If x = 10 + 6√3, Find the Value of x^(1/3) − 1
If x=10+6√3, find the value of the cube root of x minus 1, by writing the cube root as a+√b and matching coefficients.
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The Eccentricity of the Hyperbola Whose Latus Rectum Is 8 and Whose Conjugate Axis Is Equal to Half of the Distance Between the Foci Is
JEE Main 2016 PYQ: find the eccentricity of a hyperbola whose latus rectum is 8 and whose conjugate axis equals half the distance between its foci.
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Find the Coefficient of t⁴ in the Expansion of [(1 − t⁶)/(1 − t)]³
JEE Main 2019 PYQ: find the coefficient of t^4 in [(1-t^6)/(1-t)]^3 by rewriting it as (1-t^6)^3 (1-t)^-3 and using the negative-binomial expansion.
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Let A = {(x, y) : 2x + 3y = 23, x, y ∈ N} and B = {x : (x, y) ∈ A}. Then the Number of One-One Functions From A to B Is Equal To
JEE Main 2024 PYQ: A is the set of natural-number solutions to 2x+3y=23, and B is the set of their x-values. Find the number of one-one functions from A to B.
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Let |z₁ − 8 − 2i| ≤ 1 and |z₂ − 2 + 6i| ≤ 2, z₁, z₂ ∈ C. Then the Minimum Value of |z₁ − z₂| Is
JEE Main 2025 PYQ: z1 and z2 satisfy |z1-8-2i|≤1 and |z2-2+6i|≤2. Find the minimum value of |z1-z2| by interpreting the inequalities as two disjoint circular discs.
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Given a = 4i + 5j − k, b = i − 4j + 5k and c = 3i + j − k, Find a Vector d Which Is Perpendicular to Both b and c and Satisfies d·a = 21
Find a vector d that is perpendicular to both b and c, and satisfies d·a=21, given a=4i+5j-k, b=i-4j+5k, c=3i+j-k. Solved by setting up and solving a linear system.
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The Number of Triangles Whose Vertices Are at the Vertices of a Regular Octagon but None of Whose Sides Is a Side of the Octagon Is
JEE Main 2024 PYQ: find the number of triangles whose vertices are vertices of a regular octagon, but none of whose sides coincide with a side of the octagon.
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Let A(α, β), B(1, 0), C(γ, δ) and D(1, 2) Be the Vertices of a Parallelogram ABCD With α, β, γ, δ ∈ Z. If AB = √10 and the Points A and C Lie on the Line 3y = 2x + 1, Then 2(α + β + γ + δ) Is Equal To
JEE Main 2024 PYQ: A(α,β), B(1,0), C(γ,δ), D(1,2) are vertices of a parallelogram. Find 2(α+β+γ+δ) using the diagonal-bisection property of a parallelogram.
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How Many Different Words Can Be Formed by Jumbling the Letters of the Word MISSISSIPPI in Which No Two S’s Are Adjacent
AIEEE PYQ: find how many distinct arrangements of the letters of MISSISSIPPI have no two S’s adjacent, using the gap method for non-adjacent placement.
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In a Triangle ABC, AB = 8 cm, AC = 6 cm and ∠BAC = 60°. Find the Length of the Median From Vertex A to Side BC
Find the length of the median from vertex A to side BC in a triangle with AB=8cm, AC=6cm and angle BAC=60°, using the cosine rule followed by the median length formula.