PYQ Vault

Day 131: CBSE Class 12 Maths

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

  1. Question 1

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

    2
    Let R+R_+ denote the set of all non-negative real numbers. Then the function f:R+→R+f : R_+ \to R_+ defined as f(x)=x2+1f(x) = x^2 + 1 is :

    Tap an option to check your answer.

  2. Question 2

    Vector Algebra. Asked once: 2022 (same type asked 2 times)

    9 (b)
    If a⃗\vec{a} and b⃗\vec{b} are unit vectors inclined at an angle 30∘30^\circ to each other, then find the area of the parallelogram with (a⃗+3b⃗)\left(\vec{a} + 3\vec{b}\right) and (3a⃗+b⃗)\left(3\vec{a} + \vec{b}\right) as adjacent sides.

  3. Question 3

    Vector Algebra. Asked once: 2024 (same type asked 2 times)

    23
    If a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} are three unit vectors such that a⃗+b⃗−c⃗=0⃗\vec{a} + \vec{b} - \vec{c} = \vec{0}, find the angle between vectors a⃗\vec{a} and c⃗\vec{c}.

  4. Question 4

    Determinants. Asked once: 2024 (same type asked 2 times)

    34
    If A=[21−332112−1]A = \begin{bmatrix} 2 & 1 & -3 \\ 3 & 2 & 1 \\ 1 & 2 & -1 \end{bmatrix}, find A−1A^{-1} and hence solve the following system of equations : 2x+y−3z=132x + y - 3z = 13 3x+2y+z=43x + 2y + z = 4 x+2y−z=8x + 2y - z = 8

  5. Question 5

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

    34 (a)
    If N denotes the set of all natural numbers and R is the relation on N×NN \times N defined by (a, b) R (c, d), if ad(b+c)=bc(a+d)ad(b + c) = bc(a + d). Show that R is an equivalence relation.