A bag contains 6 balls Two balls are drawn from it at random and both are found to be black The probability that the bag contains at least 5 black balls is
The number of real roots of the equation $\sqrt{x^2-4 x+3}+\sqrt{x^2-9}=\sqrt{4 x^2-14 x+6}$, is:
$( S 1)(p \Rightarrow q) \vee(p \wedge(\sim q))$ is a tautology(S2) $((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)$ is a contradictionThen
Let the shortest distance between the lines $L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$ and $L_1: x+1=y-1=4-z$ be $2 \sqrt{6}$ If $(\alpha, \beta, \gamma)$ lies on $L$, then which of the following is NOT possible?
Let $\alpha \in(0,1)$ and $\beta=\log _e(1-\alpha)$ Let $P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\ldots+\frac{x^n}{n}, x \in(0,1)$ Then the integral $\int\limits_0^\alpha \frac{t^{50}}{1-t} d t$ is equal to
Let $A=\begin{pmatrix}1 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & 12 & -3\end{pmatrix}$ Then the sum of the diagonal elements of the matrix $(A+I)^{11}$ is equal to :
For all $z \in C$ on the curve $C_1:|z|=4$, let the locus of the point $z+\frac{1}{z}$ be the curve $C_2$ Then:
Let $R$ be a relation on $N \times N$ defined by $(a, b) R (c, d)$ if and only if $a d(b-c)=b c(a-d)$ Then $R$ is
A wire of length $20 m$ is to be cut into two pieces A piece of length $l_1$ is bent to make a square of area $A_1$ and the other piece of length $l_2$ is made into a circle of area $A_2$ If $2 A_1+3 A_2$ is minimum then $\left(\pi l_1\right): l_2$ is equal to:
Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ Then $S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$ :
Match List I with List II
Choose the correct answer from the options given below.
Under the same load, wire A having length $50 m$ and cross section $25 \times 10^{-5} m ^2$ stretches uniformly by the same amount as another wire $B$ of length $60 m$ and a cross section of $30 \times 10^{-5}$ $m ^2$ stretches The ratio of the Young's modulus of wire $A$ to that of wire $B$ will be :
An alternating voltage source $V =260 \sin (628 t )$ is connected across a pure inductor of $5 mH$ Inductive reactance in the circuit is :
A body is moving with constant speed, in a circle of radius $10 m$ .The body completes one revolution in 4 s .At the end of 3 rd second, the displacement of body (in mi) from its starting point is :
Considering a group of positive charges, which of the following statements is correct ?
The $H$ amount of thermal energy is developed by a resistor in $10 s$ when a current of $4 A$ is passed through it If the current is increased to $16 A$, the themal energy developed by the resistor in $10 s$ will be:
For a solid rod, the Young's modulus of elasticity is $32 \times 10^{11} Nm ^{-2}$ and density is $8 \times 10^3 kg m ^{-3}$ The velocity of longitudinal wave in the rod will be
A long conducting wire having a current I flowing through it, is bent into a circular coil of $N$ turns .Then it is bent into a circular coil of $n$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is :
The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by $50 \%$ The percentage change in voltage sensitivity of the galvanometer will be:
Given below are two statements : Statement I : For transmitting a signal, size of antenna ( $f$ ) should be comparable to wavelength of signal (at least $l=\frac{\lambda}{4}$ in dimension)Statement II : In amplitude modulation, amplitude of carrier wave remains constant (unchanged) In the light of the above statements, choose the most appropriate answer from the options given below,
A body of mass $10 kg$ is moving with an initial speed of $20 m / s$ The body stops after $5 s$ due to friction between body and the floor The value of the coefficient of friction is: (Take acceleration due to gravity $g =10 ms ^{-2}$ )
Choose the correct answer from the options given below:
Given below are two statements :Statement I : In a typical transistor, all three regions emitter, base and collector have same doping level.Statement II : In a transistor, collector is the thickest and base is the thinnest segment.In the light of the above statements, choose the most appropriate answer from the options given below.
Heat energy of 735J is given to a diatomic gas allowing the gas to expand at constant pressure Each gas molecule rotates around an internal axis but do not oscillate The increase in the intemal energy of the gas will be :
A stone of mass $1 \, kg$ is tied to end of a massless string of length $1 m$ If the breaking tension of the string is $400\, N$, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is :