Let f : R $\to$ R be defined as $f(x) = \left\{ {\matrix{ {{{\lambda \left| {{x^2} - 5x + 6} \right|} \over {\mu (5x - {x^2} - 6)}},} & {x < 2} \cr {{e^{{{\tan (x - 2)} \over {x - [x]}}}},} & {x > 2} \cr {\mu ,} & {x = 2} \cr } } \right.$ where [x] is the greatest integer is than or equal to x. If f is continuous at x = 2, then $\lambda$ + $\mu$ is equal to :
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The locus of the centroid of the triangle formed by any point P on the hyperbola $16{x^2} - 9{y^2} + 32x + 36y - 164 = …
Topic: JEE Main 2021 (25 July Morning Shift)
Let Sn be the sum of the first n terms of an arithmetic progression. If S3n = 3S2n, then the value of ${{{S_{4n}}} \ove…
Topic: JEE Main 2021 (25 July Morning Shift)
Let $f(x) = 3{\sin ^4}x + 10{\sin ^3}x + 6{\sin ^2}x - 3$, $x \in \left[ { - {\pi \over 6},{\pi \over 2}} \right]$. T…
Topic: JEE Main 2021 (25 July Morning Shift)
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The value of the definite integral $\int\limits_{\pi /24}^{5\pi /24} {{{dx} \over {1 + \root 3 \of {\tan 2x} }}} $ is :
Topic: JEE Main 2021 (25 July Morning Shift)
If b is very small as compared to the value of a, so that the cube and other higher powers of ${b \over a}$ can be negl…
Topic: JEE Main 2021 (25 July Morning Shift)
Let y = y(x) be the solution of the differential equation ${{dy} \over {dx}} = 1 + x{e^{y - x}}, - \sqrt 2 < x <…
Topic: JEE Main 2021 (25 July Morning Shift)
The area (in sq. units) of the region, given by the set $\{ (x,y) \in R \times R|x \ge 0,2{x^2} \le y \le 4 - 2x\} $ is…
Topic: JEE Main 2021 (25 July Morning Shift)
Let g : N $\to$ N be defined as g(3n + 1) = 3n + 2, g(3n + 2) = 3n + 3, g(3n + 3) = 3n + 1, for all n $\ge$ 0. Then wh…
Topic: JEE Main 2021 (25 July Morning Shift)
Let $f:[0,\infty ) \to [0,\infty )$ be defined as $f(x) = \int_0^x {[y]dy} $ where [x] is the greatest integer less th…
Topic: JEE Main 2021 (25 July Morning Shift)
The values of a and b, for which the system of equations 2x + 3y + 6z = 8, x + 2y + az = 5, 3x + 5y + 9z = b, has no so…
Topic: JEE Main 2021 (25 July Morning Shift)
Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 bal…
Topic: JEE Main 2021 (25 July Morning Shift)
The number of real roots of the equation ${e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0$ is :
Topic: JEE Main 2021 (25 July Morning Shift)
Let an ellipse $E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$, ${a^2} > {b^2}$, passes through $\left( {\…
Topic: JEE Main 2021 (25 July Morning Shift)
