1+\sqrt{1+y^4}}- \sqrt2}{y^4}
  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)

Correct answer: 1

JEE Mains 2019 question paper with solutions

Question 30

Let f:R→R be a function defined as

f(x)=\left\{\begin{matrix} 5, & if &x\leq 1 \\ a+bx, &if &1<x<3 \\b+5x , &if &3\leq x<5 \\ 30,& if &x\geq 5 \end{matrix}\right.

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

Correct answer: 4

Let f:R to R be a function defined as

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