PYQ Vault
EbooksTutor

Day 448: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 8 Apr 2024

    66
    Let f(x)f(x) be a positive function such that the area bounded by y=f(x),y=0y = f(x),y = 0 from x=0x = 0 to x=a>0x = a > 0 is e−a+4a2+a−1e^{- a}+ 4a^{2}+ a - 1. Then the differential equation, whose general solution is y=c1f(x)+c2y =c_{1}f(x) +c_{2}, where c1c_{1} and c2c_{2} are arbitrary constants, is:

    Tap an option to check your answer.

  2. Question 2

    Differentiation. Asked once: 2 Apr 2025

    54
    Let f:R→Rf:R \rightarrow R be a twice differentiable function such that (sin⁡xcos⁡y)(f(2x+2y)−f(2x−2y))=(cos⁡xsin⁡y)(f(2x+2y)+f(2x−2y))(\sin x\cos y)(f(2x+ 2y) -f(2x- 2y)) = (\cos x\sin y)(f(2x + 2y) +f(2x - 2y)), for all x,y∈Rx,y \in R. If f′(0)=12f^{'}(0) =\frac{1}{2}, then the value of 24f′′(5π3)24f^{''}\left( \frac{5\pi}{3} \right) is:

    Tap an option to check your answer.

  3. Question 3

    Indefinite Integration. Asked once: 23 Jan 2026 S2

    64
    Let I(x)=∫3dx(4x+6)(4x2+8x+3)I(x) = \int\frac{3dx}{(4x + 6)\left( \sqrt{4x^{2}+ 8x + 3} \right)} and I(0)=34+20I(0) =\frac{\sqrt{3}}{4}+ 20. If I(12)=a2 b+cI\left( \frac{1}{2} \right)=\frac{a\sqrt{2}}{\text{ }b}+ c, where a,b,c∈N,gcd(a,b)=1a,b,c \in N,gcd(a,b) = 1, then a+b+ca + b + c is equal to :

    Tap an option to check your answer.

  4. Question 4

    Inverse Trigonometric Functions. Asked once: 6 Apr 2024

    88
    For n∈Nn \in N, if cot⁡−13+cot⁡−14+cot⁡−15+cot⁡−1n=π4\cot^{- 1}3 +\cot^{- 1}4 +\cot^{- 1}5 +\cot^{- 1}n =\frac{\pi}{4}, then nn is equal to

  5. Question 5

    Limits and Continuity. Asked once: 2 Apr 2026 S1

    66
    If lim⁡x→2sin⁡(x3−5x2+ax+b)(x−1−1)log⁡e(x−1)=m\underset{x\rightarrow 2}{\lim} \frac{\sin\left( x^{3}- 5x^{2}+ax+b \right)}{(\sqrt{x- 1}- 1)\log_{e}(x- 1)}=m, then a+b+ma+b+m is equal to:

    Tap an option to check your answer.