In a hypothetical fission reaction $_{92}X^{236} \rightarrow \rightarrow_{56}Y^{141}+_{36}Z^{92}+ 3R$ The identity of emitted particles ( $R)$ is :
a.
Electron
b.
Neutron
Correct Answer
c.
$\gamma$ -radiations
d.
Proton
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Q2nat
An alternating emf $E = 110 sin 100t\sqrt{2}$ volt is applied to a capacitor of $2\mu F$ , the rms value of current in the
circuit is _____ $mA$ ,
✓ Accepted Answer:22
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Q3mcq
A thin circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its
centre and perpendicular to its plane with angular velocity $\omega$ . If another disc of same dimensions but of mass
$M/2$ is placed gently on the first disc co-axially, then the new angular velocity of the system is :
a.
$\frac{3}{2}\omega$
b.
$\frac{5}{4}\omega$
c.
$\frac{2}{3}\omega$
Correct Answer
d.
$\frac{4}{5}\omega$
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Q4nat
A body of mass $M$ thrown horizontally with velocity $v$ from the top of the tower of height $H$ touches the
ground at a distance of $100\,m$ from the foot of the tower. A body of mass $2M$ thrown at a velocity $\frac{v}{2}$ from the
top of the tower of height $4H$ will touch the ground at a distance of _____ $m$ .
✓ Accepted Answer:100
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Q5mcq
A proton and an electron have the same de Broglie wavelength. If $K_{p}$ and $K_{e}$ be the kinetic energies of proton
and electron respectively, then choose the correct relation :
a.
$K_{p} >K_{e}$
b.
$K_{p} < K_{e}$
Correct Answer
c.
$K_{p} = K_{e}$
d.
$K_{p} = K_{e}^{2}$
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Q6mcq
Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length
of the heating element should be _____ to _____ times of its initial length if the water is to be boiled in 15
minutes.
a.
decreased, $3/4$
Correct Answer
b.
increased, $4/3$
c.
decreased, 4/3
d.
increased, $3/4$
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Q7mcq
Least count of a vernier caliper is $\frac{1}{20\,N}\,cm$ . The value of one division on the main scale is $1\,mm$ . Then the
number of divisions of main scale that coincide with $N$ divisions of vernier scale is :
a.
$(2\,N -1)$
b.
$(\frac{2\,N-1}{2\,N} )$
c.
$( \frac{2\,N-1}{2})$
Correct Answer
d.
$(\frac{2\,N-1}{20\,N} )$
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Q8nat
$|$
Two slits are $1\,mm$ apart and the screen is located $1\,m$ away from the slits. A light of wavelength $500\,nm$ is
used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the
single slit pattern is _____ $\times 10^{-4}\,m$
✓ Accepted Answer:2
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Q9nat
The coercivity of a magnet is $5 \times 10^{3}\,A/m$ . The amount of current required to be passed in a solenoid of
length $30\,cm$ and the number of turns 150 , so that the magnet gets demagnetised when inside the solenoid is
_____A.
✓ Accepted Answer:10
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Q10nat
A heater is designed to operate with a power of $1000\,W$ in a $100\,V$ line. It is connected in combination with a
resistance of $10\Omega$ and a resistance $R$ , to a $100\,V$ mains as shown in figure. For the heater to operate at $62.5\,W$ ,
the value of $R$ should be _____ $\Omega$ .
✓ Accepted Answer:5
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A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross
section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ from axis of the wire is :
a.
$1 : 4$
b.
$1 : 1$
c.
$3 : 4$
d.
$4 : 1$
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A capacitor has air as dielectric medium and two conducting plates of area $12\,cm^{2}$ and they are $0.6\,cm$ apart.
When a slab of dielectric having area $12\,cm^{2}$ and $0.6\,cm$ thickness is inserted between the plates, one of the
conducting plates has to be moved by $0.2\,cm$ to keep the capacitance same as in previous case. The dielectric
constant of the slab is : (Given $\epsilon _{0} = 8.834 \times 10^{-12}\,F/m$ )
a.
$1$
b.
$1.33$
c.
$0.66$
d.
$1.50$
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Two satellite $A$ and $B$ go round a planet in circular orbits having radii $4R$ and $R$ respectively. If the speed of $A$
is $3v$ , the speed of $B$ will be :
a.
$3v$
b.
$6v$
c.
$\frac{4}{3}v$
d.
$12v$
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A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to
that in kerosene oil (specific gravity of Kerosene oil $= 0.8$ , specific gravity of ice $= 0.9$ )
a.
$1 : 1$
b.
$5 : 4$
c.
$8 : 9$
d.
$9 : 10$
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Small water droplets of radius $0.01\,mm$ are formed in the upper atmosphere and falling with a terminal
velocity of $10\,cm/s$ . Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new
terminal velocity will be _____ $cm/s$ .
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There are 100 divisions on the circular scale of a screw gauge of pitch $1\,mm$ . With no measuring quantity in
between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire
is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60
divisions on circular scale coincide with the reference line. The diameter of the wire is :
a.
$3.35\,mm$
b.
$4.65\,mm$
c.
$4.55\,mm$
d.
$4.60\,mm$
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A block is simply released from the top of
an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the
spring is :
a.
$\sqrt{6}\,m$
b.
$\sqrt{5}\,m$
c.
$1\,m$
d.
$2\,m$
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A potential divider circuit is connected with a dc source of $20\,V$ , a light emitting diode of glow in voltage
$1.8\,V$ and a zener diode of breakdown voltage of $3.2\,V$ . The length (PR) of the resistive wire is $20\,cm$ . The
minimum length of PQ to just glow the LED is _____ $cm$
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A circular table is rotating with an angular velocity of $\omega rad/s$ about its axis (see figure). There is a smooth
groove along a radial direction on the table. A steel ball is gently placed at a distance of $1\,m$ on the groove. All
the surfaces are smooth. If the radius of the table is $3\,m$ , the radial velocity of the ball w.r.t. the table at the
time ball leaves the table is $x\sqrt{2}\omega m/s$ , where the value of $x$ is _____.
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A coil of negligible resistance is connected in series with $90\Omega$ resistor across $120\,V, 60\,Hz$ supply. A voltmeter
reads $36\,V$ across resistance. Inductance of the coil is :
a.
$0.286H$
b.
$0.76H$
c.
$2.86H$
d.
$0.91H$
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An object of mass $0.2\,kg$ executes simple harmonic motion along $x$ axis with frequency of $(\frac{25}{\pi} )Hz$ . At the
position $x= 0.04\,m$ the object has kinetic energy $0.5\,J$ and potential energy $0.4\,J$ . The amplitude of
oscillation is _____ $cm$ .
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Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional
to square of molecular diameter. Statement (II) : Average kinetic energy of gas molecules is directly
proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from
the options given below :
a.
Statement I is true but Statement II is false
b.
Both Statement I and Statement II are false
c.
Both Statement I and Statement II are true
d.
Statement I is false but Statement II is true
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A given object takes $n$ times the time to slide down $45^{\circ }$ rough inclined plane as it takes the time to slide down
an identical perfectly smooth $45^{\circ }$ inclined plane. The coefficient of kinetic friction between the object and the
surface of inclined plane is :
a.
$\sqrt{1} - \frac{1}{n^{2}}$
b.
$1 - n^{2}$
c.
$1 - \frac{1}{n^{2}}$
d.
$\sqrt{1 -n^{2}}$
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$\,List - I\, \,List - II\,$
$\,(Complex ion)\, \,(Spin only magnetic moment in B.M.)\,$
$\,(A)\,[Cr(NH_{3})_{6}]^{3+} \,(I)\,4.90$
Match List - I with List - II. Choose the
$\,(B)\,[NiCl_{4}]^{2-} \,(II)\,3.87$
$\,(C)\,[CoF_{6}]^{3-} \,(III)\,0.0$
$\,(D)\,[Ni(CN)_{4}]^{2-} \,(IV)\,2.83$
correct answer from the options given below :
a.
(A)-(II), (B)-(III), (C)-(I), (D)-(IV)
b.
(A)-(II), (B)-(IV), (C)-(I), (D)-(III)
c.
(A)-(I), (B)-(IV), (C)-(II), (D)-(III)
d.
(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
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The correct sequence of acidic strength of the following aliphatic acids in their decreasing order is:
$CH_{3}CH_{2}COOH, CH_{3}COOH, CH_{3}CH_{2}CH_{2}COOH, HCOOH$
Given below are two statements : Statement (I) : A Buffer solution is the mixture of a salt and an acid or a base
mixed in any particular quantities. Statement (II) : Blood is naturally occurring buffer solution whose $pH$ is
maintained by $H_{2}CO_{3}/HCO^{-}_{3} Θ$ concentrations. In the light of the above statements, choose the correct
answer from the options given below :
a.
Statement I is true but Statement II is false
b.
Both Statement I and Statement II are true
c.
Statement I is false but Statement II is true
d.
Both Statement I and Statement II are false
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$|||$
$|||| ||||$
$|||| ||||$
Identify the incorrect statements about group 15 elements : (A) Dinitrogen is a diatomic gas which acts like an
inert gas at room temperature. (B) The common oxidation states of these elements are $-3, +3$ and +5 . (C)
Nitrogen has unique ability to form $p\pi -p\pi$ multiple bonds. (D) The stability of +5 oxidation states increases
down the group. (E) Nitrogen shows a maximum covalency of 6. Choose the correct answer from the options
given below :
a.
(A), (C), (E) only
b.
(B), (D), (E) only
c.
(D) and (E) only
d.
(A), (B), (D) only
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Two moles of benzaldehyde and one mole of acetone under alkaline conditions using aqueous $NaOH$ after
heating gives $x$ as the major product. The number of $\pi$ bonds in the product $x$ is _______
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Given below are two statements : Statement (I) : $S_{N}2$ reactions are 'stereospecific', indicating that they result in
the formation of only one stereo-isomer as the product. Statement (II) : $S_{N}1$ reactions generally result in
formation of product as racemic mixtures. In the light of the above statements, choose the correct answer from
the options given below :
a.
Both Statement I and Statement II are false
b.
Statement I is false but Statement II is true
c.
Statement I is true but Statement II is false
d.
Both Statement I and Statement II are true
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Given below are two statements : Statement (I) : Kjeldahl method is applicable to estimate nitrogen in
pyridine. Statement (II) : The nitrogen present in pyridine can easily be converted into ammonium sulphate in
Kjeldahl method. In the light of the above statements, choose the correct answer from the options given below
a.
Both Statement I and Statement II are true
b.
Both Statement I and Statement II are false
c.
Statement I is false but Statement II is true
d.
Statement I is true but Statement II is false
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In qualitative test for identification of presence of phosphorous, the compound is heated with an oxidising
agent. Which is further treated with nitric acid and ammonium molybdate respectively. The yellow coloured
precipitate obtained is :
a.
$Na_{3}PO_{4}\cdot 12MoO_{3}$
b.
$(NH_{4})_{3}PO_{4}\cdot 12MoO_{3}$
c.
$MoPO_{4}.21NH_{4}NO_{3}$
d.
$(NH_{4})_{3}PO_{4}\cdot 12(NH_{4})_{2}MoO_{4}$
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$\,(Test)\, \frac{\,(Identification)\,}{\,Phenol VIARKS\,}$
$\frac{\,(A)\,}{\,(B)\,} \,Bayer's test MARKS\, \frac{\,(I)\,}{\,(II)\,}$
Match List - I with List - II. $\,Ceric ammonium nitrate test\, \frac{\,Aldehyde\,}{\,Alcoholic-OH group\,}$
$\frac{\,(C)\,}{\,(D)\,} \,Phthalein dye test\,R\,K \frac{\,(III)\,}{\,(IV)\,}$
$\,Schiff's test\, \,Unsaturation\,$
Choose the correct answer from the options given below :
a.
(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
b.
(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
c.
(A)-(IV), (B)-(I), (C)-(II), (D)-(III)
d.
(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
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$--^{For a reaction}A^{K}\rightarrow \rightarrow^{1} \,B^{K}\rightarrow \rightarrow^{2} C^{If the rate of formation of}B^{is set to be zero then the concentration of}B^{is}$
given by :
a.
$(K_{1}+ K_{2})[A]$
b.
$(K_{1}/K_{2})[A]$
c.
$(K_{1}-K_{2})[A]$
d.
$K_{1}\,K_{2}[\,A]$
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Given below are two statements : Statement (I) : Fusion of $MnO_{2}$ with $KOH$ and an oxidising agent gives
dark green $K_{2}MnO_{4}$ . Statement (II) : Manganate ion on electrolytic oxidation in alkaline medium gives
permanganate ion. In the light of the above statements, choose the correct answer from the options given
below :
a.
Statement I is true but Statement II is false
b.
Both Statement I and Statement II are false
c.
Statement I is false but Statement II is true
d.
Both Statement I and Statement II are true
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A solution is prepared by adding 1 mole ethyl alcohol in 9 mole water. The mass percent of solute in the
solution is ________ (Integer answer) (Given : Molar mass in $gmol^{-1}$ Ethyl alcohol : 46 water: 18)
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Given below are two statements : Statement (I) : All the following compounds react with p-toluenesulfonyl
chloride. $C_{6}H_{5}NH_{2} (C_{6}H_{5})_{2}NH (C_{6}H_{5})_{3}\,N$ Statement (II) : Their products in the above reaction are
soluble is aqueous $NaOH$ . In the light of the above statements, choose the correct answer from the options
given below
a.
Statement I is false but Statement II is true
b.
Statement I is true but Statement II is false
c.
Both Statement I and Statement II are true
d.
Both Statement I and Statement II are false
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Identify the correct statements about p-block elements and their compounds. (A) Non metals have higher
electronegativity than metals. (B) Non metals have lower ionisation enthalpy than metals. (C) Compounds
formed between highly reactive nonmetals and highly reactive metals are generally ionic. (D) The non-metal
oxides are generally basic in nature. (E) The metal oxides are generally acidic or neutral in nature. Choose the
correct answer from the options given below :
a.
(B) and (D) only
b.
(A) and (C) only
c.
(D) and (E) only
d.
(B) and (E) only
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$\Delta _{vap\,}H^{\ominus }$ for water is $+40.79\,kJ\,mol^{-1}$ at 1 bar and $100^{\circ }C$ . Change in internal energy for this vapourisation
under same condition is $kJmol^{-1}$ . (Integer answer) (Given $R = 8.3JK^{-1}\,mol^{-1}$ )
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Let $S$ be the focus of the hyperbola $\frac{x^{2}}{3} - \frac{y^{2}}{5} = 1$ , on the positive $x$ -axis. Let $C$ be the circle with its centre at
$A(\sqrt{6}, \sqrt{5})$ and passing through the point $S$ . If $O$ is the origin and $SAB$ is a diameter of $C$ , then the square of
the area of the triangle OSB is equal to___________
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$-a \,if\, -a \leq x\leq 0$
Let $f(x) ={$ where $a > 0$ and $g(x) = (f(x|) -|f(x)|)/2$ . Then the function
$x+ a \,if\, 0 <x\leq a$
$g: [-a,a] \rightarrow [-\rightarrow a,a]$ is
a.
neither one-one nor onto.
b.
onto.
c.
both one-one and onto.
d.
one-one.
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Let $A$ be the region enclosed by the parabola $y^{2} = 2x$ and the line $x= 24$ . Then the maximum area of the
rectangle inscribed in the region $A$ is________
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If the line segment joining the points $(5, 2)$ and $(2,a)$ subtends an angle $\frac{\pi}{4}$ at the origin, then the absolute
value of the product of all possible values of $a$ is :
a.
6
b.
8
c.
2
d.
-4
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If the value of $\frac{3 cos 36^{\circ }+5 sin 18^{\circ }}{5 cos 36^{\circ }-3 sin 18^{\circ }}$ is $\frac{a\sqrt{5}-b}{c}$ , where $a,b,c$ are natural numbers and $gcd(a,c) = 1$ , then $a+b+c$ is
equal to :
a.
40
b.
52
c.
50
d.
54
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If $\alpha = lim_{x\rightarrow 0\rightarrow } +( \frac{e^{\sqrt{tanx}}-e^{\sqrt{x}}}{\sqrt{tanx}-\sqrt{x}} )$ and $\beta = lim_{x\rightarrow 0\rightarrow } (1 + sinx)\frac{1}{2}^{cotx}$ are the roots of the quadratic equation
$ax^{2} +bx- = 0\sqrt{e}$ , then $12 log_{e}(a + b)$ is equal to__________
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If the shortest distance between the lines $\frac{x-\lambda}{2} = \frac{y-4}{3} = \frac{z-3}{4}$ and $\frac{x-2}{4} = \frac{y-4}{6} = \frac{z-7}{8}$ is $\frac{13}{\sqrt{29}}$ , then a value of $\lambda$
is :
a.
-1
b.
$-\frac{13}{25}$
c.
$\frac{13}{25}$
d.
1
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$\{\frac{tan((a+1)x)+b tanx}{x}, x< 0$
For $a, b > 0$ , let $f(x) = 3, x= 0$ be a continous function at $x= 0$ . Then $\frac{b}{a}$ is equal to :
$\{ \frac{\sqrt{ax+b^{2}x^{2}}-\sqrt{ax}}{\,b\sqrt{a}x\sqrt{x}} , x> 0$
a.
6
b.
4
c.
5
d.
8
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$\alpha b c$
If $\alpha \neq a,\beta \neq b,\gamma \neq c$ and $a \beta c = 0$ , then $\frac{a}{\alpha -a} + \frac{b}{\beta -b} + \frac{\gamma}{\gamma -c}$ is equal to:
$a b \gamma$
a.
3
b.
0
c.
1
d.
2
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Let $\vec{a}= \hat{i}+ 2\hat{j}+ 3\hat{k}, \vec{b}= 2\hat{i}+ 3\hat{j}-5\hat{k}$ and $\vec{c}= 3\hat{i}- \hat{j}+\lambda \hat{k}$ be three vectors. Let $\vec{r}$ be anit vector along $\vec{b}+ \vec{c}$ .
If $\vec{r}\cdot \vec{a}= 3$ , then $3\lambda$ is equal to:
a.
21
b.
30
c.
25
d.
27
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The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the
chosen alphabets are not necessarily distinct, is equal to :
a.
179
b.
177
c.
181
d.
175
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If the function $f(x) = 2x^{3} -9x^{2} + 12a^{2}x+ 1, a > 0$ has a local maximum at $x=\alpha$ and a local minimum at
$x=\alpha ^{2}$ , then $\alpha$ and $\alpha ^{2}$ are the roots of the equation :
a.
$x^{2} -6x+ 8 = 0$
b.
$x^{2} + 6x+ 8 = 0$
c.
$8x^{2} + 6x-1 = 0$
d.
$8x^{2} -6x+ 1 = 0$
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Let a ray of light passing through the point $(3, 10)$ reflects on the line $2x+y= 6$ and the reflected ray passes
through the point $(7, 2)$ . If the equation of the incident ray is $ax+by+ 1 = 0$ , then $a^{2} +b^{2} + 3ab$ is equal
to_________
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Let $a, b, c \in N$ and $a < b < c$ . Let the mean, the mean deviation about the mean and the variance of the 5
observations $9, 25, a, b, c$ be 18,4 and $\frac{136}{5}$ , respectively. Then $2a + b -c$ is equal to__________
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Let $P(\alpha ,\beta ,\gamma )$ be the image of the point $Q(1, 6, 4)$ in the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ . Then $2\alpha +\beta +\gamma$ is equal
to_______
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Let $\alpha |x| = |y|e^{xy-\beta },\alpha ,\beta \in N$ be the solution of the differential equation $x\,dy- y\,dx+xy(x\,dy+y\,dx) = 0$ ,
$y(1) = 2$ . Then $\alpha +\beta$ is equal to ________
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Let $A= {2, 3, 6, 8, 9, 11}$ and $B= {1, 4, 5, 10, 15}$ . Let $R$ be a relation on $A\times B$ defined by $(a,b)R(c,d)$ if
and only if $3ad-7bc$ is an even integer. Then the relation $R$ is
a.
an equivalence relation.
b.
reflexive and symmetric but not transitive.
c.
transitive but not symmetric.
d.
reflexive but not symmetric.
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In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $\frac{70}{3}$ and the
product of the third and fifth terms is 49 . Then the sum of the $4^{th\,}, 6^{th\,}$ and $8^{th\,}$ terms is equal to :
a.
96
b.
91
c.
84
d.
78
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If $\int \frac{1}{\sqrt{(x-1)^{4}(x+3)^{6}}^{5}} \,dx= A(\frac{\alpha x-1}{\beta x+3})^{B} + C$ , where $C$ is the constant of integration, then the value of
$\alpha +\beta + 20AB$ is__________
Numerical answer locked.
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Let $\vec{a}= 4\hat{i}- \hat{j}+ \hat{k}, \vec{b}= 11\hat{i}- \hat{j}+ \hat{k}$ and $\vec{c}$ be a vector such that $(\vec{a}+ \vec{b}) \times \vec{c}= \vec{c}\times (-2\vec{a}+ 3\vec{b})$ . If
$(2\vec{a}+ 3\vec{b}) \cdot \vec{c}= 1670$ , then $|\vec{c}|^{2}$ is equal to :
a.
1609
b.
1618
c.
1600
d.
1627
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There are three bags $X,Y$ and $Z$ . Bag $X$ contains 5 one-rupee coins and 4 five-rupee coins; Bag $Y$ contains 4
one-rupee coins and 5 five-rupee coins and Bag Z contains 3 one-rupee coins and 6 five-rupee coins. A bag is
selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability,
that it came from bag Y, is :
a.
$\frac{1}{4}$
b.
$\frac{1}{2}$
c.
$\frac{5}{12}$
d.
$\frac{1}{3}$
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