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Day 72: MHT-CET Maths

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

  1. Question 1

    Limits. Asked 3 times: 11 May 2023 S2, 12 May 2024 S2, 22 Apr 2025 S2 See all 3 times it was asked

    137
    If f(x)={1−cos⁡4xx2,x<0a,x=0x(16+x)1/2−4,x>0f(x)=\begin{cases}\dfrac{1-\cos4x}{x^2}, & x<0\\ a, & x=0\\ \dfrac{\sqrt{x}}{(16+\sqrt{x})^{1/2}-4}, & x>0\end{cases} is continuous at x=0x=0, then a=a=

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  2. Question 2

    Trigonometric Functions. Asked 3 times: 3 May 2023 S1*, 9 May 2024 S1*, 22 Apr 2025 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    149
    The number of solutions of 16sin⁡2x+16cos⁡2x=1016^{\sin^{2}x}+16^{\cos^{2}x}= 10 in 0⩽x⩽2π0 \leqslant x\leqslant 2\pi are

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  3. Question 3

    Pair of Straight Lines. Asked 3 times: 9 May 2024 S1*, 20 Apr 2025 S1*, 21 Apr 2025 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    121
    The distance between the lines represented by 16x2+9y2+48x−24xy−36y+35=016x^{2}+ 9y^{2}+ 48x- 24xy- 36y+ 35 = 0 is ____\_\_\_\_ units

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  4. Question 4

    Mathematical Logic. Asked 3 times: 10 May 2024 S1, 11 May 2024 S2, 21 Apr 2025 S1 See all 3 times it was asked

    138
    The logical statement [∼(∼p∨q)∨(p∧r)]∧(∼q∧r)\left\lbrack \sim\left( \sim p\vee q \right)\vee\left( p\land r \right) \right\rbrack\land\left( \sim q\land r \right) is equivalent to

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  5. Question 5

    Applications of Derivative. Asked 3 times: 9 May 2023 S1*, 12 May 2024 S2*, 20 Apr 2025 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    111
    If the curves y2=6xy^{2}= 6x and 9x2+by2=169x^{2}+by^{2}= 16 intersect each other at right angles, then the value of bb is

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