JEE Mains 2023 : Best Question Collection in Maths | JEE Main Maths Test Series-1

1. If the sum of an infinite GP a, ar, ar², ar³, ……. is 15 and the sum of the squares of its each term is 150, then the sum of ar², ar⁴, ar⁶,

2. Let ABC be a triangle with A (-3, 1) and ∠ACB = θ,0 < θ < π/2. If the equation of the median through B is 2x + y – 3 = 0 and the equation of angle bisector of C is 7x – 4y – 1 = 0, then tan θ is equal to :

3. Let θε(0,π/2). If the system of linear equations,
(1 + cos²θ) x + sin²θ y + 4 sin3θ z = 0
cos²θ x + (1 + sin²θ) y + 4 sin3θ z = 0
cos²θ x + sin²θ y + (1 + 4 sin3θ) z = 0
has a non-trivial solution, then the value of θ is:

4. Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = 5/9,is

5. If the truth value of the Boolean expression
((p v q) ∧ (q → r) ∧ (~r)) → (p ∧ q) is false, then the truth values of the statements p,q,r respectively can be:

6. Let y = y(x) be a solution curve of the differential equation (y + 1) tan²x dx + tan x dy + ydx = 0, x ε (0,π/2) If limx→0⁺ xy(x) = 1, then the value of y(π/4) is:

7. The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. If α and √β are the mean and standard deviation respectively for correct data, then (α, β) is:

8. A plane P contains the line x + 2y + 3z + 1 = 0 = x – y – Z – 6, and is perpendicular to the plane-2x + y + z + 8 = 0. Then which of the following points lies on P?

9. On the ellipse x²/8 + y²/4 = 1 let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2y = 0. Let S and S’ be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS’ then, the value of (5 – e²). A is:

10. If a line along a chord of the circle 4x² + 4y² + 120x + 675 = 0, passes through the point (-30, 0) and is tangent to the parabola y² = 30x, then the length of this chord is :

11. Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set

12. If in a triangle ABC, AB = 5 units, ∠B = cos^–¹(3/5) and radius of circumcircle of ΔABC is 5 units, then the area (in sq. units) of ΔABC is:

13. Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is:

14. The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are:

15. The probability of selecting integers
a ε [-5, 30] such that x² + 2 (a + 4) x – 5a + 64 > 0, for all x ε R, is :