If PQR is the triangle formed by the common tangents to the circles \[{{x}^{2}}+{{y}^{2}}+6x\text{ }=\text{ }0\] and\[a{{x}^{2}}+{{y}^{2}}-2x=0\]then choose the incorrect option
An ellipse of eccentricity \[\frac{2\sqrt{2}}{3}\] is inscribed in a circle and a point with in the circle is chosen at random. The probability that this point lies outside the ellipse is:
A is one of the six horses entered for a race and one of the two jockeys B and C ride it. If B rides A, then all the six horses are equally likely to win. If C rides A, then chances of A's win will be trebled. Then, the odds in favour of A's win is
Let coordinates of the points \[A\] and \[B\] are (5, 0) and (0, 7) respectively. P and Q are the variable points lying on the x-and y-axis respectively so that PQ is always perpendicular to the line AB. Then locus of the point of intersection of BP and AQ is
If \[k\in I\] such that \[\underset{n\to \infty }{\mathop{\lim }}\,{{\left( \cos \frac{k\pi }{4} \right)}^{2n}}-{{\left( \cos \frac{k\pi }{6} \right)}^{2n}}=0,\] then
A)
k must not be divisible by 24
doneclear
B)
k is divisible by 24 or k is divisible neither by 4 nor by 6
doneclear
C)
k must be divisible by 12 but not necessarily by 24
The set of homoegeneous equations: \[tx+\left( t+1 \right)y+\left( t-1 \right)z=0;\left( t+1 \right)x+ty+\left( t+2 \right)\]\[z=0;\left( t-1 \right)x+\left( t+2 \right)y+tz=0\] has non-trivial solution for
Let f(x) and g (x) be bijective functions where \[f:\{a,b,c,d\}\to \{1,2,3,4\}\]\[g:\left\{ 3,4,5,6 \right\}\to \left\{ w,x,y,z \right\}\] respectively. The number of elements in the range set of \[g\text{ }\left( f\left( x \right) \right)\] are
Let \[\omega \] be a complex cube root of unity with \[\omega \ne 1.\] A fair die is thrown three times. If \[{{r}_{1}},{{r}_{2}}\] and \[{{r}_{3}}\] are the numbers obtained on the die, then the Probability that \[{{\omega }^{{{r}_{1}}}}+{{\omega }^{{{r}_{2}}}}+{{\omega }^{{{r}_{3}}}}=0\]is
The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as R, has the colour code (Orange, Red, Brown), The resistors \[{{R}_{2}}\] and \[{{R}_{4}}\] are \[80\Omega \] and\[40\Omega ,\], respectively.
Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as \[{{R}_{3}}\] would be:
Consider the nuclear fission\[N{{e}^{20}}\to 2H{{e}^{4}}+{{C}^{12}}.\]Given that the binding energy / nucleon of\[N{{e}^{20}},\]\[H{{e}^{4}}\]and\[{{C}^{12}}\]are, respectively, \[8.03\text{ }MeV,\]\[7.07\] \[MeV,\]and\[7.86\text{ }MeV,\] identify the correct statement:
A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are \[{{T}_{h}}\] and\[{{T}_{c}}\] respectively, then:
An unknown metal of mass 192 g heated to a temperature of\[100{}^\circ C\] was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of \[8.4{}^\circ C.\] Calculate the specific heat of the unknown metal if water temperature stabilizes at \[21.5{}^\circ C.\] (Specific heat of brass is\[394\text{ }J\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\])
Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:
The self produced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1 s, the change in the energy of the inductance is:
The actual value of resistance R, shown in the figure is \[30\Omega \] This is measured in an experiment as shown using the standard formula\[R=\frac{V}{1},\] where V and I are the readings of the voltmeter and ammeter, respectively.
If the measured value of R is \[5%\] less, then the internal resistance of the voltmeter is:
At some location on earth the horizontal component of earth's magnetic field is \[18\times {{10}^{-6}}T.\] At this location, magnetic needle of length 0.12 m and pole strength 1.8 A m is suspended from its mid-point using a thread, it makes \[45{}^\circ \] angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is:
Two vectors\[\overrightarrow{A}\] and\[\overrightarrow{B}\] have equal magnitudes. The magnitude of\[(\overrightarrow{A}+\overrightarrow{B})\] is 'n' times the magnitude of \[(\overrightarrow{A}-\overrightarrow{B})\]The angle between \[\overrightarrow{A}\]and \[\overrightarrow{B}\]is:
A metal plate of area \[1\times {{10}^{-4}}{{m}^{2}}\]is illuminated by a radiation of intensity \[16\text{ }mW/{{m}^{2}}.\] The work function of the metal is \[5eV.\] The energy of the incident photons is 10 eV and only \[10%\] of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be : \[\left[ 1eV=1.6\times {{10}^{-19}}J \right]\]
A particle which is experiencing a force, given by \[\overrightarrow{F}=3\hat{i}-12\hat{j},\]undergoes a displacement of \[\overrightarrow{d}=4\hat{i}.\] If the particle had a kinetic energy of \[3j\]at the beginning of the displacement, what is its kinetic energy at the end of the displacement?
Consider a Young's double slit experiment as shown in figure. What should be the slit separation \[d\] in terms of wavelength \[\lambda \] such that the first minima occurs directly in front of the slit \[({{S}_{1}})?\]
The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.
A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is :
The diameter and height of a cylinder are measured by a meter scale to be \[12.6\pm 0.1cm\] and\[34.2\pm 0.1cm,\] respectively. What will be the value of its volume in appropriate significant figures?
For equal point charges Q each are placed in the \[xy\]plane at \[(0,2),(4,2),(4,-2)\text{ }and\text{ (0,-2)}.\] The work required to put a fifth change Q at the origin of the coordinate system will be:
The modulation frequency of an AM radio station is \[250\text{ }kHz,\] which is \[10%\] of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot?
A closed organ pipe has a fundamental frequency of \[1.5\text{ }kHz.\] The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person can hear is \[20,000\text{ }Hz\])
The electric field of a plane polarized electromagnetic wave in free space at time\[t=0\]is given by an expression \[\overrightarrow{E}(x,y)=10\hat{j}\,cos[(6x+8z)]\] The magnetic field \[\overrightarrow{B}(x,z,t)\]is given by: (c is the velocity of light)
1 mol of \[{{N}_{2}}\] and 4 mol of \[{{H}_{2}}\] are allowed to react in a vessel and after reaction, \[{{H}_{2}}O\] is added. Aqueous solution required 1 mol of HCl for neutralization. Mol fraction of \[{{H}_{2}}\] in the remaining gaseous mixture after reaction is - #1
In ground state of P if four quantum no. are \[(4,1,0,-1/2)\,\] (for last \[{{e}^{-}}\]) then calculate the quantum no. of last \[{{e}^{-}}\] in excited state of P-
0.3 g of an oxalate salt was dissolved in 100 mL solution. The solution required 90 mL of N/20 \[KMn{{O}_{4}}\] for complete oxidation. The % of oxalate ion in salt is -
An equilibrium mix. contains \[{{N}_{2}}{{O}_{4}}\] & \[N{{O}_{2}}\] at 0.28 & 1.1 atm. resp. at 300K. If volume of container is doubled, calculate new equilibrium pressure of \[N{{O}_{2}}\]
In the reaction \[{{N}_{2}}{{O}_{4}}(g)\,\,\,\,2N{{O}_{2}}(g)\]. If D & d are the vapour densities at initial stage & at equilibrium then what will be the value of \[\frac{D}{d}\] at point A in the
The decomposition of azo methane, at certain temperature according to the equation \[{{(C{{H}_{3}})}_{2}}{{N}_{2}}\to {{C}_{2}}{{H}_{6}}+{{N}_{2}}\] is a first order reaction. After 40 minutes from the start, the total pressure developed is found to be 350 mm Hg in place of initial pressure 200 mm Hg of azo methane. The value of rate constant k is -
The lattice energy of NaCl (s) is 756 kJ/mole. The dissolution of the solid in water to form ions is endothermic to the extent of 4 kJ/mol. If the hydration energy of \[N{{a}^{+}}\]and \[C{{l}^{-}}\]are in the ratio 6 : 5, then the heat of hydration value of \[N{{a}^{+}}\]ion is -
A graph between \[\log \frac{x}{m}\] and log P is a straight line at angle of \[45{}^\circ \] with the intercept on the y-axis equal to 0.3010. Under a pressure of 0.3 atmosphere, the amount of the gas adsorbed per gram of adsorbent is -
1 mol of \[{{N}_{2}}\] at 0.8 atm takes 38 seconds to diffuse through a pin Hole, whereas 1 mol unknown compound of Xe with fluorine at 1.6 atm takes 57 seconds to diffuse through same hole. The molecular formula of the compound may be - \[[F=19]\,\,\,[Xe=131]\]
Statement-I: \[Li\] is the strongest reducing agent among alkali metals. Statement-II: \[Li\] has the highest value of ionisation energy among alkali metals.
A)
Statement-I is true, statement-II is true & statement-II is not the correct explanation for statement-I
doneclear
B)
Statement-I is true, statement-II is true and statement-II is correct explanation for statement-I
If a female having gene for hemophilia and colour-blindness on its one X-chromosome marries a normal male then what are the chances In their offsprings:
A male insect mistakes a flower of orchid to be its female due to shape and perform the act of copulation and induce pollination. This is an example of:
\[f\left( x \right)=\left\{ \begin{align} & 2-\left| {{x}^{2}}+5x+6 \right|;x\ne -2 \\ & {{a}^{2}}+1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,;x=-2 \\ \end{align} \right.\]then the range of a so that \[f\left( x \right)\] has maximum at \[x=-2\] is
If a ,b, c are all distinct, then \[a\frac{\left( x-b \right)\left( x-c \right)}{\left( a-b \right)\left( a-c \right)}+b\frac{\left( x-c \right)\left( x-a \right)}{\left( b-c \right)\left( b-c \right)}+c\frac{\left( x-a \right)\left( x-b \right)}{\left( c-a \right)\left( c-b \right)}-x\] Is equal to
Let \[f:\left[ 0,1 \right]\to \left[ 0,1 \right]\]defined by \[f\left( x \right)=\frac{1-x}{1+x},\]for \[0\le x\le 1\]and let \[g:\left[ 0,1 \right]\to \left[ 0,1 \right]\] defined by \[g\left( x \right)\]\[=4x\left( 1-x \right),0\le x\le 1.\]if range of \[fog\left( x \right)\]is \[\left[ \alpha ,\beta \right],\]then \[\alpha +\beta =\]
If \[\int\limits_{-1}^{-4}{f\left( x \right)dx-4}\,\operatorname{and}\,\int\limits_{2}^{-4}{\left( 3-f\left( x \right) \right)dx=7}\]then the value \[\,\int\limits_{-2}^{1}{f\left( -x \right)dx}\]is
A point I is the centre of a inscribed in a triangle ABC, then the vector sum \[\overrightarrow{\left| \operatorname{BC} \right|}\,\,\overrightarrow{\operatorname{IA}}+\overrightarrow{\left| \operatorname{CA} \right|}\,\,\overrightarrow{\operatorname{IB}}+\overrightarrow{\left| \operatorname{AB} \right|}\,\,\overrightarrow{\operatorname{IC}}\]is
The number of positive integer solutions \[\left( x,y,z \right)\]for the system of simultaneous \[\operatorname{equations}\left\{ \begin{align} & xy+xz=255, \\ & xy+yz=31 \\ \end{align} \right.\]is
Suppose that \[f\] is a differentiable function with the property that \[f\left( x+y \right)=f\left( x \right)+f\left( y \right)+xy\]and \[\underset{h\to 0}{\mathop{\lim }}\,\frac{1}{h}f\left( h \right)=3,\]then
Charges \[-q\] and \[+q\] located at A and B, respectively, constitute an electric dipole. Distance \[AB=2a,\text{ O}\]is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where \[OP=y\] and \[y>>2a.\] The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P' such that \[OP'=\left( \frac{y}{3} \right),\]the force on Q will be close to: \[\left( \frac{y}{3}>>2a \right)\]
Two stars of masses \[3\times {{10}^{31}}kg\] each, and at distance \[2\times {{10}^{11}}m\] rotate in a plane about their common centre of mass \[O\]. A meteorite passes through \[O\] moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at \[O\] is: (Take Gravitational constant \[G=6.67\times {{10}^{-11}}\] \[N{{m}^{2}}k{{g}^{-2}}\])
Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from \[20{}^\circ C\] to \[90{}^\circ C.\] Work done by gas is close to: (Gas constant \[R=8.31\text{ }J/mol.K\])
A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of \[10V\] between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is:
A particle starts from the origin at time\[t=0\]and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time\[t=5s\]?
A rigid massless road of length 31 has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be:
Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle \[\theta \] with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle \[\theta \] is:
A cylindrical plastic bottle of negligible mass of filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency co. If the radius of the bottle is 2.5 cm then co is close to: (density of water\[={{10}^{3}}kg/{{m}^{3}}\])
A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is:
Two kg of a monoatomic gas is at a pressure of \[4\times {{10}^{4}}N/{{m}^{2}}.\] The density of the gas is \[8kg/{{m}^{3}}.\] What is the order of energy of the gas due to its thermal motion?
Zn Amalgam is prepared by electrolysis of aqueous \[ZnC{{l}_{2}}\] using Hg cathode (9gm). How much current is to be passed through \[ZnC{{l}_{2}}\] solution for 1000 second to prepare a Zn Amalgam with 25 % Zn by wt. (Zn = 65.4)
A solution of \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\] is standardized iodimetrically against 0.1262 g of \[KBr{{O}_{3}}.\]This process requires 456 mL of the\[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]solution. What is the molarity of the\[N{{a}_{2}}{{S}_{2}}{{O}_{3}}?\]
Analysis show that nickel oxide consist of nickel ion with 96% ions having \[{{d}^{8}}\] configuration and 4% having \[{{d}^{7}}\] configuration. Which amongst the following best represent the formula of the oxide.
\[C{{H}_{3}}-\underset{\underset{o}{\mathop{\parallel }}\,}{\mathop{C}}\,-OEt>C{{H}_{3}}-\underset{\underset{o}{\mathop{\parallel }}\,}{\mathop{C}}\,-C{{H}_{3}}\](rate of base catalyzed condensation)
doneclear
D)
(rat of diazocoupling with \[Ph{{\overset{\oplus }{\mathop{\,N}}\,}_{2}}\])
Two opposite forces operate in the growth and development of every population. One of them related to the ability to reproduce at a given rate. The force opposite to it is called
Given below are four statements (A-D) each with one or two blanks. Select the option which correctly fills up the blanks in two.
Statements:
(1) Wings of butterfly and birds look alike and are the results of ..... (i)....., evolution
(2) Miller showed that \[C{{H}_{4}},{{H}_{2}},N{{H}_{3}}\] and .... (i) ... when exposed to electric discharge in a flask resulted in formation of...... (ii)....
(3) Vermiform appendix is a...... (i)..... organ and an...... (ii).... evidence of evolution.
(4) According to Darwin evolution took place due to ...... (i).... and .......(ii)..... of the fittest.
Options:
A)
(4) - (i) small variation, (ii) survival. [a] - (i) convergent
doneclear
B)
(1) - (i) convergent, [b] - (i) oxygen, (ii) nucleosides
doneclear
C)
(2) - (i) water vapour, (ii) amino acids, [c] - (i) rudimentary (ii) anatomical
doneclear
D)
(3) - (i) vestigial, (ii) anatomical, [d] (i) mutations (ii) multiplication
In genetic engineering, a DNA segment (gene) of interest, is transferred to the host cell through a vector. Consider the following four agents (A-D) in this regard and select the correct option about which one or more of these can be used as a vector/vectors: