दोस्तों यहां पर JEE Main 2021 16th March 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. 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)
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
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. The range of a ε R for which the function ƒ(x) = (49 – 3) (x + loge5) + 2(a – 7) cot (x/2) sin2 (x/2), x ≠ 2nm, n ε N
has critical points, is :
(1) [-4/3,2]
(2) [1,∞)
(3) (-∞,-1]
(4) (-3,1)
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
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
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
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
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
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
11. Let 
is equal to :
(1) tan-1(3/2)
(2) cot-1(3/2)
(3) π/2
(4) tan-1(3)
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
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
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)
15. Let 
Then, the system of linear equations 
has :
(1) No solution
(2) Exactly two solutions
(3) A unique solution
(4) Infinitely many solutions
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
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
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
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
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
| Section B |
21. Let ƒ : (0, 2) → R be defined as ƒ (x) = 
. Then, 
is equal to ______ .
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 __________.
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 _______ .
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 _______.
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 ________ .
26. If 
then a + b + c is equal to _________.
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 ___________ .
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 _________ .
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 |
