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Test: JEE Main 2024 January 31 Shift 2 - JEE MCQ


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30 Questions MCQ Test - Test: JEE Main 2024 January 31 Shift 2

Test: JEE Main 2024 January 31 Shift 2 for JEE 2024 is part of JEE preparation. The Test: JEE Main 2024 January 31 Shift 2 questions and answers have been prepared according to the JEE exam syllabus.The Test: JEE Main 2024 January 31 Shift 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: JEE Main 2024 January 31 Shift 2 below.
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Test: JEE Main 2024 January 31 Shift 2 - Question 1

Let A (a, b), B (3, 4) and (−6,−8) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point P(2a + 3,7b + 5) from the line 2x + 3y − 4 = 0 measured parallel to the line x − 2y − 1 = 0 is

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Test: JEE Main 2024 January 31 Shift 2 - Question 2

Let z1 and z2 be two complex numbers such that z1 + z2 = 5 and . Then  equals-

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Now

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Test: JEE Main 2024 January 31 Shift 2 - Question 3

Let a variable line passing through the centre of the circle x2 + y2 - 16x - 4y = 0, meet the positive co-ordinate axes at the point A and B. Then the minimum value of OA + OB, where O is the origin, is equal to

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Test: JEE Main 2024 January 31 Shift 2 - Question 4

Let f, g: (0, ∞) → R be two functions defined by and  Then the value of   is equal to

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Test: JEE Main 2024 January 31 Shift 2 - Question 5

Let (α, β, γ) be mirror image of the point (2, 3, 5) in the line Then 2α + 3β + 4γ is equal to

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Direction Ratios of PQ

Test: JEE Main 2024 January 31 Shift 2 - Question 6

Let P be a parabola with vertex (2, 3) and directrix  . Let an ellipse of eccentricity pass through the focus of the parabola P. Then the square of the length of the latus rectum of E, is

Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 6

Slope of axis =1/2

Ellipse passes through (2.4, 3.2)  

Test: JEE Main 2024 January 31 Shift 2 - Question 7

The temperature T(t) of a body at time t = 0 is 160o F and it decreases continuously as per the 
differential equation  where K is positive constant. If T(15) = 120oF, then T(45) is equal to 

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Test: JEE Main 2024 January 31 Shift 2 - Question 8

If 2nd, 8th, 44th terms of A.P. are 1st, 2nd and 3rd terms respectively of G.P. and first term of A.P. is 1 then the sum of first 20 terms of A.P. is 

Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 8

a + d, a + 7d and a + 43d are 1st, 2nd, 3rd term of G.P.

= 10 [95 + 2] 

= 970

Test: JEE Main 2024 January 31 Shift 2 - Question 9

Let f: → R → (0, ∞)  be a strictly increasing function such that  Then, the value of  is equal to

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Test: JEE Main 2024 January 31 Shift 2 - Question 10

The area of the region enclosed by the parabola  is equal to

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Solution:

Test: JEE Main 2024 January 31 Shift 2 - Question 11

Let the mean and the variance of 6 observation a, b, 68, 44, 48, 60 be 55 and 194, respectively if  a > b, then a + 3b is 

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Test: JEE Main 2024 January 31 Shift 2 - Question 12

If the function f : (-∞, -1) → (a,b) defined by  is one-one and onto, then the distance of the point P(2b + 4,a + 2) from the line x + e-3 y = 4 is

Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 12



Test: JEE Main 2024 January 31 Shift 2 - Question 13

Consider the function f : (0, ∞) → defined by  If m and n be respectively the number of points at which f is not continuous and f is not differentiable, then m+n is

Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 13



m = 0 (No point at which function is not continuous)
n = 1 (Not differentiable)
∴ m + n =1

Test: JEE Main 2024 January 31 Shift 2 - Question 14

The number of solutions, of the equation esin x - 2e -sin x = 2 is

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Test: JEE Main 2024 January 31 Shift 2 - Question 15

, then  is equal to

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Test: JEE Main 2024 January 31 Shift 2 - Question 16

If for some m, n;  and , then  is equal to

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Test: JEE Main 2024 January 31 Shift 2 - Question 17

A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-

Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 17

 Let probability of tail is 1/3

⇒ Probability of getting head =2/3

∴ Probability of getting 2 tails and 1 head

Test: JEE Main 2024 January 31 Shift 2 - Question 18

Let A be a 33 real matrix such that

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Test: JEE Main 2024 January 31 Shift 2 - Question 19

The shortest distance between lines L1 and L2, where  and L2 is the line passing through the points A(-4,4,3).B(-1,6,3) and perpendicular to the line  is

Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 19

*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 20

is equal to .


Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 20

*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 21

Let a, b, c be the length of three sides of a triangle satisfying the condition (a+b2) x- 2b (a + c)x + (b2 + c2) = 0. If the set of all possible values of x is the interval (α, β), then 12 (α2 + β2) is equal to


Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 21





*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 22

Let  A(–2, –1), B(1, 0), C(α,β) and  be the vertices of a parallelogram ABCD . If the point C lies on  and the point D lies on  , then the value of  is equal to _______ .


Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 22

*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 23

Let the coefficient of xr in the expansion of 


Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 23


*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 24

Let A be a 3 x3 matrix and det (A) = 2. If  

Then the remainder when n is divided by 9 is equal to ___________.


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*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 25

Let  and  be a vector such that  and . Then  is equal to _____.


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*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 26

 then 16(a2 + b2 + c2) is equal to ______. 


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*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 27

A line passes through A(4, –6, –2) and B(16, –2,4). The point P(a, b, c) where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4,  –12, 3) is equal to ____. 


Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 27

*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 28

Let y = y(x) be the solution of the differential equation 

Then e is equal to ______. 


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*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 29

Let A = {1, 2, 3, ………100}. Let R be a relation on A defined by (x, y) ∈R if and only if 2x = 3y. Let R1 be a symmetric relation on A such that  and the number of elements in R1 is n. Then, the minimum value of n is ___________. 


Detailed Solution for Test: JEE Main 2024 January 31 Shift 2 - Question 29

R {( 3, 2 ) , ( 6, 4 ) , ( 9, 6 ) , (12, 8 ) , ......... (99, 66 )}
n(R ) = 33

66

*Answer can only contain numeric values
Test: JEE Main 2024 January 31 Shift 2 - Question 30

A light string passing over a smooth light fixed pulley connects two blocks of masses and . If the acceleration of the system is , then the ratio of masses is


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