Let f : R $-$ {3} $ \to $ R $-$ {1} be defined by f(x) = ${{x - 2} \over {x - 3}}$.Let g : R $ \to $ R be given as g(x) = 2x $-$ 3. Then, the sum of all the values of x for which f^$-$1(x) + g^$-$1(x) = ${{13} \over 2}$ is equal to :

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Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be a…

Topic: JEE Main 2021 (18 March Evening Shift)

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Define a relation R over a class of n $\times$ n real matrices A and B as "ARB iff there exists a non-singular matrix P…

Topic: JEE Main 2021 (18 March Evening Shift)

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In a triangle ABC, if $|\overrightarrow {BC} | = 8,|\overrightarrow {CA} | = 7,|\overrightarrow {AB} | = 10$, then the …

Topic: JEE Main 2021 (18 March Evening Shift)

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Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $-$a. Also by adding a …

Topic: JEE Main 2021 (18 March Evening Shift)

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Let g(x) = $\int_0^x {f(t)dt} $, where f is continuous function in [ 0, 3 ] such that ${1 \over 3}$ $ \le $ f(t) $ \le …

Topic: JEE Main 2021 (18 March Evening Shift)

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Let \; f:\mathbb{R}\to\mathbb{R} \text{ be defined as} \[ f(x) = \begin{cases} \dfrac{\sin\!\big((a+1)x\big)+\sin 2x}{2…

Topic: JEE Main 2021 (18 March Evening Shift)

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Let a complex number be w = 1 $-$ ${\sqrt 3 }$i. Let another complex number z be such that |zw| = 1 and arg(z) $-$ arg(…

Topic: JEE Main 2021 (18 March Evening Shift)

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Let $\overrightarrow a $ and $\overrightarrow b $ be two non-zero vectors perpendicular to each other and $|\overrighta…

Topic: JEE Main 2021 (18 March Evening Shift)

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If 15sin4$\alpha$ + 10cos4$\alpha$ = 6, for some $\alpha$$\in$R, then the value of 27sec6$\alpha$ + 8cosec6$\alpha$ is…

Topic: JEE Main 2021 (18 March Evening Shift)

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The area bounded by the curve 4y2 = x2(4 $-$ x)(x $-$ 2) is equal to :

Topic: JEE Main 2021 (18 March Evening Shift)

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Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arith…

Topic: JEE Main 2021 (18 March Evening Shift)