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Day 216: MHT-CET Maths

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

  1. Question 1

    Determinants and Matrices. Asked once: 19 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    66
    If A=[aij]3×3A = [a_{ij}]_{3 \times 3}, where aij={1,if i+j is even0,if i+j is odda_{ij} = \begin{cases} 1, & \text{if } i + j \text{ is even} \\ 0, & \text{if } i + j \text{ is odd} \end{cases}, then adj(A)=…\mathrm{adj}(A) = \ldots

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  2. Question 2

    Straight Line. Asked once: 20 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    58
    The area of a triangle formed by a line with the coordinate axes is 4949 sq. units. If the perpendicular drawn from the origin to this line makes an angle of 45∘45^\circ with the positive X-axis, then the equation of line is....

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  3. Question 3

    Vectors. Asked once: 4 May 2023 S2 (same type asked 4 times) See all 4 of this type

    106
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are non-coplanar vectors and p⃗=b⃗×c⃗[a⃗b⃗c⃗],q⃗=c⃗×a⃗[a⃗b⃗c⃗],r⃗=a⃗×b⃗[a⃗b⃗c⃗]\vec{p}=\frac{\vec{b}\times\vec{c}}{[\vec{a}\vec{b}\vec{c}]}, \vec{q}=\frac{\vec{c}\times\vec{a}}{[\vec{a}\vec{b}\vec{c}]}, \vec{r}=\frac{\vec{a}\times\vec{b}}{[\vec{a}\vec{b}\vec{c}]}, then 2a⃗⋅p⃗+b⃗⋅q⃗+c⃗⋅r⃗=2\vec{a}\cdot\vec{p}+\vec{b}\cdot\vec{q}+\vec{c}\cdot\vec{r}=

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  4. Question 4

    Applications of Definite Integral. Asked once: 15 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    84
    If the area bounded by the curve x2=byx^2 = by and the lines y=1,y=4y = 1, y = 4 in the first quadrant is 2828 sq. units, then the value of b is...

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  5. Question 5

    Limits. Asked once: 17 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    60
    If lim⁡x→1sin⁡(3x2−4x+1)−x2+12x3−7x2+ax+b=−2\lim_{x \to 1}\dfrac{\sin(3x^2 - 4x + 1) - x^2 + 1}{2x^3 - 7x^2 + ax + b} = -2, then the quadratic equation having roots aa and bb is

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