PYQ Vault
EbooksTutor

Day 57: MHT-CET Maths

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

  1. Question 1

    Determinants and Matrices. This type asked 4 times: 21 Apr 2025 S2, 18 Apr 2026 S1, 19 Apr 2026 S2, 12 May 2026 S1. This one: 12 May 2026 S1 See all 4 of this type

    68
    Let AA be an invertible matrix. Identify the correct statement(s) from the following. (I) A(adj A−1)=1∣A∣A2A(\mathrm{adj}\,A^{-1}) = \dfrac{1}{|A|}A^2 (II) (adj A−1)−1=1∣A∣A−1(\mathrm{adj}\,A^{-1})^{-1} = \dfrac{1}{|A|}A^{-1} (III) (adj A)=1∣A∣A−1(\mathrm{adj}\,A) = \dfrac{1}{|A|}A^{-1}

    Tap an option to check your answer.

  2. Question 2

    Indefinite Integration. This type asked 4 times: 16 May 2023 S2, 17 Apr 2026 S1, 20 Apr 2026 S1, 12 May 2026 S1. This one: 12 May 2026 S1 See all 4 of this type

    77
    For x≠0x \neq 0, the value of I=∫x2−1(x4+3x2+1)tan⁡−1(x+1x) dxI = \displaystyle\int\dfrac{x^2 - 1}{(x^4 + 3x^2 + 1)\tan^{-1}\left(x + \dfrac{1}{x}\right)}\,dx is ...

    Tap an option to check your answer.

  3. Question 3

    Determinants and Matrices. This type asked 4 times: 9 May 2023 S2, 21 Apr 2025 S1, 19 Apr 2026 S1, 20 Apr 2026 S2. This one: 20 Apr 2026 S2 See all 4 of this type

    65
    Let A=[312120114]A = \begin{bmatrix} 3 & 1 & 2 \\ 1 & 2 & 0 \\ 1 & 1 & 4 \end{bmatrix} and pC11+4C21−5C32=−2pC_{11} + 4C_{21} - 5C_{32} = -2, where CijC_{ij} denotes the cofactor of an element aija_{ij} of matrix AA, then the value of pp is :

    Tap an option to check your answer.

  4. Question 4

    Straight Line. This type asked 4 times: 10 May 2023 S2, 9 May 2024 S2, 20 Apr 2026 S1, 20 Apr 2026 S2. This one: 20 Apr 2026 S2 See all 4 of this type

    55
    A straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is 4 units, then the equation of the line is ......

    Tap an option to check your answer.

  5. Question 5

    Vectors. This type asked 4 times: 3 May 2023 S1, 4 May 2023 S2, 11 May 2023 S1, 20 Apr 2026 S2. This one: 20 Apr 2026 S2 See all 4 of this type

    90
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three non-coplanar vectors and p⃗,q⃗,r⃗\vec{p}, \vec{q}, \vec{r} are defined as p⃗=b⃗×c⃗[a⃗ b⃗ c⃗],q⃗=c⃗×a⃗[a⃗ b⃗ c⃗],r⃗=a⃗×b⃗[a⃗ b⃗ c⃗]\vec{p} = \dfrac{\vec{b} \times \vec{c}}{[\vec{a}\,\vec{b}\,\vec{c}]}, \vec{q} = \dfrac{\vec{c} \times \vec{a}}{[\vec{a}\,\vec{b}\,\vec{c}]}, \vec{r} = \dfrac{\vec{a} \times \vec{b}}{[\vec{a}\,\vec{b}\,\vec{c}]}, then [(a⃗+b⃗)⋅p⃗+(b⃗+c⃗)⋅q⃗+(c⃗+a⃗)⋅r⃗][(\vec{a} + \vec{b})\cdot\vec{p} + (\vec{b} + \vec{c})\cdot\vec{q} + (\vec{c} + \vec{a})\cdot\vec{r}] is equal to

    Tap an option to check your answer.