PYQ Vault
EbooksTutor

Day 104: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked 2 times: 14 May 2024 S1, 20 Apr 2026 S1 See all 2 times it was asked

    92
    If aˉ,bˉ\bar{a}, \bar{b} and cˉ\bar{c} are three vectors such that ∣aˉ+bˉ+cˉ∣=1,cˉ=λ(aˉ×bˉ)|\bar{a} + \bar{b} + \bar{c}| = 1, \bar{c} = \lambda(\bar{a} \times \bar{b}) and ∣aˉ∣=13,∣bˉ∣=12,∣cˉ∣=16|\bar{a}| = \dfrac{1}{\sqrt{3}}, |\bar{b}| = \dfrac{1}{\sqrt{2}}, |\bar{c}| = \dfrac{1}{\sqrt{6}}, then the angle between aˉ\bar{a} and bˉ\bar{b} is

    Tap an option to check your answer.

  2. Question 2

    Limits. Asked 2 times: 3 May 2023 S2, 19 Apr 2026 S2 See all 2 times it was asked

    70
    If the function f(x)=(5x−88−3x)32x−4f(x) = \left(\dfrac{5x - 8}{8 - 3x}\right)^{\frac{3}{2x - 4}}, for x≠2x \neq 2 is continuous at x=2x = 2, then the value of f(2)f(2) is...

    Tap an option to check your answer.

  3. Question 3

    Line and Plane. Asked 2 times: 21 Apr 2025 S1*, 19 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    93
    The shortest distance between the lines r⃗=(4i^−j^)+λ(i^+2j^−3k^)\vec{r} = (4\hat{i} - \hat{j}) + \lambda(\hat{i} + 2\hat{j} - 3\hat{k}) and r⃗=(i^−j^+2k^)+μ(i^+4j^−5k^)\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(\hat{i} + 4\hat{j} - 5\hat{k}) is...

    Tap an option to check your answer.

  4. Question 4

    Applications of Derivative. Asked 2 times: 12 May 2024 S2, 19 Apr 2026 S1 See all 2 times it was asked

    75
    A tank with a rectangular base and rectangular sides, open at the top is made. Depth of the tank is 44 m and its volume is 3636 cubic meters. For making a tank cost of base material used is Rs. 100100 per sq. meter and that of sides is Rs. 5050 per sq. meter. Then minimum cost of tank is ..............

    Tap an option to check your answer.

  5. Question 5

    Limits. Asked 2 times: 10 May 2024 S2*, 19 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    61
    The value of lim⁡x→0(8x8)[1−cos⁡x22−cos⁡x24+cos⁡x22⋅cos⁡x24]\lim_{x \to 0}\left(\dfrac{8}{x^8}\right)\left[1 - \cos\dfrac{x^2}{2} - \cos\dfrac{x^2}{4} + \cos\dfrac{x^2}{2} \cdot \cos\dfrac{x^2}{4}\right] is equal to ...

    Tap an option to check your answer.