List of practice Questions

If the mean of first n natural numbers is equal to $\frac{n + 7}{3}$, then n is equal to

If the length of three sides of a trapezium other than base are equal to $10 \,cm$, then find the area of trapezium when it is maximum.

If the line $3x - 4y + 5 = 0$ is a tangent to the parabola $y^2 = 4ax,$ then $a$ is equal to

If the line $ax + by + c = 0$ is a tangent to the curve $xy = 4,$ then

If the line joining $(2, 3, -1)$ and $(3, 5, -3)$ is perpendicular to the line joining $(1, 2, 3)$ and $(3, 5, \lambda)$, then $A =$

If the internal bisector of $\angle AOB$ where $O = (0, 0, 0), A= (3, 4, 12), B = (1, 2, 2)$ intersects AB at C then $C_y$ =

If the ionisation energy of hydrogen atom is $13.6\,eV$, the energy required to excite it from ground state to the next higher state is approximately

If the $j^{th}$ term and $k^{th}$ term of an A.P. are k and j respectively, the ( k + j) th term is:?

If the leaves on the stem show distichous condition, the

If the general formula for aldehyde is written as ${C_n H_{2n+1}CHO}$, the value of n for isobutyraldehyde is

If the half life of a radioactive substance is T, then its decay constant $\lambda$ is given by :

If the initial velocity of a body is $V_1$ and final velocity is $V_2$ and the angle between $V_1$ and $V_1$ is $\phi$ then the change in velocity is.

If the instantaneous current in a circuit is given by $I=2\,\cos(\omega+ \phi)$ ampere, the rms value of the current is.

If the events $A$ and $B$ are independent, then $P(A \cap B)$ is equal to

If the four points $\left(3, -2 , -1\right), \left(2, 3, -4\right)$, $\left(-1, 1, 2\right)$ and $\left(4, 5, \lambda\right)$ are coplanar then $\lambda$ is equal to

If the functions $f : R \rightarrow R , g : R \rightarrow R$ are defined as $f(x) = 2x +3, g(x) = x^2 + 7$ and $f[g(x)] = 25$ then $x = $

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