# JEE Main 2021 24th 1st Shift February Math Question Paper || JEE Main 2021 Math question paper for February 24

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. The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a moving point of the parabola, is another parabola whose directrix is:

【1】 x = a
【2】 x = 0
【3】 x=-a/2
【4】 x = a/2

【2】 x = 0

2. A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number offoreigners as Indians. Then the number of ways, the committee can beformed is:

【1】 560
【2】 1050
【3】 1625
【4】 575

【3】 1625

3. The equation of the plane passing through the point (1, 2, -3)and perpendicular to the planes
3x + y – 2z = 5 and 2x – 5y – z = 7,is:

【1】 3x – 10y – 2z + 11 = 0
【2】 6x – 5y – 2z – 2 = 0
【3】 11x + y + 17z + 38 = 0
【4】 6x – 5y + 2z + 10 = 0

【3】 11x + y + 17z + 38 = 0

4. A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 1/4. Three stones A, B and C are placed at the points (1, 1), (2, 2) and (4, 4) respectively. Then which of these stones is/are on the path of the man ?

【1】 B only
【2】 A only
【3】 All the three
【4】 C only

【1】 B only

5. The statement among the following that is a tautology is:

【1】 A ∧ (A ∨ B)
【2】 B → [A ∨ (A → B)]
【3】 A ∨ (A ∧ B)
【4】 [A ∧ (A → B)] → B

【1】 A ∧ (A ∨ B)

6. Let ƒ : R → R be defined as ƒ(x) = 2x – 1 and g : R – {1} → R be defined as Then the composition function ƒ(g(x)) is :

【1】 Both one-one and onto
【2】 Onto but not one-one
【3】 Neither one-one nor onto
【4】 One-one but not onto

【4】 One-one but not onto

7. If ƒ : R → R is a function defined by where [] denotes the greatest integer function, then ƒ is :

【1】 discontinuous only at x = 1
【2】 discontinuous at all integral values of x except at x = 1
【3】 continuous only at x = 1
【4】 continuous for every real x

【4】 continuous for every real x

8. The function  (1)

9. The distance of the point (1,1,9) from the point of intersection of the line and the plane x + y + z = 17 is:

【1】 √38
【2】 19√2
【3】 2√19
【4】 38

【1】 √38

10. is equal to :

【1】 2/3
【2】 0
【3】 1/15
【4】 3/2

【1】 2/3

11. Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:

【1】 25
【2】 20√3
【3】 30
【4】 25√3

【4】 25√3

12. If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1:2 is :

【1】 −2t3
【2】 -t3
【3】 0
【4】 2t3

【1】 −2t3

13. The area (in sq. units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is :

【1】 24π + 3√3
【2】 12π + 3√3
【3】 12π – 3√3
【4】 24π – 3√3

【4】 24π – 3√3

14. If where c is a constant of integration, then the ordered pair (a, b) is equal to :

【1】 (1, -3)
【2】 (1, 3)
【3】 (-1, 3)
【4】 (3, 1)

【2】 (1, 3)

15. The population P = P(t) at time ‘t’ of a certain species follows the differential equation dp/dt = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is :

【1】 ½ loge 18
【2】 2loge 18
【3】 loge9
【4】 loge18

【2】 2loge 18

16. The value of –15C1 + 2.15C2 – 3.15C2 +…. – 15.15C15 + 14C7 + 14C2 + 14C3 + … + 14C11 is:

【1】 214
【2】 213 – 13
【3】 216 – 1
【4】 213 – 14

【4】 213 – 14

17. An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :

【1】 3/16
【2】 1/2
【3】 5/16
【4】 1/32

【2】 1/2

18. Let p and q be two positive numbers such that p + q = 2 and p4 + q4 = 272. Then p and q are roots of the equation :

【1】 x2 – 2x + 2 = 0
【2】 x2 – 2x + 8 = 0
【3】 x2 – 2x + 136 = 0
【4】 22 – 2x + 16 = 0)

【4】 22 – 2x + 16 = 0)

19. If satisfies the equation t2 – 9t + 8 = 0, then the value of 【1】 3/2
【2】 2√3
【3】1/2
【4】 √3

【3】1/2

20. The system of linear equations

3x – 2y – kz = 10
2x – 4y – 2z = 6
x + 2y – z = 5m

is inconsistent if :

【1】 k = 3, m = 4/5
【2】k ≠ 3, m ∈ R
【3】 k ≠ 3, m ≠ 4
【4】 k = 3, m ≠ 4/5

【4】 k = 3, m ≠ 4/5

 Section B

21. Let where α ∈ R. Suppose Q = [qij] is a matrix satisfying PQ = kl3 for some non-zero k ∈ R. If q23 = -k/8 and |Q|=k²/2, then α² + K² is equal to………..

15

22. Let B1 (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1, occur is α , only B2 occurs is β  and only B3 occurs is γ. Let p be the probability that none of the events B1 occurs and these 4 probabilities satisfy the equations (α – 2β)p = αβ and (β – 3γ) p = 2βγ (All the probabilities are assumed to lie in the interval (0, 1)). Then p(B1)/p(B2)is equal to :

6

23. The minimum value of a for which the equation – a has at least one solution in (0, π/2) is —

9

24. If one of the diameters of the circle x² + y² – 2x – 6y + 6 = 0 is a chord of another circle ‘C’ whose center is at (2, 1), then its radius is .

3

25. is equal to –

1

26. IF (|x|+|x–2|) dx = 22, (a > 2) and [x] denotes the greatest integer ≤ x, then (x+[x])dx is equal to __

3

27. Let three vectors , and be such that is coplanar with and , . = 7 and is perpendicular to  where and then the value of 2| + + |2 is ____ .

75

28. Let A = {n ∈ N : n is a 3-digit number} B = {9k +2 : k ∈ N} and C = {9k +  : k ∈ N} for some (0 < < 9)

If the sum of all the elements of the set A (B ∪ C) is 274 x 400, then ℓ is equal to ……….

.

5

29. If the least and the largest real values of α , for which the equation z + α |z – 1| + 2i = 0 (z ∈ and i = √-1) has a solution, are p and q respectively; then 4(p2+ q3) is equal to ……….. .

10

30. Let M be any 3 x 3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of MTM is seven, is______ .

540

Contents

## JEE Main Solved Paper Question Answer With Solutions

### JEE Main 2021 Paper with Solutions

 ⚫ JEE Main 2021 Paper with Solutions –  24th February – Shift 1 1. JEE Main Physics Question Paper 2. JEE Main Chemistry Question Paper 3. JEE Main Maths Question Paper