Exams › JEE Advanced › Maths
Match each item in List-I with its correct value from List-II. List-I (P) The volume of the parallelepiped with coterminous edges 2(a x b), 3(b x c), (c x a) is V, given that the parallelepiped with coterminous edges a, b, c has volume 2. Find V. (Q) The volume of the parallelepiped with coterminous edges 3(a+b), (b+c), 2(c+a) is V, given that the parallelepiped with coterminous edges a, b, c has volume 5. Find V. (R) The area of the triangle with adjacent sides (2a+3b) and (a-b) is A, given that the triangle with adjacent sides a and b has area 20. Find A. (S) The area of the parallelogram with adjacent sides (a+b) and a is A, given that the parallelogram with adjacent sides a and b has area 30. Find A. List-II (1) 100 (2) 30 (3) 24 (4) 60 (5) 20
- P->3; Q->4; R->1; S->1
- P->3; Q->4; R->2; S->1
- P->3; Q->4; R->2; S->2
- P->3; Q->4; R->1; S->2
Correct answer: P->3; Q->4; R->1; S->2
Solution
P->24->3; Q->60->4; R->100->1; S->30->2. This matches option D.
Related JEE Advanced Maths questions
- Given that cos α ≠ 1, cos β ≠ 1, and cos γ ≠ 1, the vectors →a = i cos α + j cos β + k cos γ, →b = i + j cos β + k, and →c = i + j + k cos γ are
- Given the vectors →a = a→i + 2→j − 3→k, →b = →i + 2a→j − 2→k, and →c = 2→i − a→j + →k, if (→a × →b) × (→b × →c) × (→c × →a) equals →0, what is the value of a?
- In the triangle ΔPQR, the vectors →a, →b, and →c represent →QR, →RP, and →PQ respectively. If the magnitudes are |→a| = 12 and |→b| = 4√3, and the dot product →b ⋅ →c equals 24, which of the following statements is correct?
- Consider three vectors →x, →y, and →z, each having a magnitude of √2, with the angle between any two of them being π/3. If →a is a non-zero vector orthogonal to both →y and →z, and →b is a non-zero vector orthogonal to both →x and →z, which of the following is true?
- Let a, b, and c represent three unit vectors that are not in the same plane, with the angle between each pair being π/3. If the expression a × b + b × c equals pa + qb + rc, where p, q, and r are constants, what is the value of (p² + 2q² + r²)/q²?
- The vector a = (1, 3, sin 2α) forms an angle greater than 90° with the z-axis. Given that 2α is negative, and vectors b and c are perpendicular, b ⋅ c equals zero. The equation tan² α − tan α − 6 = 0 has solutions tan α = 3 or −2. If tan α = 3, then sin 2α = 2 tan α / (1 + tan² α) = 3/5, which is positive and contradicts the condition (2α < 0). Thus, tan α = −2. For this value, sin 2α = 2 tan α / (1 − tan² α) = 4/3, which is greater than zero. However, sin 2α must be negative, placing 2α in the third quadrant and α/2 in the first quadrant. The square root of sin(α/2) is valid, and α is given by (4n + 1)π − tan⁻¹ 2.
⚔️ Practice JEE Advanced Maths free + battle 1v1 →