JEE Main 2023 · 11 Apr 2023 Shift 1

An organization awarded 48 medals in event ‘A’, 25 in event ‘B’ and 18 in event ‘C’. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

1. A15
2. B9
3. C10
4. D21

Let (α, β, γ) be the image of the point P (2, 3, 5) in the plane 2x + y − 3z = 6. Then α + β + γ is equal to

1. A12
2. B10
3. C9
4. D5

Consider ellipses Eₖ : kx² + k²y² = 1, k = 1, 2,..., 20. Let Cₖ be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse Eₖ. If rₖ is the radius of the circle Cₖ, then the value of ∑ₖ₌₁²⁰ 1/rₖ² is

1. A2870
2. B3080
3. C3210
4. D3320

The number of triplets (x, y, z), where x, y, z are distinct non negative integers satisfying x + y + z =15, is

1. A136
2. B114
3. C92
4. D80

The number of integral solutions x of log₍ₓ₊₇⁄₂₎ ((x − 7)/(2x − 3))² ≥ 0 is

1. A8
2. B7
3. C6
4. D5

Let A be a 2 × 2 matrix with real entries such that A′ = α A + I, where α ∈ R − {−1, 1}. If det (A² − A) = 4, then the sum of all possible values of α is equal to

1. A5/2
2. B3/2
3. C2
4. D0

Let f(x) = [x² − x] + |−x + [x]|, where x ∈ R and [t] denotes the greatest integer less than or equal to t. Then, f is

1. Anot continuous at x=0 and x=1
2. Bcontinuous at x=0 and x=1
3. Ccontinuous at x=0, but not continuous at x=1
4. Dcontinuous at x=1, but not continuous at x=0

If equation of the plane that contains the point (−2,3,5) and is perpendicular to each of the planes 2x + 4y + 5z = 8 and 3x − 2y + 3z = 5 is αx + βy + γz +97 = 0 then α + β + γ =

1. A15
2. B16
3. C17
4. D18