βHe often _____ the numbers. False claims are not going to help. Honesty _____ trustβ, said the manager. Choose the option with the correct order of words to fill the blanks.
a.
exaggerates; engenders
Correct Answer
b.
excels; encourages
c.
aggravates; alleviates
d.
diminishes; eliminates
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Q2mcq
In the sequence of tiles shown below, the missing tile indicated by the question mark should be
a.
b.
Correct Answer
c.
d.
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Q3mcq
A school has 100 students distributed among 1 st to 10 th standards. Based on this, which one of the following statements is always correct?
a.
There are at least 10 students who belong to the same standard.
Correct Answer
b.
There is at least one student in each standard.
c.
There are at most 10 students in 10 th standard.
d.
The total number of students from 1 st to 5 th standards is at least 50.
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Q4mcq
How many 3-digit numbers can be formed using three distinct single digit prime numbers?
a.
64
b.
24
Correct Answer
c.
12
d.
4
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Q5mcq
In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is ____
a.
18
b.
20
c.
24
Correct Answer
d.
32
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Q6mcq
Charity: P:: Retaliation: Q Choose the appropriate pair of words P and Q that fit the analogy.
a.
P = Parsimonious; Q = Vengeful
b.
P = Altruistic; Q = Amicable
c.
P = Resentful; Q = Spiteful
d.
P = Magnanimous; Q = Vindictive
Correct Answer
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Q7mcq
A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?
a.
Only (i) can correspond to the unfolded cube in Panel I.
Correct Answer
b.
Only (ii) can correspond to the unfolded cube in Panel I.
c.
Both (i) and (ii) can correspond to the unfolded cube in Panel I.
d.
Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.
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Q8mcq
Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such that any two corners that are connected by an edge must be of different colors. The minimum number of colors required to achieve this is ________
a.
8
b.
4
c.
3
d.
2
Correct Answer
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Q9mcq
Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them: i. Neither H2 nor H3 is the easternmost hill. ii. Neither H2 nor H3 is the westernmost hill. iii. Neither the easternmost hill nor the westernmost hill is the southernmost iv. Two hills are located to the west of H2. v. The southernmost hill has at least two hills to its east.
hill. The southernmost hill is ________.
a.
H1
b.
H2
c.
H3
Correct Answer
d.
H4
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Q10mcq
As shown in the figure, circle $C$ 1 with center $O$ 1 and radius $r$ 1 touches the square $VWXY$ at points $P$ and $Q$ while circle $C$ 2 with center $O$ 2 and radius $r$ 2 touches the square $VWXY$ at points $R$ and $S.$ The two circles touch each other at $T.$
Μ Μ Μ Μ Μ = 4 cm, $r$ = _____ cm. Given $r$ = 1 cm and Μ Μ Μ Μ $VY$ = $VW$
2 1
a.
4 - $3\sqrt{2}$
b.
1 + $2\sqrt{2}$
c.
7 - $4\sqrt{2}$
Correct Answer
d.
5 + $3\sqrt{2}$
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For the following reaction,
5 If the value of $Ξ$ β‘ $U o$ = $RT,$ then the value of β β‘ $H o$ is
2 (X β‘ is an activated complex; $Ξ$ β‘ $U o$ is standard change in internal energy; $Ξ$ β‘ $H o$ is standard enthalpy of activation; R is gas constant; T is temperature)
a.
1 $RT$ 2
b.
3 $RT$ 2
c.
7 $RT$ 2
d.
5 $RT$ 2
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In the 1 H NMR spectrum of compound X, the coupling constant (J ab) between H a and H b is 3 Hz. The amino alcohol(s) that give(s) X on reaction with methyl iodide followed by heating is(are)
a.
b.
c.
d.
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The difference in the number of gauche interactions present in diaxial and diequatorial chair conformations of trans-1,2-dimethylcyclohexane is ______ (in integer).
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The total number of symmetry operations (order, h) present in the point group of [PdCl 6 ] 2- is x and that in trans-[PdBr 2 Cl 4 ] 2- is y. The value of x β y is ______ (in integer).
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A 0.005 M solution of compound X transmits 80% of the incident light of wavelength $()$ 500 nm. The absorbance of 0.01 M solution of X is ______ (rounded off to three decimal places). (Given: path length = 1.0 cm)
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The microwave spectrum of gaseous HF consists of a series of lines separated by 41.11 cm β1. The bond length (in Γ ) of HF is ______ (rounded off to two decimal places). (Given: Atomic mass (in amu): H = 1.008, F = 18.998; 1 amu = 1.661 $$ 10 β27 kg; h = 6.626 $$ 10 β34 J s; c = 2.998 $$ 10 8 m s β1)
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In a 1 H NMR spectrum obtained from a spectrometer operating at a magnetic field of 14.1 T, two resonances are observed at 1.25 ppm and 5.75 ppm. The separation between the two resonances (in Hz) is ______ (rounded off to one decimal place). (Given: gyromagnetic ratio ($$) of H = 2.675 $$ 10 8 T β1 s β1)
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The maximum work (|W max |, in kJ) that can be obtained by complete combustion of 1.0 mol of CH 4 at constant pressure and 25 $C$ is ______ (rounded off to one decimal place). (Given: ΞS = β241.60 J K β1 mol β1; ΞH = β890.01 kJ mol β1; R = 8.314 J mol β1 K β1)
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If the ionic mobility of Ag + ion in a very dilute aqueous solution of AgNO 3 at 298 K is y $$ 10 β8 m 2 V β1 s β1, then the value of y is ______ (rounded off to two decimal places). (Given: viscosity of water at 298 K = 8.94 $$ 10 β4 kg m β1 s β1; k = 1.38 $$ 10 β23 J K β1; F = 96500 C mol β1; R = 8.314 J mol β1 K β1; Stokes radius of Ag + = 0.15 nm)
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The correct match for the protons labeled in compound X in Column M with the corresponding chemical shifts (Ξ΄, ppm) in Column N is Column M Column N P H a I 7.00 (ddd, J = 8.4, 7.3, 1.4 Hz, 1H) Q H b II 7.17 (dd, J = 8.4, 1.4 Hz, 1H) R H c III 7.59 (ddd, J = 8.4, 7.3, 1.4 Hz, 1H) S H d IV 8.12 (dd, J = 8.4, 1.4 Hz, 1H)
a.
P $\to$ II; Q $\to$ III; R $\to$ I; S $\to$ IV
b.
P $\to$ I; Q $\to$ IV; R $\to$ II; S $\to$ III
c.
P $\to$ II; Q $\to$ IV; R $\to$ I; S $\to$ III
d.
P $\to$ I; Q $\to$ III; R $\to$ II; S $\to$ IV
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Consider the figure given below, where M is a metal and L is a monodentate ligand. The $-bonding$ ligand group orbital (LGO) having same symmetry with $d z$ 2 orbital of M in the octahedral coordination geometry is
a.
b.
c.
d.
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The correct electronic configuration of central metal ion in ferrocene with z-axis passing through the centre of two C 5 H 5- rings and the metal ion is
The correct option for the average value of kinetic energy and the average value of potential energy of a one-dimensional harmonic oscillator with frequency $Ξ½$ in its ground state is
a.
$hΞ½$ 2
b.
$hΞ½$ 2
c.
$hΞ½$ 4
d.
$hΞ½$ and $hΞ½$, respectively 4 2
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For a reaction between neutral molecules X and Y in a solution at temperature T, the measured rate of reaction is equal to the rate of diffusion. Assume X is stationary and Y is moving. If the diameter of the molecule X is five times that of Y, then the rate constant for the reaction is $(Ξ·$ is viscosity of the solvent; $k$ is Boltzmann constant)
a.
$8kT$ β $3Ξ·$
b.
$4kT$ β $Ξ·$
c.
$24kT$ β
$5Ξ·$
d.
$15kT$ β
$4Ξ·$
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Chymotrypsin selectively cleaves a peptide at the carboxyl side of the amino acids having an aryl sidechain. The tripeptide(s) formed on hydrolysis of the peptide, Val-Phe-Leu-Met-Tyr-Pro-Gly-Trp-Cys, with chymotrypsin is(are)
a.
Leu-Met-Tyr
b.
Phe-Leu-Met
c.
Pro-Gly-Trp
d.
Tyr-Pro-Gly
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Consider the given pairs of complex ions. The correct pair(s) in which each complex ion exhibits three spin-allowed d-d transitions (excluding those arising due to distortions) is(are)
a.
[V(H 2 O) 6 ] 3+ and [Ni(H 2 O) 6 ] 2+
b.
[Cr(H 2 O) 6 ] 3+ and [NiCl 4 ] 2-
c.
[Ti(H 2 O) 6 ] 3+ and [Mn(H 2 O) 6 ] 2+
d.
[FeF 6 ] 3- and [FeCl 4 ] 2-
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The pair(s) of lanthanide ions whose ground state term symbols have same spin multiplicity (2S+1) and orbital angular momentum (L), but different spin-orbit coupling (J) is(are) (Given: Atomic number: Nd = 60; Pm = 61; Ho = 67; Er = 68)
a.
Pm 3+ and Ho 3+
b.
Nd 3+ and Er 3+
c.
Pm 3+ and Nd 3+
d.
Ho 3+ and Er 3+
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Consider the following reaction sequence, where A and B are the major products. In proton-decoupled 13 C NMR spectra, the total number of carbon signals observed for A and B is ______ (in integer).
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On heating, the compound Z undergoes a series of 1,5-H/D shifts to give a mixture of its isomers. The total number of isomers present in the mixture (including Z) is ______ (in integer).
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The positions of two atoms in spherical polar coordinates (r, ΞΈ, Ξ¦) are (1,,) and $Ο Ο$
2 2 $Ο 3Ο$ (1,,), where the distance is in Γ and the angles are in radian. The interatomic 4 2 distance (in Γ ) is ______ (rounded off to two decimal places).
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If the translational partition function for H 2 confined in a 1 L vessel at 300 K is y $$ 10 27, then the value of y is ______ (rounded off to one decimal place). (Given: Atomic mass (in amu): H = 1.008; 1 amu = 1.661 $$ 10 β27 kg; h = 6.626 $$ 10 β34 J s; k = 1.381 $$ 10 β23 J K β1)
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In a calibrated pH meter comprising of glass electrode-standard calomel electrode, the potential for a buffer solution of pH 4.01 is measured as 0.814 V at 25 $C.$ For a 4.0 $$ 10 β3 M solution of acetic acid, the measured potential (in V) is ______ (rounded off to three decimal places). (Given: K a of acetic acid at 25 $C$ = 1.75 $$ 10 β5; 2.303RT/F = 0.059; Assume: $a H$ + = [H + ])
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The Brunauer-Emmett-Teller (BET) surface area measurement data for adsorption of N 2 gas at 77 K on 1.0 g of an adsorbent fits into a straight line, when is
$z$
$(1-z)V$ plotted against $z.$ The slope and intercept of the straight line are 6 $$ 10 β4 mm β3 and 4 $$ 10 β6 mm β3, respectively. The surface area (in m 2 g β1) of the adsorbent is ______ (rounded off to one decimal place). (Given: 1 mm 3 of N 2 gas corresponds to 2.7 $$ 10 16 molecules and each molecule occupies 0.16 nm 2. V is the volume of gas adsorbed in mm 3, $z$ is p/p o, where p is the pressure of the N 2 gas and p o is equilibrium vapour pressure of liquid N 2)
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The orbital angular momentum (L) of an electron is $\sqrt{12Δ§}.$ The minimum angle between L and its z-component (in degrees) is ______ (rounded off to one decimal place).
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