The center of the circle (x-1)<sup>2</sup>+(y+3)<sup>2</sup> is:
The center of the circle (x-1)2+(y+3)2 is:
(1,-3) | |
(-1,-3) | |
(1,3) | |
(-1,3) |
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The general equation of second degree: ax<sup>2</sup>+by<sup>2</sup>+2hxy+2gx+2fy+c=0 is a parabola if
The general equation of second degree: ax2+by2+2hxy+2gx+2fy+c=0 is a parabola if
\[{h^2} - ab > 0\] | |
\[{h^2} - ab \ne 0\] | |
h2 - ab = 0 | |
\[{h^2} - ab < 0\] |
In equation of circle, coefficient of each of x<sup>2</sup> and y<sup>2</sup> are:
In equation of circle, coefficient of each of x2 and y2 are:
Not Equal | |
None of These | |
Equal | |
Opposite in Signs |
The order of a differential equation \(y\frac{{dy}}{{dx}} + 2x = 0\) is:
The order of a differential equation \(y\frac{{dy}}{{dx}} + 2x = 0\) is:
None of these | |
1 | |
2 | |
0 |
Solution of differential equation \(\frac{{dy}}{{dx}} = \cos x\) is:
Solution of differential equation \(\frac{{dy}}{{dx}} = \cos x\) is:
\(y = \cot x + c\) | |
\(y = \sin x + c\) | |
\(y = \tan x + c\) | |
\(x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\) |
Solution of differential equation \(\frac{{dy}}{{dx}} = - y\) is:
Solution of differential equation \(\frac{{dy}}{{dx}} = - y\) is:
\(y = {e^x}\) | |
\(y = x{e^{ - x}}\) | |
\(y = c{e^{ - x}}\) | |
\(y = {e^{ - x}}\) |
The solution of differential equation \(\frac{{dy}}{{dx}} = {\sec ^2}x\) is:
The solution of differential equation \(\frac{{dy}}{{dx}} = {\sec ^2}x\) is:
y = cosx + c | |
y = secx + c | |
\(y = {\csc ^2}x + c\) | |
y = tanx + c |
Solution of differential equation, \(\frac{{dy}}{{dx}} = y\) is:
Solution of differential equation, \(\frac{{dy}}{{dx}} = y\) is:
\(c{e^{ - x}}\) | |
\({e^x}\) | |
\(c{e^x}\) | |
\({e^{ - x}}\) |
Solution of differential equation \(\frac{{dy}}{{dx}} = \csc x\cot x\) is y = _____.
Solution of differential equation \(\frac{{dy}}{{dx}} = \csc x\cot x\) is y = _____.
cscx+c | |
-cot+c | |
cotx+c | |
-cscx+c |
\(\int\limits_a^b {f(x)dx} \) as the area under the curve y = f(x) from x = a to x = b and the x-axis is called:
\(\int\limits_a^b {f(x)dx} \) as the area under the curve y = f(x) from x = a to x = b and the x-axis is called:
None of these | |
Definite integral | |
Differentiation | |
Integration by parts |
If the graph of f is entirely below the x-axis, then the definite integral is:
If the graph of f is entirely below the x-axis, then the definite integral is:
Positive | |
Negative | |
Positive or negative | |
Positive and negative |
\(\int\limits_0^3 {\frac{1}{{\sqrt {9 - {x^2}} }}} \) is equal to:
\(\int\limits_0^3 {\frac{1}{{\sqrt {9 - {x^2}} }}} \) is equal to:
\(\frac{{\pi}}{2}\) | |
\(\frac{{ - \pi }}{2}\) | |
\(\frac{ -2 }{\pi }\) | |
\(\frac{2}{\pi }\) |
\(\int\limits_1^2 {a{}^xdx} \) equals:
\(\int\limits_1^2 {a{}^xdx} \) equals:
\(\frac{a}{{{{(\ln a)}^2}}}\) | |
\(\frac{{{a^2}}}{{\ln a}}\) | |
\(\frac{{{a^2}}}{{\ln a}} - \frac{a}{{\ln a}}\) | |
\(\frac{{{a^2}}}{{{{(\ln a)}^2}}}\) |
\(\int\limits_{\frac{1}{{\sqrt 2 }}}^{\frac{{\sqrt 3 }}{2}} {\frac{{dx}}{{\sqrt {1 - {x^2}} }}} = \)
\(\int\limits_{\frac{1}{{\sqrt 2 }}}^{\frac{{\sqrt 3 }}{2}} {\frac{{dx}}{{\sqrt {1 - {x^2}} }}} = \)
\(\frac{\pi }{4}\) | |
\(\frac{\pi }{3}\) | |
\(\frac{\pi }{12}\) | |
\(\frac{\pi }{6}\) |
\(f{e^x}(\cos x + \sin x)dx = \)
\(f{e^x}(\cos x + \sin x)dx = \)
\({e^x}\sin x + c\) | |
\( - {e^x}\cos x + c\) | |
\({e^x}\cos x + c\) | |
\( - {e^x}\sin x + c\) |
\(\int {\ln xdx = } \)
\(\int {\ln xdx = } \)
\(x\ln x - x + c\) | |
\(x\ln x + x + c\) | |
\(x - x\ln x + c\) | |
\(x + x\ln x + c\) |
\(f{e^x}(x + 1)dx = \)
\(f{e^x}(x + 1)dx = \)
\({e^x}.\frac{{{x^2}}}{2}\) | |
\({e^x}\) | |
\(x{e^x}\) | |
None of these |
\(\int {\frac{{{{\sec }^2}x}}{{\sqrt {\tan x} }}} dx\) is equal to:
\(\int {\frac{{{{\sec }^2}x}}{{\sqrt {\tan x} }}} dx\) is equal to:
\(\sqrt {\tan x} + c\) | |
\(\ln \sqrt {\tan x} + c\) | |
\(2\sqrt {\tan x} + c\) | |
\( - 2\sqrt {\tan x} + c\) |
\(\int {\frac{1}{{\sqrt {1 - {x^2}} }}} dx = \_\_\_\_\_:\)
\(\int {\frac{1}{{\sqrt {1 - {x^2}} }}} dx = \_\_\_\_\_:\)
cos-1x | |
sin-1x | |
-sin-1x | |
-cos-1x |
\(\int {{{\sin }^2}xdx} = ?\)
\(\int {{{\sin }^2}xdx} = ?\)
\(\frac{1}{2}\left( {x + \sin 2x} \right) + c\) | |
\(\frac{1}{2}\left( {x - \sin 2x} \right) + c\) | |
\(\frac{1}{2}\left( {x + \frac{{\sin 2x}}{2}} \right) + c\) | |
\(\frac{1}{2}\left( {x - \frac{{\sin 2x}}{2}} \right) + c\) |