List of practice Questions

Let $P$ be the statement Ravi races and let $Q$ be the statement Ravi wins. Then, the verbal translation of $ \tilde{\ }(p\vee (\tilde{\ }q)) $ is

The quantities RC and $ \left( \frac{L}{R} \right) $ ( where $R, L$ and $C$ stand for resistance, inductance and capacitance respectively ) have the dimensions of

If $\displaystyle\sum^{9}_{i-1}\left(x_{i}-5\right)=9$ and $\displaystyle\sum^{9}_{i-1}\left(x_{i}-5\right)^{2}=45$ , then the standard deviation of the $9$ items $x_{1}, x_{2} ,\cdots, x_{9}$ is

The value of $\displaystyle \lim_{x \to 3} \frac{x^{5}-3^{5}}{x^{8}-3^{8}}$ is equal to

The vector equation of the straight line $ \frac{1-x}{3}=\frac{y+1}{-2}\,=\frac{3-z}{-1} $

Let $a =\hat{ i }-2 \hat{ j }+3 \hat{ k }$. If $b$ is a vector such that $a \cdot b =| b |^{2}$ and $| a - b |=\sqrt{7}$, then $| b |$ is equal to

If $\lambda\left(3\hat{i}+2\hat{j}-6\hat{k}\right)$ is a unit vector, then the values of $\lambda$ are

Let $ {{a}_{n}}={{i}^{{{(n+1)}^{2}}}}, $ where $ i=\sqrt{-1} $ and $ n=1,2,3..... $ . Then the value of $ {{a}_{1}}+{{a}_{3}}+{{a}_{5}}+...+{{a}_{25}} $ is

If $*$ is defined by $a*b$ = $a - b^2$ and $\oplus$ is defined by $\oplus$ = $a^2 + b$, where a and b are integers, then ($3 \oplus 4) * 5$ is equal to

The number of functions that can be defined from the set $A \,= \{a, b, c, d\}$ into the set $B\, =\{1,2,3\}$ is equal to

The perpendicular distance from the point $(1, -1)$ to the line $x + 5y - 9 = 0$ is equal to

Two finite sets $A $ and$ B $ have m and n elements respectively. If the total number of subsets of $A $ is 112 more than the total number of subsets of $B$, then the value of m is

For any two statements $p$ and $q$, the statement $\sim\left(p \vee q\right) \vee \left(\sim p \wedge q\right)$ the is equivalent to

The equation of the tangent to the curve $ y={{(1+x)}^{y}}+{{\sin }^{-1}}({{\sin }^{2}}x) $ at $ x=0 $ is:

If $\begin{bmatrix}1&x&1\end{bmatrix} \begin{bmatrix}1&3&2\\ 2&5&1\\ 15&3&2\end{bmatrix}\begin{bmatrix}1\\ 2\\ x\end{bmatrix} = 0 $, then x can be

Equation of the plane passing through the intersection of the planes $ x+y+z=6 $ and $ 2x+3y+4z+5=0 $ and the point $(1, 1, 1)$ is

The area of the plane region bounded by the curve $ x={{y}^{2}}-2 $ and the line $ y=-x $ is (in square units)

The chord joining the points $(5, 5)$ and $(11, 227)$ on the curve $y =3x^{2}-11x-15$ is parallel to tangent at a point on the curve. Then the abscissa of the point is

Two distinct numbers $x$ and $y$ are chosen from $1,2,3,4,5$. The probability that the arithmetic mean of $x$ and $y$ is an integer is

If $a = e^{i \theta}$ , then $\frac{1 + a}{1-a}$ is equal to

If $A = \begin{pmatrix}1&0\\ 1&1\end{pmatrix}$ , then $A^n + nI$ is equal to

If $ y={{\sin }^{-1}}\sqrt{1-x}, $ then $ \frac{dy}{dx} $ is equal to

An insoluble dye is reduced to a soluble colourless leuco form by an alkaline reducing agent. The fibre is soaked in the dye solution and then exposed to air to develop the colour. The dye is

The reaction of $H_2$ is given below $H_2 + CO + R - CH = CH_2 \to R - CH_2 - CH_2 - CHO$ is specifically called as