List of practice Questions

Let $PQR$ be a triangle Let $\vec{a} = \overrightarrow{QR}, \, \vec{ b} = \overrightarrow{RP} and \vec{c} = \overrightarrow{PQ}$. If $\left|\vec{a}\right| = 12, \left|\vec{b}\right| = 4\sqrt{3}$ and $\vec{b}. \vec{c} = 24$, then which of the following is (are) true ?

Let $X$ and $Y$ be two arbitrary, $3 \times 3$, non-zero, skew-symmetric matrices and $Z$ be an arbitrary $3 \times 3$, nonzero, symmetric matrix. Then which of the following matrices is (are) skew symmetric ?

The area (in sq units) of the quadrilateral formed by the tangents at the end points of the latusrectum recta to the ellipse $\frac{x^2}{9} +\frac{y^2}{ 5}=1 is $

Leaf tendrils are found in

In the lead-acid battery during charging, the cathode reaction is

In Mendel's experiments with garden pea, round seed shape (RR) was dominant over wrikled seed (rr), yellow cotyledon (YY) was dominant over green cotyledon (yy). What are the expected phenotypes in the $F_{2}$ generation of the cross R R Y Y- rryy?

In a lake phytoplankton grow in abundance in

The complex number $ z = x + iy $ satisfy the equation $ |\frac {z-5i}{z+5i}| = 1 $ lies on

The equation of the curve satisfying the differential equation $ y(x+y^3)dx = x(y^3- x)dy $ and passing through the point $ (1, 1) $ is

For all real $ x, 4^{sin^2x}+ 4cos^{2x} $ is

Given that $ \int_{0}^{\infty}\frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)\left(x^{2}+c^{2}\right)} $ dx = $ \frac{\pi}{2\left(a+b\right)\left(b+c\right)\left(c+a\right)'} $ then $ \int_{0}^{\infty}\frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)} $ is

The length of the perpendicular drawn from $(1,2,3)$ to the line $ \frac{x-6}{3} = \frac {y-7}{2} = \frac {z-7}{-2} $ is

$ lim_{n\rightarrow \infty} \frac {(n!)^{1/n}}{n} $ equals

The equation $ \sqrt{\left(x-2\right)^{2}+y^{2}}+\sqrt{\left(x+2\right)^{2}+y^{2}}=4 $ represents

If $ C_o, C_1,C_2,....C_{15} $ are the binomial coefficients in the expansion of $ (1+x)^{15} $ then $ \frac {C_1}{C_o} +\frac {2C_2}{C_1}+\frac {3C_3}{C_2} +....+\frac {15C_{15}}{C_{14}} $ is equal to

From a solid sphere of mass $M$ and radius $R$, a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is

For an amplitude modulated wave the maximum amplitude is found to be $ 10\,V $ while the minimum amplitude is found to be $ 2V $ , the modulation index is

Floral formula of family-Fabaceae is

Examples of secondary air pollutants is /are

During meiosis $ -I,$ the number of chromosomes is

DNA replication takes place during

$Fe^{3+}$ is reduced to $Fe^{2+}$ by using -

The correct statement(s) about $Cr^{2+}$ and $Mn^{3+}$ is (are) - [Atomic numbers of $Cr = 24$ and $Mn = 25$]

Consider a ray of light travelling from a denser to a rarer medium. If it is incident at the critical angle then

Consider a bi-convex lens and a plano-convex lens, with radii of curvature of all the curved surfaces being same. If $f$ is the focal length of bi-convex lens then, the focal length of the plano-convex lens is