List of top Questions asked in KEAM

If $z = i^9 + i^{19}$ , then $z$ is equal to

Let $S_{1}$ be a square of side $5\,cm$. Another square $S_{2}$ is drawn by joining the midpoints of the sides of $S_{1}$ Square $S_{3}$ is drawn by joining the midpoints of the sides of $S_{2}$ and so on. Then (area of $S_{1}$ + area of $S_{2}$ + area of $S_{3}$ $+\ldots+$ area of $S_{10}$) =

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 $ \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

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

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

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

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

Which one of the following amines forms a non-acidic and alkali insoluble product with p-toluenesulphonyl chloride?

The ratio of hydraulic stress to the corresponding strain is known as

Consider the following statements concerning $N_2H_4$ 1. It is an exothermic compound 2. It burns in air with the evolution of heat 3. It has kinetic stability 4. In reduces $Fe^{3+}$ to $Fe^{2+}$ in acidic medium Which of the following combination is correct?