If the Determinant |x−2, 2x−3, 3x−4; 2x−3, 3x−4, 4x−5; 3x−5, 5x−8, 10x−17| = Ax³ + Bx² + Cx + D, Then B + C Is Equal To
JEE Main 2018 PYQ: expand a 3×3 determinant in x as Ax³+Bx²+Cx+D using column operations to create zeros, then find B+C.
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Let PQR Be a Triangle With A, B and C on the Sides QR, RP and PQ Such That QA/AR = RB/BP = PC/CQ = 1/2. Then Area(PQR)/Area(ABC) Is Equal To
JEE Main 2023 PYQ: triangle PQR with A,B,C on its sides dividing them in ratio 1:2. Find Area(PQR)/Area(ABC) using position vectors and the cross-product area formula.
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A Straight Line Cuts Off the Intercepts OA = a and OB = b on the Positive Directions of the x-axis and y-axis. If the Perpendicular From the Origin Makes an Angle π/6 With the Positive Direction of the y-axis and the Area of Triangle OAB Is 98√3/3, Then a² − b² Is Equal To
JEE Main 2023 PYQ: a line has intercepts OA=a, OB=b, with the perpendicular from the origin at angle π/6 to the y-axis and area of ΔOAB = 98√3/3. Find a²−b² using the normal form of a line.
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If f(x) + 6f(1/x) = 35/(3x) − 7/2 for x ∈ R − {0}, and the Limit of (1/(αx) + f(x)) as x → 0 Exists Finitely and Is Equal to β, Then α − 2β Is
JEE Main 2025 PYQ: f(x) satisfies f(x)+6f(1/x)=35/(3x)-7/2. If lim(x→0)[1/(αx)+f(x)] exists finitely and equals β, find α-2β by first solving for f(x).
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The Distance Between the Two Points A and A’ Which Lie on y = 2 Such That Both the Line Segments AB and A’B, Where B Is the Point (2, 3), Subtend an Angle π/4 at the Origin Is Equal To
JEE Main 2022 PYQ: A and A’ lie on y=2 such that segments AB and A’B (B=(2,3)) subtend angle π/4 at the origin. Find the distance AA’ using the angle-between-two-lines formula.
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Let z₁ and z₂ Be Two Complex Numbers Such That z₁ + z₂ = 5 and z₁³ + z₂³ = 20 + 15i. Then |z₁⁴ + z₂⁴| Equals
JEE Main 2024 PYQ: given z1+z2=5 and z1³+z2³=20+15i, find |z1⁴+z2⁴| by working through z1z2, then z1²+z2², using the standard algebraic identities.
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Let |z−i|/|2z+i| = 1/3, z ∈ C, Be the Equation of a Circle With Centre at C. If the Area of the Triangle Whose Vertices Are (0,0), C and (α, 0) Is 11 Square Units, Then α² Equals
JEE Main 2025 PYQ: |z-i|/|2z+i|=1/3 traces a circle with center C. Given the triangle (0,0), C, (α,0) has area 11, find α² using the circle equation and area formula.
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Let S Be the Set of All Values of a₁ for Which the Mean Deviation About the Mean of 100 Consecutive Positive Integers a₁, a₂, …, a₁₀₀ Is 25. Then S Is
JEE Main 2023 PYQ: find the set S of all values of a1 for which the mean deviation about the mean of 100 consecutive positive integers equals 25.
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If the Set of All a ∈ R for Which 2x² + (a−5)x + 15 = 3a Has No Real Root Is the Interval (α, β), and X = {x ∈ Z : x Lies Between α and β}, Then the Sum of x² Over X Is Equal To
JEE Main 2025 PYQ: find the interval (α,β) of a for which 2x²+(a-5)x+15=3a has no real root, then sum the squares of every integer strictly between α and β.
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A Square Is Inscribed in the Circle x² + y² − 10x − 6y + 30 = 0. One Side of This Square Is Parallel to y = x + 3. If (xᵢ, yᵢ) Are the Vertices of the Square, Then the Sum of (xᵢ² + yᵢ²) Is Equal To
A square is inscribed in the circle x²+y²−10x−6y+30=0 with one side parallel to y=x+3. Find Σ(xᵢ²+yᵢ²) over the four vertices, using the fact that the square’s diagonals lie along the horizontal and vertical through the centre.