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 + 31/2 = 0, then the value of α⁹⁶(β12– 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) –100C₁₆
(2) 100C₁₆
(3) 100C₁₅
(4) –100C₁₅
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 + loge3
(2) 10 – loge(1 + e)
(3) 10 + loge2
(4) 10 + loge(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 = [aij] 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 ea, 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 + y2 = 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 = [bij] 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 – 20th July – Shift 1 |
| 1. | JEE Main Physics Question Paper |
| 2. | JEE Main Chemistry Question Paper |
| 3. | JEE Main Maths Question Paper |
