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 in a triangle ABC, AB = 5 units, ∠B = cos ^{–}¹(3/5) and radius of circumcircle of ΔABC is 5 units, then the area (in sq. units) of ΔABC is:**

(1) 6+8√3

(2) 8+2√2

(3) 4+2√3

(4) 10+6√2

**2. Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is:**

(1) 1/9

(2) 1/66

(3) 2/11

(4) 1/11

**3. The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are:**

(1) 10,11

(2) 8, 13

(3) 1,20

(4) 3, 18

**4. Let ^{} is a vector such that angle between then the value of is :**

(1) 2/3

(2) 4

(3) 3

(4) 3/2

**5. The value of the integral is equal to:**

**6. The probability of selecting integers
a ε [-5, 30] such that x² + 2 (a + 4) x – 5a + 64 > 0, for all x ε R, is :**

(1) 1/4

(2) 7/36

(3) 2/9

(4) 1/6

**7. Let y = y(x) be the solution of the differential equation
Then the area of the region bounded by the curves x = 0, x = 1/√2 and y = y(x) in the upper half plane is :**

**8. If α and β are the distinct roots of the equation x² + (3) ^{1/4} x + 3^{1/2} = 0, then the value of α⁹⁶(β^{12}– 1) + % (β¹² -1) is equal to:**

(1) 56 *x* 3²⁵

(2) 52 *x* 3²⁴

(3) 56 *x* 3²⁴

(4) 28 *x* 3²⁵

**9. Let a function ƒ: R→R be defined as **

**where [x] is the greatest integer less than or equal to x. If ƒ is continuous on R, then (a + b) is equal to:**

(1) 5

(2) 3

(3) 2

(4) 4

**10. Let y = y(x) be the solution of the differential equation Then, the value of (y(3))²– is equal to:**

(1) 1 + 4e³

(2) 1 + 4e⁶

(3) 1 – 4e⁶

(4) 1 – 4e³

**11. If z and w are two complex numbers such that |zω| = 1 and arg(z) – arg(ω) = 3Ω/2 then is:
(Here arg(z) denotes the principal argument of complex number z)**

(1) 3π/4

(2) -π/4

(1) -3π/4

(4) π/4

**12. Let [x] denote the greatest integer ≤ x, where x ε R. If the domain of the real valued function **

**a<b<c, then the value of a + b +c is:**

(1) -3

(2) 1

(3) -2

(4) 8

**13. The number of real roots of the equation is :**

(1) 0

(2) 4

(3) 1

(4) 2

**14. The coefficient of x²⁵⁶ in the expansion of (1 – x)¹⁰¹ (x² + x +1)¹⁰⁰ is:**

(1) –^{100}C₁₆

(2) ^{100}C₁₆

(3) ^{100}C₁₅

(4) –^{100}C₁₅

**15. Let the tangent to the parabola S : y²= 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then, the area (in sq. units) of the triangle PQR is equal to:**

(1) 25

(2) 25/2

(3) 15/2

(4) 35/2

**16. Let a be a positive real number such that **

**where [ x] is the greatest integer less than or equal to x. Then, a is equal to:**

(1) 10 + log_{e}3

(2) 10 – log_{e}(1 + e)

(3) 10 + log_{e}2

(4) 10 + log_{e}(1 + e)

**17. Let’a’ be a real number such that the function ƒ(x) = ax² + 6x – 15, x ε R is increasing in (∞, 3/4) and decreasing in (3/4 , ∞). Then the function g(x) = ax² – 6x + 15, x ε R has a:**

(1) ocal minimum at x =-3/4

(2) local maximum at x =3/4

(3) local minimum at x =3/4

(4) local maximum at x =-3/4

**18. Let A = [a _{ij}] be a 3 x 3 matrix, where
Let a function ƒ: R → R be defined as ƒ(x) = det(A). Then the sum of maximum and minimum values of ƒ on R is equal to:**

(1) 20/27

(2) -88/27

(3) -20/27

(4) 88/27

**19. Let be written as
P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to:**

(1) 24

(2) 18

(3) 45

(4) 36

**20. The Boolean expression (p ∧~9)=(q ∨~p) is equivalent to:**

(1) ~ q ⇒ p

(2) p ⇒ ∼ 9

(3) p ⇒ ~ 9

(4) q ⇒ p

Section B |

**21. Let T be the tangent to the ellipse E : x² + 4y² = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = √5 is √5α + β + γ cos ^{–}¹ ( 1/√5) then |α+ β +γ| is equal to……**

**22. The number of rational terms in the binomial
expansion of is ………**

**23. There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is_____**

**24. Let be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle θ, with the vector Then, 36 cos² 2θ is equal to_____**

**25. Let P be a plane passing through the points (1, 0, 1), (1, -2, 1) and (0,1, -2). Let a vector be such that ^{} is parallel to the plane P, perpendicular to and = 2, then (α + β + γ )² equals ______**

**26. Let a, b, c, d be in arithmetic progression with common difference λ. If **

**then value of λ² is equal to_____**

**27. If the value of ^{} is equal to e^{a}, then a is equal to______**

**28. If the shortest distance between the lines
then a is equal to _____**

**29. Let y = mx + c m > O be the focal chord of
y² = -64x, which is tangent to (x + 10)² + y ^{2} = 4. Then, the value of 4√2 (m+c) is equal to_____**

**30. Let A = and B = 7A²⁰ – 20A⁷ + 21, where I is an identity matrix of order 3 x 3. If B = [b _{ij}] then b₁₃ is equal to_____**

## JEE Main Solved Paper Question Answer With Solutions

### JEE Main 2021 Paper with Solutions

⚫ |
JEE Main 2021 Paper with Solutions – 20^{th} July – Shift 1 |

1. |
JEE Main Physics Question Paper |

2. |
JEE Main Chemistry Question Paper |

3. |
JEE Main Maths Question Paper |