# JEE Main 2021 16th March Shift 1 Math Question Paper || JEE Main 2021 Math question paper for 16th March

दोस्तों यहां पर  का Solved Paper दिया गया है तथा आपको JEE Main का ऑनलाइन टेस्ट भी इस वेबसाइट पर दिया गया है।

 Section A

1. Consider three observations a, b and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true ?

(1) b2 = a2 + c2 + 3d2
(2) b2 = 3 (a2 + c2) – 9d2
(3) b2 = 3 (a2 + c2) + 9d2
(4) b2 = 3 (a2 + c2 + d2)

(4) b2 = 3 (a2 + c2 + d2

2. Let a vector αi + βj be obtained by rotating the vector √3i + j by an angle 45° about the origin in counter clockwise direction in the first quadrant. Then the area of triangle having vertices (α, b), (0, β) and (0, 0) is equal to :

(1) 1
(2) 1/2
(3) 1/√2
(4) 2√2

(2) 1/2

3. If for a > 0, the feet of perpendiculars from the points A (a, -2a, 3) and B (0, 4, 5) on the plane lx + my + nz = 0 are points C (0, -a, -1) and Drespectively, then the length of line segment CD is equal to :

(1) √41
(2) √55
(3) √131
(4) √166

(4) √166

4. The range of a ε R for which the function ƒ(x) = (49 – 3) (x + loge5) + 2(a – 7) cot (x/2) sin(x/2), x ≠ 2nm, n ε N
has critical points, is :

(1) [-4/3,2]
(2) [1,∞)
(3) (-∞,-1]
(4) (-3,1)

(1) [-4/3,2]

5. Let the functions ƒ: R → R and g : R → be defined as : Then, the number of points in R where (ƒog) (x) is NOT differentiable is equal to :

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

(1) 1

6. Let a complex number z, |z| ≠ 1, satisfy ≤ 2.Then, the largest value of |z| is equal to ________ .

(1) 5
(2) 8
(3) 6
(4) 7

(4) 7

7. A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :

(1) 3/4
(2) 52/867
(3) 39/50
(4) 22/425

(3) 39/50

8. If n is the number of irrational terms in the expansion of then, (n−1) is divisible by :

(1) 8
(2) 26
(3) 7
(4) 30

(2) 26

9. Let the position vectors of two points P and Q be respectively. Let R. and S be two points such that the direction ratios of lines PR and QS are (4,-1, 2) and (-2,1,-2) respectively. Let lines PR and QS intersect at T. If the vector is perpendicular to both and the length of vector is √5 units, then the modulus of a position vector of A is :

(1) √5
(2) √171
(3) √227
(4) √482

(2) √171

10. If the three normals drawn to the parabola, y2 = 2x pass through the point (a,0) a ≠ 0, then’d’ must be greater than:

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

(1) 1

11. Let is equal to :

(1) tan-1(3/2)
(2) cot-1(3/2)
(3) π/2
(4) tan-1(3)

(2) cot-1(3/2)

12. The number of roots of the equation, (81)sin2x +(81)cos2x = 30 in the interval [0, π] is equal to :

(1) 3
(2) 2
(3) 4
(4) 8

(3) 4

13. If y = y (x) is the solution of the differential equation, dy/dx + 2y tanx = sinx, y(π/3)=0, then the maximum value of the function y(x) over R is equal to :

(1) 8
(2) 1/2
(3) -15/4
(4) 1/8

(4) 1/8

14. Which of the following Boolean expression is a tautology ?

(1) (p ∧ 9) ∧ (p → 9)
(2) (p ∧ 9) ∨ (p ∨ q)
(3) (p ∧ 9) ∨ (p → 9)
(4) (p ∧ 9) → (p → 9)

(4) (p ∧ 9) → (p → 9)

15. Let Then, the system of linear equations has :

(1) No solution
(2) Exactly two solutions
(3) A unique solution
(4) Infinitely many solutions

(1) No solution

16. If for x ε (0,π/2), log10sinx + log10cosx = -1 and log10 (sin x + cos x) = 1/2 (log10 n – 1), n > 0, then the value of n is equal to :

(1) 16
(2) 20
(3) 12
(4) 9

(3) 12

17. The locus of the midpoints of the chord of the circle, x2 + y2 = 25 which is tangent to the hyperbola, x2/9- y2/16 = 1 is :

(1) (x2 + y2)2 – 16x2 + 9y2 = 0
(2) (x2 + y2)2 – 9x2 +144y2 = 0
(3) (x2 + y2)2 – 9x2 – 16y = 0
(4) (x2 + y2 )2 – 9x2 + 16y2 = 0

(4) (x2 + y2 )2 – 9x2 + 16y2 = 0

18. Let [x] denote greatest integer less than or equal to x. If for  is equal to :

(1) 1
(2) n
(3) 2n-1
(4) 2

(1) 1

19. Let P be a plane lx + my + nz = 0 containing the line, . If plane P divides the line segment AB joining points A(-3, -6, 1) and B(2, 4, -3) in ratio k : 1 then the value of k is equal to :

(1) 1.5
(2) 2
(3) 4
(4) 3

(2) 2

20. The number of elements in the set {x ε R: (|x| -3) |x + 4| = 6} is equal to :

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

(1) 2

 Section B

21. Let ƒ : (0, 2) → R be defined as ƒ (x) = . Then, is equal to ______ .

1

22. The total number of 3 x 3 matrices A having entries from the set {0, 1, 2, 3} such that the sum of all the diagonal entries of AAT is 9, is equal to __________.

766

23. Let ƒ : R → R be a continuous function such that ƒ(x) + ƒ(x + 1) = 2, for all x ε R. If then the value of I1 + 2I2 is equal to _______ .

16

24. Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these two series is equal to _______.

3

25. If the normal to the curve at a point (a, b) is parallel to the line x + 3y = -5, a > 1, then the value of |a + 6b] is equal to ________ .

406

26. If then a + b + c is equal to _________.

4

27.  Let ABCD be a square of side of unit length. Let a circle C1 centered at A with unit radius is drawn. Another circle C2 which touches C and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E. If the length of EB is α + √3β, where α, β are integers, then α + β is equal to _______.

28. Let z and ω be two complex number such that and Re(ω) has mininum value. Then, the minimusm value of n ε N for which ωn is real, is equal to ________ .

29. where ω = and I3 be THE identity matrix of order 3. If the determinant of the matrix (P-1AP – I3)2 is ∝ω2, then the value of ∝ is equal to ___________ .

36

30. Let the curve y = y (x) be the solution of the differential equation, dy/dx = 2(x+1). If the numerical value of area bounded by the curve y = y(x) and x-axis is 4√8/3 , then the value of y(1) is equal to _________ .

Contents

## JEE Main Solved Paper Question Answer With Solutions

### JEE Main 2021 Paper with Solutions

 ⚫ JEE Main 2021 Paper with Solutions – 16th March – Shift 1 1. JEE Main Physics Question Paper 2. JEE Main Chemistry Question Paper 3. JEE Main Maths Question Paper