List of top Questions asked in KEAM

If $ \alpha ,\beta ,\gamma $ are the cube roots of a negative number $p$, then for any three real numbers, $ x,y,z $ the value of $ \frac{x\alpha +y\beta +z\gamma }{x\beta +y\gamma +z\alpha } $ is

If one of the roots of the quadratic equation $ax^2 - bx + a = 0$ is $6$, then value of $\frac{ b}{ a}$ is equal to

If $ {{x}^{2}}-px+q=0 $ has the roots $ \alpha $ and $ \beta $ then the value of $ {{(\alpha -\beta )}^{2}} $ is equal to

Let $x_{1},x_{2},\cdots,x_{n}$ be in an $A.P$. If $x_{1}+x_{4}+x_{9}+x_{11}+x_{20}+x_{22}+x_{27}+x_{30}=272, $ then $x_{1}+x_{2}+x_{3}+\cdots+x_{30}$ is equal to

If $a + 1, 2a + 1, 4a - 1$ are in arithmetic progression, then the value of $a$ is

A fighter aircraft is looping in a vertical plane. The minimum velocity at the highest point is (Given, r = radius of the loop)

Two soap bubbles each with radius $r_1$ and $r_2$ coalesce in vacuum under isothermal conditions to form a bigger bubble of radius $R$. Then $R$ is equal to

The compressibility of water is $ 6\times {{10}^{-10}}{{N}^{-1}}{{m}^{2}} $ . If one litre is subjected to a pressure of $ 4\times {{10}^{7}}N{{m}^{-2}}, $ the decrease in its volume is

In a typical eukaryotic cell cycle, Gap 1, Synthesis and Gap 2 are the three phases included in the

A circuit is made using $R_1, R_2, R_3, R_4$ and a battery as shown in the following figure. Find the equivalent resistance of the given circuit and the current passing through $R_3$

The resistance $R = \frac{V}{I}$ where $V = (100 \pm 5) V $ and $I = (10 \pm 0.2) A.$ The percentage error in R is

A child of blood group O cannot have parents of blood groups

6-furfuryl amino purine, 2 ,4-dichlorophenoxy acetic acid and indole-3 acetic acid are examples respectively for

A cybrid is a hybrid carrying

0ne hormone helps in ripening of fruits while the other stimulates closure of stomata.- These are respectively

$- 1^{\circ} C$ to $13^{\circ} C$ annual variations in the intensity and duration of temperature and $50$ to $250\, cm$. annual variation in precipitation, account for the formation of a major biome as:

Consider a cylindrical conductor of Length L and area of cross section A. The specific conductivity varies as $\sigma (x) = \sigma_0 \frac{L}{\sqrt{x}}$ where x is the distance along the axis of the cylinder from one of its ends. The resistance of the system along the cylindrical axis is

$\displaystyle \int^{\sqrt{\pi}/2}_0$ $2x^{3} sin\left(x^{2}\right) dx =$dx is equal to

If $ {{a}_{1}},{{a}_{2}},.....,{{a}_{n}} $ are in AP with common difference $ d\ne 0, $ then $ (\sin d) $ $ [\sec {{a}_{1}}\sec {{a}_{2}}+ $ $ \sec {{a}_{2}}\sec {{a}_{3}}+...+\sec {{a}_{n-1}}\sec {{a}_{n}}] $ is equal to

Benzoic acid when heated with soda ltme yields

The correct order of ease of cleavage of ether linkage by hydrogen halide follows

The crystal field splitting energy for octahedral $(\Delta_0)$ and tetrahedral $(\Delta_t) $complexes is related as

If $ {{E}_{c}}=20\,\,\sin \,{{10}^{5}}\,\pi t $ and $ {{E}_{m}}=10\sin 400\pi t $ it are carrier and modulating signals, the modulation index is

The expression for van der Waals equation for the gas law is

Consider a circular loop of radius R on the xy-plane carrying a steady current anticlockwise. The magnetic field at the center of the loop is given by