List of practice Questions

If the curves $x^2 = 9A (9 - y)$ and $x^2 = A(y + 1)$ intersect orthogonally, then the value of A is

If the difference of two unit vectors is again a unit vector, then the angle between them is

If the direction consines of a vector of magnitude 3 are $\frac{2}{3 }, \frac{-a}{3},\frac{2}{3},a>0$ then the vector is

If the components of a force. are P along east and along north direction ,then the force is

If the coordinates of four concyclic points on the rectangular hyperbola $xy = c^2$ are $(ct_i, c / t_i ), \,i = 1, 2, 3, 4$ then

If the coefficients of $x^7$ and $x^8$ in $\left( 2 + \frac{x}{3} \right)^n$ are equal, then n is

If the binding energy per nucleon of deuterium is $1.115 \,MeV$, its mass defect in atomic mass unit is

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