A hyperbola passes through the foci of the ellipse ${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is :

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The following system of linear equations :- 2x + 3y + 2z = 9, 3x + 2y + 2z = 9, x $-$ y + 4z = 8

Topic: JEE Main 2021 (25 February Evening Shift)

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If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line seg…

Topic: JEE Main 2021 (25 February Evening Shift)

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If for the matrix, $A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]$, $A{A^T…

Topic: JEE Main 2021 (25 February Evening Shift)

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In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are …

Topic: JEE Main 2021 (25 February Evening Shift)

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If ${I_n} = \int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\cot }^n}x\,dx} $, then :

Topic: JEE Main 2021 (25 February Evening Shift)

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The minimum value of $f(x) = {a^{{a^x}}} + {a^{1 - {a^x}}}$, where a, $x \in R$ and a > 0, is equal to :

Topic: JEE Main 2021 (25 February Evening Shift)

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If $\alpha$, $\beta$ $\in$ R are such that 1 $-$ 2i (here i2 = $-$1) is a root of z2 + $\alpha$z + $\beta$ = 0, then ($…

Topic: JEE Main 2021 (25 February Evening Shift)

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Let A be a 3 $\times$ 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing…

Topic: JEE Main 2021 (25 February Evening Shift)

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cosec$\left[ {2{{\cot }^{ - 1}}(5) + {{\cos }^{ - 1}}\left( {{4 \over 5}} \right)} \right]$ is equal to :

Topic: JEE Main 2021 (25 February Evening Shift)

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If 0 < x, y < $\pi$ and cosx + cosy $-$ cos(x + y) = ${3 \over 2}$, then sinx + cosy is equal to :

Topic: JEE Main 2021 (25 February Evening Shift)