List of top Questions asked in KEAM

The acceleration of a moving body is found from the

If the amount of heat given to a system is $35\, J$ and the amount of work done on the system is $15\, J$, then the change in internal energy of the system is

$ \displaystyle\lim_{x\rightarrow0} \frac{1}{3-2^{\frac{1}{x}}}$ is equal to

If $ \tan \alpha =\frac{b}{a},a>b>0 $ and if $ 0

If $y = x + \frac{1}{x}, x \ne 0$, then the equation $\left(x^{2}-3x+1\right)\left(x^{2}-5x+1\right)=6x^{2}$ reduces to

The value of $\sum\limits^{n}_{k=0}\left(i^{k}+i^{k+1}\right)$, where $i^2 = -1$, is equal to

The negation of $\left(p\vee\sim q\right)\wedge q$ is

Let $p$ : roses are red and q : the sun is a star. Then, the verbal translation of $ (-\text{ }p) \vee q $ is

$\int \frac{e^{x}}{x}\left(x\,log\,x+1\right)dx$ 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 $S_{10}$) =

If z =$\frac{2-i}{i}$ = , then Re(z$^2$) + lm(z$^2$) is equal to

If the equation $2x^2 - (a+3)x + 8 = 0$ has equal roots, then one of the values of $a$ is

If $ {{x}^{2}}+4ax+2>0 $ for all values of $ x, $ then $a$ lies in the interval

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

The plane $ \overrightarrow{r}=s(\hat{i}+2\hat{j}-4\hat{k})+t(3\hat{i}+4\hat{j}-4\hat{k}) $ $ +(1-t)(2\hat{i}-7\hat{j}-3\hat{k}) $ is parallel to the line

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

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