दोस्तों यहां पर **JEE Main 2021 20th July Shift 1 Math** का Solved Paper दिया गया है तथा आपको JEE Main का **ऑनलाइन टेस्ट **भी इस वेबसाइट पर दिया गया है।

Section A |

**1. If the sum of an infinite GP a, ar, ar², ar³, ……. is 15 and the sum of the squares of its each term is 150, then the sum of ar², ar⁴, ar⁶,**

(1) 1/2

(2) 2/5

(3) 25/2

(4) 9/2

**2. Let ABC be a triangle with A (-3, 1) and ∠ACB = θ,0 < θ < π/2. If the equation of the median through B is 2x + y – 3 = 0 and the equation of angle bisector of C is 7x – 4y – 1 = 0, then tan θ is equal to :**

(1) 4/3

(2) 1/2

(3) 2

(4) 3/4

**3. Let θε(0,π/2). If the system of linear equations,
(1 + cos²θ) x + sin²θ y + 4 sin3θ z = 0
cos²θ x + (1 + sin²θ) y + 4 sin3θ z = 0
cos²θ x + sin²θ y + (1 + 4 sin3θ) z = 0
has a non-trivial solution, then the value of θ is:**

(1) 4π/9

(2) π/18

(3) 5π/18

(4) 7π/18

**4. The sum of solutions of the equation
is.**

(1) -11π/30

(2) -7π/30

(3) -π/15

(4) π/10

**5. Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = 5/9,is**

(1) 1/4

(2) 2/9

(3) 1/3

(4) 5/12

**6. If the truth value of the Boolean expression
((p v q) ∧ (q → r) ∧ (~r)) → (p ∧ q) is false, then the truth values of the statements p,q,r respectively can be:**

(1) FFT

(2) FTF

(3) TFT

(4) TFF

**7. The value of is:**

(1) 1/4 tan^{-1 }(4)

(2) tan^{-1} (4)

(3) 1/4 tan^{-1} (2)

(4) 1/2 tan^{-1 }(4)

**8. Let y = y(x) be a solution curve of the differential equation (y + 1) tan² x dx + tan x dy + ydx = 0, x ε (0,π/2) If limx→0^{+} xy(x) = 1, then the value of y(π/4) is:**

(1) π/4-1

(2) π/4+1

(3) π/4

(4) -π/4

**9. The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. If α and √β are the mean and standard deviation respectively for correct data, then (α, β) is:**

(1) (11, 25)

(2) (11,26)

(3) (10.5, 26)

(4) (10.5, 25)

**10. let ƒ(x) = 0 < x < 1. Then:**

(1) (1 + x)²ƒ'(x) + 2(ƒ(x))² = 0

(2) (1 – x)² { ƒ'(x) + 2(ƒ(x))² = 0

(3) (1 + x)² ƒ'(x) – 2(ƒ(x))² = 0

(4) (1 – x)²ƒ'(x) – 2((x))² = 0

**11. The sum of the series.
when x = 2 is :**

**12. If ²⁰ Cr is the coefficient of xr in the expansion of (1 + x)²⁰, then the value of is equal to:**

(1) 420 x 2¹⁹

(2) 420 x 2¹⁸

(3) 380 x 2¹⁸

(4) 380 x 2¹⁹

**13. A plane P contains the line x + 2y + 3z + 1 = 0 = x – y – Z – 6, and is perpendicular to the plane-2x + y + z + 8 = 0. Then which of the following points lies on P?**

(1) (1,0,1)

(2) (2,-1,1)

(3) (-1, 1, 2)

(4) (0,1,1)

**14. On the ellipse x^{2}/8 + y^{2}/4 = 1 let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2y = 0. Let S and S’ be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS’ then, the value of (5 – e²). A is:**

(1) 24

(2) 6

(3) 14

(4) 12

**15. The value of d x is:**

(1) log_{e} 4

(2) log_{e} 16

(3) 4 log_{e} (3+2√2)

(4) 2 log_{e} 16

**16. The equation arg(z-1/z+1) represents a circle with:**

(1) centre at (0, -1) and radius √2

(2) centre at (0, 1) and radius 2

(3) centre at (0, 1) and radius √2

(4) centre at (0,0) and radius √2

**17. If a line along a chord of the circle 4x² + 4y² + 120x + 675 = 0, passes through the point (-30, 0) and is tangent to the parabola y² = 30x, then the length of this chord is :**

(1) 5

(2) 3√5

(3) 7

(4) 5√3

**18. Let is a vector such that is equal to :**

(1) -2

(2) 6

(3) 2

(4) -6

**19. If A = **

**Q = A ^{T}BA, then the inverse of the matrix A Q^{2021} A^{T} is equal to :**

**20. Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set**

(1) {80,83, 86, 89}

(2) {79, 81, 83, 85}

(3) {84, 87, 90, 93}

(4) {84, 86, 88, 90}

Section B |

**21. The sum of all integral values of k (k≠ 0) for which the equation in x has no real roots, is ____**

**22. The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1), (1, 1) is 18 units. is a circle of diameter d. Then d ^{2} is equal to_____**

**23. If y = y(x) is an implicit function of x such that loge (x + y) = 4xy, then d ^{2}y/dx^{2} at x = 0 is equal to _____**

**24. The area of the region
S = {(x, y): 3x² ≤ 4y ≤ 6x + 24 } is_____**

**25. Let a, b ε R,b ≠ 0. Define a function
**

**If f is continuous at x = 0, then 10 – ab is equal to ____**

**26. If ¹P₁ +2.²P₂, +3.³P₃ +…..15. ¹⁵P₁₅ = ^{q}P_{r} – s,**

0 ≤ s ≤ 1, then ^{q+s}C_{r-s} is equal to______

**27. A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then (4/π+1) k is equal to ____**

**28. Let the line L be the projection of the line :
in the plane x – 2y – Z = 3. If d is the distance of the point (0, 0, 6) from L, then d² is equal to___**

**29. Let Then the value of
is ___**

**30. The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is______**

## JEE Main Solved Paper Question Answer With Solutions

### JEE Main 2021 Paper with Solutions

⚫ |
JEE Main 2021 Paper with Solutions – 26^{th} August – Shift 1 |

1. |
JEE Main Physics Question Paper |

2. |
JEE Main Chemistry Question Paper |

3. |
JEE Main Maths Question Paper |