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) b^{2} = a^{2} + c^{2} + 3d^{2}

(2) b^{2} = 3 (a^{2 }+ c^{2}) – 9d^{2}

(3) b^{2} = 3 (a^{2} + c^{2}) + 9d^{2}

(4) b^{2} = 3 (a^{2 }+ c^{2 }+ d^{2})

**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 + log _{e}5) + 2(a – 7) cot (x/2) sin^{2 }(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, y ^{2} = 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/d x + 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), log _{10}sinx + log_{10}cosx = -1 and log_{10} (sin x + cos x) = 1/2 (log_{10} 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, x ^{2} + y^{2} = 25 which is tangent to the hyperbola, x^{2}/9- y^{2}/16 = 1 is :**

(1) (x^{2} + y^{2})^{2} – 16x^{2} + 9y^{2} = 0

(2) (x^{2} + y^{2})^{2} – 9x^{2} +144y^{2} = 0

(3) (x^{2} + y^{2})^{2} – 9x^{2} – 16y = 0

(4) (x^{2} + y^{2} )^{2} – 9x^{2} + 16y^{2} = 0

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

(1) 1

(2) n

(3) 2^{n-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 AA ^{T} 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 I _{1} + 2I_{2} 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 C _{1} centered at A with unit radius is drawn. Another circle C_{2} 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 C_{2} 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 ω ^{n} is real, is equal to ________ .**

**29. **

**where ω = and I _{3} be THE identity matrix of order 3. If the determinant of the matrix (P^{-1}AP – I_{3})2 is ∝ω^{2}, 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 – 16^{th} March – Shift 1 |

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JEE Main Physics Question Paper |

2. |
JEE Main Chemistry Question Paper |

3. |
JEE Main Maths Question Paper |