JEE Main 2021 20th July Shift 1 Math Question Paper || JEE Main 2021 Math question paper for July 20th

दोस्तों यहां पर 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 = cos¹(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

(1) 6+8√3

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

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(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

(1) 10,11

4. Let is a vector such that angle between then the value of is :

(1) 2/3
(2) 4
(3) 3
(4) 3/2

(4) 3/2

5. The value of the integral is equal to:

(4)

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

(3) 2/9

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 :

(3)

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

(2) 52 x 3²⁴

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

(2) 3

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

(3) 1 – 4e⁶

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

(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

(3) -2

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

(1) 0
(2) 4
(3) 1
(4) 2

(1) 0

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

(3) 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

(2) 25/2

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)

(3) 10 + loge2

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

(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

(2) -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

(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

(2) p ⇒ ∼ 9

 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 cos¹ ( 1/√5) then |α+  β +γ| is equal to……

1.25

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

21

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_____

777

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_____

4

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 ______

81

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

then value of λ² is equal to_____

1

27. If the value of is equal to ea, then a is equal to______

3

28. If the shortest distance between the lines

then a is equal to _____

6

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_____

34

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_____

910

Contents

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