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
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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 :
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:
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 :
A microscope is focused on an object at the bottom of a bucket If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by $30\, cm$ to focus the object again The height of the liquid in the bucket is :
In Dumas method for the estimation of $N _2$, the sample is heated with copper oxide and the gas evolved is passed over :
When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of $A$?
Arrange the following orbitals in decreasing order of energy A. $n=3, l =0, m =0$ B. $n =4, l =0, m =0$ C. $n =3, l =1, m =0$ D. $n =3, l =2, m =1$ The correct option for the order is :
Which of the following compounds are not used as disinfectants? A. ChloroxylenolB. BithionalC. VeronalD. ProntosilE. TerpineolChoose the correct answer from the options given below:
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)Assertion (A): The first ionization enthalpy of $3d$ series elements is more than that of group 2 metalsReason (R): In $3d$ series of elements successive filling of d-orbitals takes placeIn the light of the above statements, choose the correct answer from the options given below :
Evaluate the following statements for their correctness A. The elevation in boiling point temperature of water will be same for $01 \,M \,NaCl$ and $01\, M$ urea B. Azeotropic mixtures boil without change in their compositionC. Osmosis always takes place from hypertonic to hypotonic solution D. The density of $32 \% H _2 SO _4$ solution having molarity $409\, M$ is approximately $126\, g mL ^{-1}$ E. A negatively charged sol is obtained when KI solution is added to silver nitrate solutionChoose the correct answer from the options given below :
Given below are two statements : Statement I : Upon heating a borax bead dipped in cupric sulphate in a luminous flame, the colour of the bead becomes green.Statement II : The green colour observerd is due to the formation of copper(I) metaborate.In the light of the above statements, choose the most appropriate answer from the options given below :
Compound $A , C _5 H _{10} O _5$, given a tetraacetate with $AC _2 O$ and oxidation of $A$ with $Br _2- H _2 O$ gives an acid, $C _5 H _{10} O _6$ Reduction of $A$ with $HI$ gives isopentane The possible structure of $A$ is: