List of practice Questions

If the carbon atoms fixed by producers already have passed through three species, the trophic level of the last species would be

If the chord of contact of tangents from a point $ P (x_1, y_1)$ to the circle $x^2 + y^2 = a^2$ touches the circle $ x^2 + y^2 = r^2$, then the locus of $(x_1,y_1)$ is

If the chords of contact of tangents from two points $(x_1,\,y_1)$ and $(x_2,\,y_2)$ to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ are at right angles, then $\frac{x_1\,x_2}{y_1\,y_2}$ is equal to

If the angle between two lines is $\frac{\pi}{4}$ and slope of one of the lines is $\frac{1}{2}$, find the slope of the other line.

If the atmospheric pressure is 76cm of Hg at what depth of water in a lake the pressure will become 2 atmospheres nearly.

If the Avogadro's number was to tend to infinity; the phenomenon of Brownian motion would:

If $tanA + cotA = 4$, then $tan^4A + cot^4A$ is equal to

If tangent to the curve $y^2 = x^3$ at its point $(m^2, m^3)$ is also normal to the curve at $(M^2, M^3)$, then what is the value of mM ?

If the algebraic sum of deviations of 20 observation from 30 is 20, then the mean of the observation is

If $\tan (\cot \, x) = \cot (\tan \, x)$, then $\sin \, 2x $ is equal to :

If $\tan \, \theta + sec \, \theta = p$, then what is the value of $\sec \, \theta$ ?

If $tanA=\frac{1}{2}$, $tanB=\frac{1}{3}$, then $tan\left(2A+B\right)$ is equal to

If $t$ is the parameter for one end of a focal chord of the parabola $y^2 = 4ax$, then its length is

If $T_n$ denotes the $nth$ term of the series $2 + 3 + 6 + 11 + 18 + ...... ,$ then $T_{50}$ is equal to

If $\tan^{-1}\frac{1-x}{1+x}=\frac{1}{2}\tan^{-1}x$, then the value of $x$ is

If $\tan^{-1} \left(2x\right) + \tan^{-1} \left(3x\right) = \frac{\pi}{4} $ then x is equal to :

If $sin\,x \frac{dy}{dx}+y\,cos\,x=x\,sinx$, then $\left(y-1\right)\,sin\,x=$

If $sinA=\frac{3}{5}$ and $A$ is in first quadrant, then the values of $sin2A$, $cos2A$ and $tan2A$ are

If spheres of radius $'r'$ are arranged in ccp fashion (ABCABC.....), the vertical distance between any two consecutive A layers is

If $\sin \alpha + \sin \beta = 0 = \cos \alpha + \cos \beta$, then $\cos 2\alpha + \cos 2\beta =$

If $\sin \, \theta = \frac{24}{25} $ and $0^{\circ} < \theta < 90^{\circ}$ then what is the value of $\sin \left( \frac{\theta}{2} \right)$ ?

If $\sin \, x + cosec \, x = 2$ then $\sin^n \, x + cosec^n \, x (n > 2)$ is equal to

If $\frac{sin\,A}{sin\,B}=m$ and $\frac{cos\,A}{cos\,B}=n$ then find the value of $tan \,B$; $n^2 < 1 < m^2$.

If $\sin \, 4A - \cos \, 2A = \cos \, 4A- \sin \, 2A \left( 0 < A < \frac{\pi}{4} \right)$ then the value of tan 4A =

If $\sin 6\theta + \sin 4\theta + \sin 2\theta = 0$, then general value of $\theta$ is