If $\mathop {\lim }\limits_{x \to \infty } \left( {\sqrt {{x^2} - x + 1} - ax} \right) = b$, then the ordered pair (a, b) is :
Previous 10 Questions — JEE Main 2021 (27 August Evening Shift)
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The value of the integral $\displaystyle \int_{0}^{1} \frac{\sqrt{x}\,dx}{(1+x)(1+3x)(3+x)}$ is:
Topic: JEE Main 2021 (27 August Evening Shift)
If $y(x)=\cot^{-1}\!\left(\dfrac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right),\; x\in\left(…
Topic: JEE Main 2021 (27 August Evening Shift)
The area of the region bounded by the parabola (y $-$ 2)2 = (x $-$ 1), the tangent to it at the point whose ordinate is…
Topic: JEE Main 2021 (27 August Evening Shift)
Let Z be the set of all integers,$A = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {y^2} \le 4\} $, $B = \{ (x,y) \in Z \times…
Topic: JEE Main 2021 (27 August Evening Shift)
The set of all values of K > $-$1, for which the equation ${(3{x^2} + 4x + 3)^2} - (k + 1)(3{x^2} + 4x + 3)(3{x^2} +…
Topic: JEE Main 2021 (27 August Evening Shift)
A box open from top is made from a rectangular sheet of dimension a x b by cutting squares each of side x from eac…
Topic: JEE Main 2021 (27 August Evening Shift)
Let [$\lambda$] be the greatest integer less than or equal to $\lambda$. The set of all values of $\lambda$ for which t…
Topic: JEE Main 2021 (27 August Evening Shift)
If the solution curve of the differential equation (2x $-$ 10y3)dy + ydx = 0, passes through the points (0, 1) and (2, …
Topic: JEE Main 2021 (27 August Evening Shift)
If two tangents drawn from a point P to the parabola y2 = 16(x $-$ 3) are at right angles, then the locus of point P i…
Topic: JEE Main 2021 (27 August Evening Shift)
Let M and m respectively be the maximum and minimum values of the function f(x) = tan$-$1 (sin x + cos x) in $\left[ {…
Topic: JEE Main 2021 (27 August Evening Shift)
