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Day 100: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Conic Sections. This type asked 2 times: 21 Jan 2026 S2, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 2 of this type

    74
    Let A,BA,B and C be the vertices of a variable right angled triangle inscribed in the parabola y2=16xy^{2} = 16x. Let the vertex BB containing the right angle be (4,8)(4,8) and the locus of the centroid of △ABC\bigtriangleup ABC be a conic C0C_{0}. Then three times the length of latus rectum of C0C_{0} is ____\_\_\_\_ .

  2. Question 2

    Permutations and Combinations. This type asked 2 times: 1 Feb 2024, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 2 of this type

    67
    Let A={(a,b,c):a,b,c\mathbf{A = \{(a,b,c):a,b,c} are non-negative integers and a+b+2c=22}a + b + 2c = 22\}. The n(A)n(A) is equal to :

    Tap an option to check your answer.

  3. Question 3

    Probability. This type asked 2 times: 2 Apr 2025, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 2 of this type

    71
    From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to ab\frac{a}{b}, where a,b∈Na,b \in N and gcd(a,b)=1gcd(a,b) = 1, then a+ba + b is equal to ____\_\_\_\_ .

  4. Question 4

    Conic Sections. This type asked 2 times: 31 Jan 2023, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 2 of this type

    63
    Suppose the two chords, drawn from the point (1, 2) on the circle x2+y2+x−3y=0x^{2}+y^{2}+x- 3y= 0 are bisected by the y -axis. If the other ends of these chords are R and S , and the midpoint of the line segment RS is (α,β)(\alpha,\beta), then 6(α+β)6(\alpha+\beta) is equal to :

    Tap an option to check your answer.

  5. Question 5

    Trigonometric Identities. This type asked 2 times: 28 Jan 2025, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 2 of this type

    73
    If A=sin⁡3∘cos⁡9∘+sin⁡9∘cos⁡27∘+sin⁡27∘cos⁡81∘A = \frac{\sin 3^{\circ}}{\cos 9^{\circ}} + \frac{\sin 9^{\circ}}{\cos 27^{\circ}} + \frac{\sin 27^{\circ}}{\cos 81^{\circ}} and B=tan⁡81∘−tan⁡3∘B = \tan81^{\circ} - \tan3^{\circ}, then BA\frac{B}{A} is equal to ____\_\_\_\_ .