PYQ Vault

Day 127: CBSE Class 12 Maths

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

  1. Question 1

    Matrices. Asked once: 2025 (same type asked 2 times)

    2
    If A=[−100030005]A = \begin{bmatrix} -1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix}, then A is a/an :

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  2. Question 2

    Relations and Functions. Asked once: 2023 (same type asked 2 times)

    34 (b)
    Let f:R−{−43}→Rf : \mathbb{R} - \left\{-\dfrac{4}{3}\right\} \to \mathbb{R} be a function defined as f(x)=4x3x+4f(x) = \dfrac{4x}{3x + 4}. Show that f is a one-one function. Also, check whether f is an onto function or not.

  3. Question 3

    Relations and Functions. Asked once: 2024 (same type asked 2 times)

    35
    A relation R on set A={x:−10≤x≤10,x∈Z}A = \{x : -10 \le x \le 10, x \in Z\} is defined as R={(x,y):(x−y)R = \{(x, y) : (x - y) is divisible by 5}5\}. Show that R is an equivalence relation. Also, write the equivalence class [5][5].

  4. Question 4

    Three Dimensional Geometry. Asked once: 2023 (same type asked 2 times)

    33 (b)
    A line ll passes through point (−1-1, 3, −2-2) and is perpendicular to both the lines x1=y2=z3\frac{x}{1} = \frac{y}{2} = \frac{z}{3} and x+2−3=y−12=z+15\frac{x + 2}{-3} = \frac{y - 1}{2} = \frac{z + 1}{5}. Find the vector equation of the line ll. Hence, obtain its distance from origin.

  5. Question 5

    Three Dimensional Geometry. Asked once: 2026 (same type asked 2 times)

    3
    Direction ratios of lines l1l_1 and l2l_2 respectively are <1,0,0><1, 0, 0> and <0,−1,0><0, -1, 0>. The direction ratios of the line perpendicular to both l1l_1 and l2l_2 are :

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