PYQ Vault

Day 54: CBSE Class 12 Maths

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

  1. Question 1

    Relations and Functions. This type asked 2 times: 2024, 2026. This one: 2026

    26 (b)
    Let n be a fixed positive integer. A relation R is defined in set Z\mathbb{Z} such that R={(x,y):(x−y)R = \{(x, y) : (x - y) is divisible by n,  x,y∈Z}n, \; x, y \in \mathbb{Z}\}. Determine if R is an equivalence relation.

  2. Question 2

    Three Dimensional Geometry. This type asked 2 times: 2023, 2026. This one: 2026

    25 (b)
    Find the vector equation of a line passing through the origin and perpendicular to both the lines r⃗=2i^−j^+2k^+λ(3i^+4j^+2k^)\vec{r} = 2\hat{i} - \hat{j} + 2\hat{k} + \lambda(3\hat{i} + 4\hat{j} + 2\hat{k}) and r⃗=μ(i^−j^+k^)\vec{r} = \mu(\hat{i} - \hat{j} + \hat{k}).

  3. Question 3

    Three Dimensional Geometry. This type asked 2 times: 2023, 2026. This one: 2026

    10
    Direction ratios of lines l1l_1 and l2l_2 respectively are <1,−2,3><1, -2, 3> and <−2,p,−6><-2, p, -6>. The value of p for which l1 ∥ l2l_1 \,\|\, l_2, is :

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  4. Question 4

    Three Dimensional Geometry. This type asked 2 times: 2023, 2026. This one: 2026

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : Lines given by x=py+qx = py + q, z=ry+sz = ry + s and x=p′y+q′x = p'y + q', z=r′y+s′z = r'y + s' are perpendicular to each other when pp′+rr′=1pp' + rr' = 1. Reason (R) : Two lines r⃗=a⃗1+λb⃗1\vec{r} = \vec{a}_1 + \lambda\vec{b}_1 and r⃗=a⃗2+μb⃗2\vec{r} = \vec{a}_2 + \mu\vec{b}_2 are perpendicular to each other if b⃗1⋅b⃗2=0\vec{b}_1 \cdot \vec{b}_2 = 0.

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  5. Question 5

    Vector Algebra. This type asked 2 times: 2025, 2026. This one: 2026

    17
    Three points A(0, 1, 1), B(2, 0, −1-1) and C(1, 0, 3) form Δ\Delta ABC. The ar (Δ\Delta ABC) is :

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