Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match List I with List II
List - I
List - II
A
Surface tension
I.
kgm−1s−1
B
Pressure
II.
kgms−1
C
Viscosity
III.
kgm−1s−2
D
Impulse
IV.
kgs−2
Choose the correct answer from the options given below:
Question No. 2
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100g. The time period of the motion of the particle will be (approximately)
(take g=10ms−2, radius of earth =6400km)
Question No. 3
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match List I with List II
List – I (Current configuration)
List – II (Magnetic field at pointO)
A
I.
B0=μ0I4πr[π+2]
B
II.
B0=μ04Ir
C
III.
B0=μ0I2πr[π−1]
D
IV.
B0=μ0I4πr[π+1]
Choose the correct answer from the option given below:
Question No. 4
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
An ideal gas goes through a reversible cycle a→b→c→d→a has the V - T diagram shown below. Process d→aandb→c are adiabatic. The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :
Question No. 5
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Electron beam used in an electron microscope, when accelerated by a voltage of 20kV has a de-Broglie wavelength of λ0. If the voltage is increased to 40kV then the de-Broglie wavelength associated with the electron beam would be:
Question No. 6
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x times its initial resonant frequency ω0. The value of x is:
Question No. 7
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross-section of each rod is 4cm2. End of copper rod is maintained at 100°C. Where as ends of brass and steel are kept at 0°C. Lengths of the copper, brass and steel rods are 46,13and 12cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92,0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :
Question No. 8
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
T is the time period of simple pendulum on the earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be:
Question No. 9
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A car travels a distance of x with speed v1 and then same distance x with speed v2 in the same direction. The average speed of the car is:
Question No. 10
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The ratio of the density of oxygen nucleus (O816) and helium nucleus (He24) is
Question No. 11
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A car is moving with a constant speed of 20ms−1 in a circular horizontal track of radius 40m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g=10ms−2)
Question No. 12
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
All electromagnetic wave is transporting energy in the negative z direction. At a certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of the magnetic field of the wave at that point and instant?
Question No. 13
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A uniform metallic wire carries a current 2A, when 3.4V battery is connected across it. The mass of uniform metallic wire is 8.92×10−3kg, density is 8.92×103kgm−3 and resistivity is 1.7×10−8Ω−m The length of wire is :
Question No. 14
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The root mean square velocity of molecules of gas is
Question No. 15
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
In Young's double slits experiment, the position of 5th bright fringe from the central maximum is 5cm. The distance between slits and screen is 1m and wavelength of used monochromatic light is 600nm. The separation between the slits is:
Question No. 16
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
An object of mass 8kg is hanging from one end of a uniform rod CD of mass 2kg and length 1m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is:
(Take g=10ms−2)
Question No. 17
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Photodiodes are used in forward bias usually for measuring the light intensity.
Reason R: For a p−n junction diode, at applied voltage V the current in the forward bias is more than the current in the reverse bias for |Vz|>±V≥|V0| where V0 is the threshold voltage and Vz is the breakdown voltage.
In the light of the above statements, choose the correct answer from the options given below
Question No. 18
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2m long and 0.2m in diameter. The magnetic intensity at the center of the solenoid when a current of 2A flows through it is:
Question No. 19
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A parallel plate capacitor has plate area 40cm2 and plates separation 2mm. The space between the plates is filled with a dielectric medium of a thickness 1mm and dielectric constant 5. The capacitance of the system is:
Question No. 20
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a,b,c are positive constants?
Physics Numerical (Maximum Marks: 20)
Question No. 1
Numerical Type The answer has to be filled into the input box provided below.
An object of mass m initially at rest on a smooth horizontal plane starts moving under the action of force F=2N. In the process of its linear motion, the angle θ (as shown in figure) between the direction of force and horizontal varies as θ=kx, where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be E=nksinθ. The value of n is ______.
Question No. 2
Numerical Type The answer has to be filled into the input box provided below.
In the given circuit, the equivalent resistance between the terminal A and B is ____ Ω
Question No. 3
Numerical Type The answer has to be filled into the input box provided below.
As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45° with the load axis. The length of wire is 62.8cm and its diameter is 4mm. The Young's modulus is found to be x×104Nm−2
The value of x is _______.
Question No. 4
Numerical Type The answer has to be filled into the input box provided below.
A ray of light is incident from air on a glass plate having thickness 3√cm and refractive index 2√. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ____×10−2cm . (given sin15°=0.26)
Question No. 5
Numerical Type The answer has to be filled into the input box provided below.
ICM is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. IAB is its moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance 23R from center, where R is the radius of the disc. The ratio of IAB and ICM is x:9. The value of x is ______.
Question No. 6
Numerical Type The answer has to be filled into the input box provided below.
The distance between two consecutive points with phase difference of 60° in a wave of frequency 500Hz is 6.0m. The velocity with which wave is travelling is ______ kms−1.
Question No. 7
Numerical Type The answer has to be filled into the input box provided below.
If P⃗ =3iˆ+3√jˆ+2kˆ and Q⃗ =4iˆ+3√jˆ+2.5kˆ then, the unit vector in the direction of P⃗ ×Q⃗ is 1x(3√iˆ+jˆ−23√kˆ). The value of x is
Question No. 8
Numerical Type The answer has to be filled into the input box provided below.
An LCR series circuit of capacitance 62.5nF and resistance of 50Ω, is connected to an A.C. source of frequency 2.0kHz. For maximum value of amplitude of current in circuit, the value of inductance is ____mH.(Takeπ2=10)
Question No. 9
Numerical Type The answer has to be filled into the input box provided below.
The wavelength of the radiation emitted is λ0 when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be 20xλ0. The value of x is________.
Question No. 10
Numerical Type The answer has to be filled into the input box provided below.
A uniform electric field of 10NC−1 is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5eV. The length of each plate is 10cm. The angle (θ) of deviation of the path of electron as it comes out of the field is ______(in degree).
Chemistry Single Correct (Maximum Marks: 80)
Question No. 1
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given EoCr3+/Cr=−0.74 V; EoMnO−4/Mn2+=1.51V EoCr2O2−7/Cr3+=1.33 V; EoCl2∣∣Cl−=1.36V Based on the data given above, strongest oxidising agent will be:
Question No. 2
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Assertion: Among the carbon allotropes, diamond is an insulator, whereas, graphite is a good conductor of electricity. Reason: Hybridization of carbon in diamond and graphite are sp3 and sp2 respectively.
Question No. 3
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The radius of the 2nd orbit of Li2+ is x. The expected radius of the 3rd orbit of Be3+ is
Question No. 4
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The correct order in aqueous medium of basic strength in case of methyl substituted amines is:
Question No. 5
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: Acetal/Ketal is stable in basic medium.
Reason R: The high leaving tendency of alkoxide ion gives the stability to acetal/ketal in basic medium.
In the light of the above statements, choose the correct answer from the options given below:
Question No. 6
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
In the cumene to phenol preparation in presence of air, the intermediate is
Question No. 7
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The rate coefficient (k) for a particular reactions is 1.3×10−4M−1s−1 at 100∘C, and 1.3×10−3M−1s−1 at 150∘C. What is the energy of activation (EA) (in kJ) for this reaction? (R= molar gas constant =8.314JK−1mol−1 )
Question No. 8
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match items of Row I with those of Row II.
Row I:
(P)
(Q)
(R)
(S)
Row II:
(i) α‐D‐(—) Fructofuranose.
(ii) β‐D‐(—) Fructofuranose.
(iii) α‐D‐(‐) Glucopyranose.
(iv) β‐D‐(‐) Glucopyranose.
Correct match is
Question No. 9
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with OH– is
Question No. 10
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Identify the product formed (A and E)
Question No. 11
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Stability of the species Li2,Li−2andLi+2 increases in the order of
Question No. 12
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Consider the reaction : H2SO3(aq)+Sn4+(aq)+H2O(l)→Sn2+(aq)+HSO−4(aq)+3H+(aq) Which of the following statements is correct ?
Question No. 13
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The following statements concern elements in the periodic table. Which of the following is true?
Question No. 14
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A gaseous compound of nitrogen and hydrogen contains 12.5% (by mass) of hydrogen. The density of the compound relative to hydrogen is 16. The molecular formula of the compound is:
Question No. 15
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which of the following statements/relationships is not correct in thermodynamic changes ?
Question No. 16
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Match the List-I with List-II :
Cations
Group reaction
P→Pb2+,Cu2+
H2S gas in presence of dilute HCl
Q→Al3+,Fe3+
(NH4)2CO3 in presence of NH4OH
R→Co2+,Ni2+
NH4OH in presence of NH4CI
S→Ba2+,Ca2+
H2S in presence of NH4OH
Question No. 17
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Inert gases have positive electron gain enthalpy. Its correct order is
Question No. 18
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which of the following conformations will be the most stable?
Question No. 19
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
In which of the following exothermic reactions, the heat liberated per mole is the highest ?
Question No. 20
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The correct sequence of reagents for the preparation of Q and R is:
Chemistry Numerical (Maximum Marks: 20)
Question No. 1
Numerical Type The answer has to be filled into the input box provided below.
Consider the cell Pt(s)|H2(s)(latm)|H+(aq,[H+]=1)∣∣∣∣Fe3+(aq),Fe2+(aq)∣Pt(s)
Given: EFe3+/Fe2+°=0.771V and EH+/12H2°=0V,T=298K
If the potential of the cell is 0.712V the ratio of concentration of Fe2+ to Fe3+ is (Nearest integer)
Question No. 2
Numerical Type The answer has to be filled into the input box provided below.
In sulphur estimation. 0.471g of an organic compound gave 1.4439g of barium sulphate. The percentage of sulphur in the compound is _______(Nearest Integer)
(Given: Atomic mass Ba: 137u:S:32u,O:16u )
Question No. 3
Numerical Type The answer has to be filled into the input box provided below.
The density of a monobasic strong acid (Molar mass 24.2gmol) is 1.21kgL. The volume of its solution required for the complete neutralization of 25mL of 0.24MNaOH is 10−2mL (Nearest integer)
Question No. 4
Numerical Type The answer has to be filled into the input box provided below.
The osmotic pressure of solutions of PVC in cyclohexanone at 300K are plotted on the graph. The molar mass of PVC is gmol−1 (Nearest integer)
(Given : R=0.083LatmK−1mol−1 )
Question No. 5
Numerical Type The answer has to be filled into the input box provided below.
The number of paramagnetic species from the following is
[Ni(CN)4]2−,[Ni(CO)4],[NiCl4]2−
[Fe(CN)6]4−,[Cu(NH3)4]2+
[Fe(CN)6]3− and [Fe(H2O)6]2+
Question No. 6
Numerical Type The answer has to be filled into the input box provided below.
For the first order reaction A→B the half life is 30min. The time taken for 75% completion of the reaction is mm. (Nearest integer)
Given : log2=0.3010
log3=0.4771
log5=0.6989
Question No. 7
Numerical Type The answer has to be filled into the input box provided below.
How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? ________
(Given: Atomic number:V,23;Cr,24;Fe,26;Ni,28)
V3+,Cr3+,Fe2+,Ni3+
Question No. 8
Numerical Type The answer has to be filled into the input box provided below.
The total number of lone pairs of electrons on oxygen atoms of ozone is
Question No. 9
Numerical Type The answer has to be filled into the input box provided below.
A litre of buffer solution contains 0.1 mole of each of NH3 and NH4Cl. On the addition of 0.02 mole of HCl by dissolving gaseous HCl, the pH of the solution is found to be _____×10−3 (Nearest integer)
Given: pKb(NH3)=4.745
log2=0.301
log3=0.477
T=298K]
Question No. 10
Numerical Type The answer has to be filled into the input box provided below.
An athlete is given 100g of glucose (C6H12O6) for energy. This is equivalent to 1800kJ of energy. The 50% of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of energy, the weight of extra water he would need to perspire is _____g (Nearest integer) Assume that there is no other way of consuming stored energy.
Given : The enthalpy of evaporation of water is 45kJmol−1
Molar mass of C,H&O are 12.1 and 16gmol−1.
Mathematics Single Correct (Maximum Marks: 80)
Question No. 1
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let z1=2+3i and z2=3+4i. The set S={z∈C:|z−z1|2−|z−z2|2=|z1−z2|2} represents a
Question No. 2
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The number of distinct real roots of the equation, ∣∣∣∣cosxsinxsinxsinxcosxsinxsinxsinxcosx∣∣∣∣=0 in the interval [−π4,π4] is :
Question No. 3
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The value of
limn→∞1+2−3+4+5−6+…+(3n−2)+(3n−1)−3n2n4+4n+3−√n4+5n+4√ is
Question No. 4
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let f:(0,1)→R be a function defined by f(x)=11−e−x, and g(x)=(f(−x)−f(x)). Consider two statements
(I) g is an increasing function in (0,1)
(II) g is one-one in (0,1) Then,
Question No. 5
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The minimum value of the function f(x)=∫20e∣∣x−t∣∣dt is
Question No. 6
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:
Question No. 7
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If the vectors a→=iˆ−jˆ+2kˆ,b→=2iˆ+4jˆ+kˆ and c→=λiˆ+jˆ+μkˆ are mutually orthogonal, then (λ,μ)=
Question No. 8
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The vector a⃗ =−iˆ+2jˆ+kˆ is rotated through a right angle, passing through the y-axis in its way and the resulting vector is b⃗ . Then the projection of 3a⃗ +2√b⃗ on c⃗ =5iˆ+4jˆ+3kˆ is
Question No. 9
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The integral ∫7π/37π/4tan2x−−−−−√dx is equal to :
Question No. 10
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let x=2 be a local minima of the function f(x)=2x4−18x2+8x+12,x∈(−4,4). If M is local maximum value of the function f in (−4,4), then M=
Question No. 11
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The points of intersection of the line ax+by=0, (a≠b) and the circle x2+y2−2x=0 are A(α,0) and B(1,β). The image of the circle with AB as a diameter in the line x+y+2=0 is :
Question No. 12
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let f(x)=∫2x(x2+1)(x2+3)dx. If f(3)=12(loge5−loge6), then f(4) is equal to
Question No. 13
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The area of triangle formed by the lines joining the vertex of the parabola, x2=8y, to the extremities of its latus rectum is
Question No. 14
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12 . If the new mean of the marks is 10.2. then their new variance is equal to:
Question No. 15
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The distance of the point P(4,6,−2) from the line passing through the point (−3,2,3) and parallel to a line with direction ratios 3,3,−1 is equal to:
Question No. 16
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Consider the lines L1 and L2 given by
L1:x−12=y−31=z−22
L2:x−21=y−22=z−33
A line L3 having direction ratios 1,−1,−2, intersects L1 and L2 at the points P and Q respectively. Then the length of line segment PQ is
Question No. 17
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let y=y(x) be the solution curve of the differential equation dydx=yx(1+xy2(1+logex)), x>0,y(1)=3. Then y2(x)9 is equal to :
Question No. 18
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let x,y,z>1 and A=⎡⎣⎢1logyxlogzxlogxy2logzylogxzlogyz3⎤⎦⎥. Then ∣∣adj(adjA2)∣∣ is equal to
Question No. 19
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let M be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space S={x∈Z:x(66−x)≥59M} and the event A={x∈S:x is a multiple of 3}. Then P(A) is equal to
Question No. 20
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let y(x)=(1+x)(1+x2)(1+x4)(1+x8)(1+x16). Then y′−y′′ at x=−1 is equal to
Mathematics Numerical (Maximum Marks: 20)
Question No. 1
Numerical Type The answer has to be filled into the input box provided below.
If the sum of all the solutions of tan−1(2x1−x2)+cot−1(1−x22x)=π3, −1<x<1,x≠0, is α−43√, then α is equal to _____ .
Question No. 2
Numerical Type The answer has to be filled into the input box provided below.
Let S={1,2,3,5,7,10,11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____ .
Question No. 3
Numerical Type The answer has to be filled into the input box provided below.
Let x and y be distinct integers where 1≤x≤25 and 1≤y≤25. Then, the number of ways of choosing x and y, such that x+y is divisible by 5 , is _____ .
Question No. 4
Numerical Type The answer has to be filled into the input box provided below.
If ∫12dx(x2−2x+4)32=kk+5, then k is equal to
Question No. 5
Numerical Type The answer has to be filled into the input box provided below.
The constant term in the expansion of (2x+1x7+3x2)5 is _____ .
Question No. 6
Numerical Type The answer has to be filled into the input box provided below.
If the area enclosed by the parabolas P1:2y=5x2 and P2:x2−y+6=0 is equal to the area enclosed by P1 and y=αx,α>0, then α3 is equal to _____ .
Question No. 7
Numerical Type The answer has to be filled into the input box provided below.
If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is 32 units, then its eccentricity is e, find 1e.
Question No. 8
Numerical Type The answer has to be filled into the input box provided below.
For some a,b,c∈N, let f(x)=ax−3 and g(x)=xb+c,x∈R. If (fog)−1(x)=(x−72)13, then (f∘g)(ac)+(g∘f)(b) is equal to _____ .
Question No. 9
Numerical Type The answer has to be filled into the input box provided below.
Let S={α:log2(92α−4+13)−log2(52⋅32α−4+1)=2}. Then the maximum value of β for which the equation x2−2(∑α∈sα)2x+∑a∈s(α+1)2β=0 has real roots, is _____ .
Question No. 10
Numerical Type The answer has to be filled into the input box provided below.
Let A1,A2,A3 be the three A.P. with the same common difference d and having their first terms as A,A+1,A+2, respectively. Let a,b,c be the 7th ,9th ,17th terms of A1,A2,A3, respectively such that ∣∣∣∣a2bc71717111∣∣∣∣+70=0. If a=29, then the sum of first 20 terms of an AP whose first term is c−a−b and common difference is d12, is equal to _____ .
Question Paper Physics Single Correct (Maximum Marks: 80) Question No. 1 Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. A body of mass is taken from earth surface to the height h equal to twice the radius of earth ( R e ) , the increase in potential energy will be : ( g = acceleration due to gravity on the surface of earth) 3 m g R e 1 3 m g R e 2 3 m g R e 1 2 m g R e Question No. 2 Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. The resistance of a wire is 5 Ω . Its new resistance in ohm, if stretched to 5 times of its original length will be : 625 125 5 25 Question No. 3 Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Every planet revolves around the sun in an elliptical orbit : A. The force acting on a planet is inversely proportional to square of distance fro...
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