JEE Main Mock Test-2 2023 : JEE Main Free Online Test For English Medium 2023: Attempt Mock Tests For Free | Test Practice

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:

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:

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:

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 ?

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

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 :

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

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

9. is equal to :

10. 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:

11. 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 :

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

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

14. 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 :

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