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Day 286: MHT-CET Maths

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

  1. Question 1

    Limits. Asked once: 19 Apr 2025 S2 (same type asked 6 times) See all 6 of this type

    133
    lim⁡x→0∣x∣∣x∣+x2=\underset{x\rightarrow 0}{\lim} \frac{|x|}{|x| +x^{2}}=

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  2. Question 2

    Trigonometric Functions. Asked once: 21 Apr 2025 S2 (same type asked 6 times) See all 6 of this type

    132
    In a triangle ABC , with usual notations, tan⁡(A2)=56,tan⁡(C2)=25\tan\left( \frac{A}{2} \right)=\frac{5}{6},\tan\left( \frac{C}{2} \right)=\frac{2}{5}, then

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  3. Question 3

    Determinants and Matrices. Asked once: 11 Apr 2026 S1 (same type asked 6 times) See all 6 of this type

    64
    If A=[2ii3i21]A = \begin{bmatrix} 2i & i^3 \\ i^2 & 1 \end{bmatrix}, then A−1A^{-1} is equal to

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  4. Question 4

    Indefinite Integration. Asked once: 16 Apr 2026 S2 (same type asked 6 times) See all 6 of this type

    77
    If f(x)=cos⁡xf(x) = \cos x, then the value of ∫ef(x)(xsin⁡3x+f(x))1−(f(x))2 dx=\displaystyle\int\dfrac{e^{f(x)}(x\sin^3 x + f(x))}{1 - (f(x))^2}\,dx =

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  5. Question 5

    Complex Numbers. Asked once: 17 Apr 2026 S1 (same type asked 6 times) See all 6 of this type

    51
    If α\alpha and β\beta are the distinct roots of the equation x2−x+1=0x^2 - x + 1 = 0, then the value of α200+β206+2\alpha^{200} + \beta^{206} + 2 is equal to

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