AP EAPCET 2021 - 19th August Morning Shift

The line which is parallel to X-axis and crosses the curve \(y=\sqrt x\) at an angle of 45\(\Upsilon\) is

If the error committed in measuring the
radius of a circle is 0.05%, then the
corresponding error in calculating its area
would be

The stationary points of the curve \(y=8 x^2-x^4-4\) are

The distance between the origin and the normal to the curve \(y=e^{2 x}+x^2\) drawn at \(x=0\) is units

Find the equations of the tangents drawn to the circle \(x^2+y^2=50\) at the points where the line \(x+7=0\) meets it.

If the chord of contact of tangents from a point on the circle \(x^2+y^2=r_1^2\) to the circle \(x^2+y^2=r_2^2\) touches the circle \(x^2+y^2=r_3^2\), then \(r_1, r_2\) and \(r_3\) are in

Find the equation of the circle passing through \((1,-2)\) and touching the \(X\)-axis at \((3,0)\).

Let \(L_1\) be a straight line passing through the origin and \(L_2\) be the straight line \(x+y=1\). If the intercepts made by the circle \(x^2+y^2-x+3 y=0\) on \(L_1\) and \(L_2\) are equal, then which of the following equations represent...

The radius of the circle whose center lies at \((1,2)\) while cutting the circle \(x^2+y^2+4 x+16 y-30=0\) orthogonally, is units.

The point which has the same power with respect to each of the circles \(x^2+y^2-8 x+40=0, x^2+y^2-5 x+16=0\) and \(x^2+y^2-8 x+16 y+160=0\) is

\((\sin \theta-i \cos \theta)^3\) is equal to

Real part of \((\cos 4+i \sin 4+1)^{2020}\) is

\(\int_2^4\{|x-2|+|x-3|\} d x\) is equal to

\(\int\limits_{-1 / 2}^{1 / 2}\left\{[x]+\log \left(\frac{1+x}{1-x}\right)\right\} d x\) is equal to

The solution of the differential equation \(\frac{d^2 y}{d x^2}+y=0\) is

If \(y=x+\frac{1}{x}\), then which among the following holds?

If \(3 \sin x y+4 \cos x y=5\), then \(\frac{d y}{d x}\) is equal to

\(f(x)=\sqrt{x^2+1}: g(x)=\frac{x+1}{x^2+1}: h(x)=2 x-3\), then the value of \(f^{\prime}\left[h^{\prime}\left(g^{\prime}(x)\right)\right]\) is equal to

For which value(s) of \(a\) \(f(x)=-x^3+4 a x^2+2 x-5\) is decreasing for every \(x\) ?

If a point \(P(x, y)\) moves along the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) and if \(C\) is the center of the ellipse, then the sum of maximum and minimum values of \(C P\) is

Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)=2 x+1\) and \(g(x)=x^2-2\) determine \((g \circ f)(x)\) is equal to

Given, the function \(f(x)=\frac{a^x+a^{-x}}{2},(a>2)\), then \(f(x+y)+f(x-y)\) is equal to

If \(f\) is a function defined on \((0,1)\) by \(f(x)=\min \{x-[x],-x-[x]\}\), then \((f \circ f o f o f)(x)\) is equal to \(\rightarrow([\cdot]\) greatest integer function)

If \({({x^2} + 5x + 5)^{x + 5}} = 1\), then the number of integers satisfying this equation is

If \(\frac{x^4}{(x-1)(x-2)}=f(x)+\frac{A}{x-1}+\frac{B}{x-2}\), then

Which statement among the following is true?
(i) the function \(f(x)=x|x|\) is strictly increasing on \(R-\{0\}\).
(ii) the function \(f(x)=\log _{(1 / 4)} x\) is strictly increasing on \((0, \infty)\).
(iii) a one-one function is always an...

The asymptotes of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), with any tangent to the hyperbola form a triangle whose area is \(a^2 \tan (\alpha)\). Then, its eccentricity equals

\(\int \frac{e^x(x+3)}{(x+5)^3} d x\) is equal to

If \(\int \frac{(x-1)^2}{\left(x^2+1\right)^2} d x=\tan ^{-1}(x)+g(x)+k\), then \(g(x)\) is equal to

If \(\int \frac{1-(\cot x)^{2021}}{\tan x+(\cot x)^{2022}} d x=\frac{1}{A} \log\left|(\sin x)^{2023}+(\cos x)^{2023}\right|+c\), then \(A\) is equal to

If \(\tan ^{-1}\left[\frac{1}{1+1 \cdot 2}\right]+\tan ^{-1}\left[\frac{1}{1+2 \cdot 3}\right]+\ldots+\tan ^{-1} \left[\frac{1}{1+n(1+1)}\right]=\tan ^{-1}[x]\), then \(x\) is equal to

If \(y=\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)\), where \(x^2 \leq 1\). Then, find \(\frac{d y}{d x}\) is equal to

If \(\int \frac{d x}{x\left(\sqrt{\left.x^4-1\right)}\right.}=\frac{1}{k} \sec ^{-1}\left(x^k\right)\), then the value of \(k\) is equal to

\(\lim _\limits{z \rightarrow 1} \frac{z^{(1 / 3)}-1}{z^{(1 / 6)}-1}\) is equal to

$$f(x)=\left\{\begin{array}{cc} \frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}}, & x \neq 0 \\ K \log 2 \log 3, & x=0 \end{array}\right.$$
Find the value of \(k\) for which the function \(f\) is continuous.

If the function \(f(x)\), defined below is continuous in the interval \([0, \pi]\), then $$f(x)=\left\{\begin{array}{cc}x+a \sqrt{2}(\sin x) & , \quad 0 \leq x < \frac{\pi}{4} \\ 2 x(\cot x)+b, & \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\ a...

\(n \in N\) then, the statement \(8 n+16 \leq 2^n\) is true for

The equation whose roots are the values of the equation \(\left| {\matrix{ 1 & { - 3} & 1 \cr 1 & 6 & 4 \cr 1 & {3x} & {{x^2}} \cr } } \right| = 0\) is

Let a and b be non-zero real numbers such that \(ab=5/2\) and given \(A = \left[ {\matrix{ a & { - b} \cr b & a \cr } } \right]\) and \(A{A^T} = 20I\) (\(l\) is unit matrix), then the equation whose roots are a and b is

If $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], 10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]$$ and \(B=A^{-1}\), then the value of \(\alpha\) is

The rank of the matrix $$\left[\begin{array}{ccc}4 & 2 & (1-x) \\ 5 & k & 1 \\ 6 & 3 & (1+x)\end{array}\right]$$ is 1 , then,

If \(a_1, a_2, \ldots . a_9\) are in GP, then $$\left|\begin{array}{lll}\log a_1 & \log a_2 & \log a_3 \\ \log a_4 & \log a_5 & \log a_6 \\ \log a_7 & \log a_8 & \log a_9\end{array}\right|$$ is equal to

If \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\), then the value of $$\left|\...

If one end of focal chord of the parabola \(y^2=8x\) is \(\left(\frac{1}{2},2\right)\), then the length of the focal chord is ................ units.

If a person has 3 coins of different denominations, the number of different sums can be formed is

There are 7 identical white balls and 3 identical black balls. The number of distinguishable arrangements in a row of all the balls, so that no two black balls are adjacent is

The number of ways of distributing eight identical rings to three different girls so that every girl gets at least one ring is

If the letters of the word REGULATIONS be
arranged in such a way that relative positions
of the letters of the word GULATIONS
remain the same, then the probability that
there are exactly 4 letters between R and E is

12 balls are distributed among 3 boxes, then the probability that the first box will contain 3 balls is

A random variable X has the probability distribution

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