The number of \( \boldsymbol{H}^{+} \) ions in \( 1 \mathrm{cc} \) of \( \mathrm{a} \)
solution of \( p H=13 \) is:
A. \( 6.023 \times 10^{7} \)
B. \( 1 \times 10^{-13} \)
c. \( 6.023 \times 10^{13} \)
D. \( 1 \times 10^{16} \)


During photosynthesis, which gas is used by the plants to prepare food?
\( A \cdot O_{2} \)
в. \( C O_{2} \)
c. \( C O \)
D. \( N_{2} \)


Name the most acceptable theory of origin of life. Who gave this theory?


State whether the following statements
are true or false.

Veins generally have thicker walls than
arteries.
A. True
B. False


In a parabola, length of the latus rectum
is 4a.
A . True
B. False


Construct a quadrilateral \( A B C D \) with \( A B=2.5 \mathrm{cm}, B C=3.5 \mathrm{cm}, C D= \)
\( 4.5 \mathrm{cm}, \angle A=90^{\circ} \) and \( \angle B=120^{\circ} \)


If quantities \( \Delta T_{f}, \Delta T_{b}, \Delta p \) and \( \pi \) without subscript refer to the electrolyte solution and these with subscript refer to non-electrolyte solution then which one is wrong?
\( ^{\mathbf{A}} \cdot_{i}=\frac{\Delta T_{f}}{\left(\Delta T_{f}\right)_{0}} \)
в. \( _{i}=\frac{\Delta T_{b}}{\left(\Delta T_{b}\right)_{0}} \)
c. \( _{i}=\frac{\Delta P}{\left(P^{0}\right)_{0}} \)
D. \( _{i}=\frac{\pi}{(\pi)_{0}} \)


What will be standard cell potential of galvanic cell with the following
reaction?
\( \boldsymbol{2} \boldsymbol{C r}_{(s)}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{d}_{(a q)}^{2+} \rightarrow \boldsymbol{2} \boldsymbol{C r}_{(a q)}^{3+}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{d}_{(s)} \)
\( \left[\text { Given: } \boldsymbol{E}_{C r^{3+} / C r}^{o}=-\mathbf{0 . 7 4 V} \) and \right.
\( \boldsymbol{E}_{C d^{2+} / C d}^{o}=-\mathbf{0 . 4 0 V} \)
\( \mathbf{A} \cdot 0.74 \mathrm{v} \)
B. \( 1.14 \mathrm{V} \)
c. \( 0.34 v \)
D. \( -0.34 \mathrm{v} \)


Assertion
Coupling of \( P h N H_{2} \) with aniline is
faster than with phenol.
Reason
Aniline is more \( \bar{e} \) donating than phenol.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In North west corner rule, if the supply
in the row is satisfied one must move
A. down in the next row
B. up in the next row
c. right cell in the next column
D. left cell in the next row


Read the given statements to identify the phytohormone that performs these functions.
(i) Horizontal growth of seedlings, swelling of the axis and apical hook formation in dicot seedlings.
(ii) Promoting senescence and abscission of leaves and flowers.
(iii) Breaking seed and bud dormancy.
(iv) Initiating germination in peanut seeds.
(v) Sprouting of potato tubers.
\( A \cdot \) ABA
B. Ethylene
\( c \cdot \) GА
D. cytokinins


Find the interval of increase and
decrease of the following functions. \( f(x)=\frac{x}{\ln x} \)


In a squared sheet, draw two triangles
of equal areas such that
(i) the triangles are congruent.
(ii) the triangles are not congruent What can you say about their perimeters?


The radius of a circle with centre \( \boldsymbol{P} \) is
\( 25 \mathrm{cm} \) and the length of the chord is 48 \( \mathrm{cm} . \) The distance of the chord from
centre \( P \) of the circle is
\( \mathbf{A} \cdot 24 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .7 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)


The mass of earth is 80 times that of
moon. Their diameters are \( 12800 K m \)
and \( 3200 K m \) respectively. The value
of g on moon will be if its
value on earth is \( 980 \mathrm{cm} / \mathrm{s}^{2} \)
A \( \cdot 98 \mathrm{cm} / \mathrm{s}^{2} \)
В \( \cdot 196 \mathrm{cm} / \mathrm{s}^{2} \)
c. \( 100 \mathrm{cm} / \mathrm{s}^{2} \)
D. \( 294 \mathrm{cm} / \mathrm{s}^{2} \)


Two cylindrical rod have area of cross-
section \( \boldsymbol{A}_{\mathbf{1}} \boldsymbol{A}_{\mathbf{2}} . \) If \( \boldsymbol{A}_{\mathbf{1}} \) is greater than \( \boldsymbol{A}_{\mathbf{2}} \)
Then which of the following is correct?
A. The resistivity of the cylinder having area of crosssection \( A_{1} \) is higher than the cylinder of cross-section \( A_{2} \)
B. The resistivity of the cylinder having area of crosssection \( A_{2} \) is higher than the cylinder of cross-section
\( A_{1} \)
C. The resistivity of the cylinder having area of crosssection \( A_{1} \) is same as the cylinder of cross-section \( A_{2} \)
D. None of the above


In producing a pure spectrum, the
incident light is passed through a
narrow slit placed in the focal plane of
an achromatic lens because a narrow
slit
A. produces less diffraction
B. increases intensity
C. allows only one colour at a time
D. allows a more parallel beam when it passes through the lens


Form the differential equation from the following primitive where constant is arbitrary. \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{a}^{2} \)


The nature of bonding forces in adsorption is:
A. purely physical such as van der Waals forces
B. purely chemical
c. both chemical and physical are possible
D. none of these


\[
f(x)=\left\{\begin{array}{ll}
\frac{\sin a x}{\sin b x}, & x \neq 0 \\
\frac{a}{b}, & x=0
\end{array}\right.
\]
Test the continuity of function at \( x=0 \)


Sum of \( \frac{\mathbf{8}}{\mathbf{4}}, \frac{\mathbf{9}}{\mathbf{6}}, 1, \frac{\mathbf{3}}{\mathbf{5}} \) is equal to
A \( \cdot \frac{152}{30} \)
в. \( 5 \frac{3}{30} \)
c. \( 5 \frac{2}{30} \)
D. \( _{5} \frac{1}{30} \)


The main explanation for the lack of a continuing abiotic origin of life on the Earth today is that
A. There is not sufficient lightning to provide an energy source
B. Our oxidising atmosphere is not conducive to the spontaneous formation of complex molecules
c. There is much less visible light reaching Earth to serve as an energy source
D. There are no molten surfaces on which weak solutions of organic molecules would polymerise


Assertion
Although the surface of goggles' lens is curved, it does not have any optical
power.
Reason
In case of goggles, both the curved surfaces have equal radii of curvature
and have centre of curvature on the
same side.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( x^{2}-\frac{k}{2} x=2 p \)
In the quadratic equation above, \( k \) and \( p \) are constants. What are the solutions
for \( x ? \)
A \( x=\frac{k}{4} \pm \frac{\sqrt{k^{2}+2 p}}{4} \)
B. \( x=\frac{k}{4} \pm \frac{\sqrt{k^{2}+32 p}}{4} \)
c. \( _{x}=\frac{k}{2} \pm \frac{\sqrt{k^{2}+2 p}}{2} \)
D. \( x=\frac{k}{2} \pm \frac{\sqrt{k^{2}+32 p}}{4} \)


If the half lives of a radioactive element
for \( \alpha \) and \( \beta \) decay are 4 years and 12 years respectively, then the percentage
of the element that remains after 12
years will be
A . \( 6.25 \% \)
B . \( 12.5 \% \)
c. \( 25 \% \)
D. 50 \%


If two particles \( A \) and \( B \) having masses in the ratio 1: 4 are moving with same velocity, the ratio of wavelengths associated with them will be in the
ratio:
\( A \cdot 1: 4 \)
B. 4:
c. 2:
D. 1:


The chemical that changes its colour
when it is left open in sunlight is:
\( \mathbf{A} \cdot \operatorname{Fe} S O_{4}(s) \)
B . \( P b\left(N O_{3}\right)_{2}(s) \)
c. \( A g C l(s) \)
D. \( B a C l_{2}(a q) \)


Obtain as the limit of sum \( \int_{\log _{e}^{3}} e^{x} d x \)


If three particles each of mass \( m \) are placed at the corners of an equilateral triangle of side \( a \), the potential energy of the system and the work done if the side of the triangle is changed from \( a \) to
\( \mathbf{2} \boldsymbol{a}, \) are
\( ^{\mathbf{A}} \cdot \frac{3 G M}{a^{2}}, \frac{3 G M}{2 a} \)
в. \( -\frac{3 G M^{2}}{a}, \frac{3 G M^{2}}{2 a} \)
c. \( -\frac{3 G M^{2}}{a^{2}}, \frac{3 G M^{2}}{4 a^{2}} \)
D. \( -\frac{3 G M^{2}}{a}, \frac{3 G M}{2 a} \)


The resistance of a wire at temperature
\( 30^{\circ} \mathrm{C} \) is found to be \( 10 \Omega . \) Now to
increase the resistance by \( 10 \%, \) the temperature of the wire must be ( The temperature coefficient of resistance of the material of the wire is \( 0.002^{\circ} \mathrm{C}^{-1} \)
and reference temperature is \( 0^{\circ} C \) ).
A \( \cdot 35^{\circ} \mathrm{C} \)
B . \( 36^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 33^{\circ} C \)
D. \( 83^{\circ} \mathrm{C} \)


A logic gate which has an output' \( 1^{\prime} \)
only when the inputs are complement to
each other is.
A. AND
B. NAND
c. Nor
D. EXOR


Chipko andolan originated in
A. Karnataka
B. Uttarakhand
c. Kerala
D. Rajasthan


The value of \( \int \frac{1}{\sqrt{\sin ^{3} x \cos ^{5} x}} d x \) is
A \( \cdot \frac{-2}{\sqrt{\tan x}}+\frac{2}{3}(\tan x)^{3 / 2}+C \)
в. \( \frac{2}{\sqrt{\tan x}}-\frac{2}{3}(\tan x)^{3 / 2}+C \)
c. \( \frac{-2}{\sqrt{\tan x}}+\frac{2}{3}(\tan x)^{1 / 2}+C \)
D. None of these


Assertion
Spring balances show incorrect
readings after using for a long time.
Reason
On using for a long time, springs in the
balances lose their elastic strength
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


An \( \alpha \) particle and a proton travel with same velocity in a magnetic field perpendicular to the direction of their
velocities. Find the ratio of the radii of
their circular paths.
A .4:
B. 1:
c. 2:
D. 1:


What is the reason for the stability of colloidal sols?


You want to show that \( \Delta \mathrm{ART} \cong \Delta \mathrm{PEN} \).
If it is given that \( A T=P N \) and you are to
use ASA criterion, you need to have?


Phellogen and phellem respectively denote
A. Cork and cork cambium
B. Cork cambium and cork
c. Secondary cortex and cork.
D. cork and secondary cortex.


Find total number of subsets of \( \mathrm{B}=\{\mathrm{a} \)
\( \mathbf{b}, \mathbf{c}\} \)


Calculate the heat of combustion (in KJ)
of
methane from the following data
i) \( \mathrm{C}(\text { graphite })+2 \mathrm{H}_{2}(\mathrm{g}) \rightarrow \mathrm{CH}_{4}(\mathrm{g}), \Delta \mathrm{H}= \)
\( -74.8 k J \)
ii) \( C(\text { graphite })+O_{2}(g) \rightarrow C O_{2}(g), \Delta H= \)
\( -393.5 \mathrm{kJ} \)
iii) \( \mathrm{H}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(l), \Delta \mathrm{H}=-286.2 \)
KJ.
A. - 891.1
B . -816.3
c. -965.9
D. -1040.7


Two charges of \( +10 \mu \mathrm{C} \) and \( +20 \mu \mathrm{C} \) are separated by a distance of 2 cm. The net potential (electric) due to the pair at the middle point of the line joining the two charges, is :
A . 27 MV
B. 18 MV
c. 20 MV
D. 23 MV


The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
reaction
\( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \)
is 1 at \( 27 C \) and 4 at 47 .
For the reaction calculate enthalpy
change for the
\( \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{A}(\boldsymbol{g}) \)
\( (\text {Given }: \boldsymbol{R}=\mathbf{2 c a l} / \boldsymbol{m o l}-\boldsymbol{K}) \)
\( \mathbf{A} \cdot 13.31 \mathrm{kcal} / \mathrm{mol} \)
в. \( 14.31 \mathrm{kcal} / \mathrm{mol} \)
c. \( 19.2 \mathrm{kcal} / \mathrm{mol} \)
D. 55.63 kcal/mol


The classification, category below the level of family is
A. Class
B. Species
c. Phylum
D. Genus


A very long (length \( L \) ) cylindrical galaxy is made of uniformly distributed mass and has radius \( R(R<<L) . \) A star
outside the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time
period of star is \( T \) and its distance from
the galaxy s axis is \( r, \) then:
A \( \cdot T^{2} \propto r^{3} \)
B. \( T \propto r \)
c. \( T \propto r^{2} \)
D. \( T \propto \sqrt{r} \)


Match the column
Column -II Column-I
\( (A) \)
(i) Citric acid Acetobacter aceti (1)
(B) (ii)Latic \( d \) Clostridium butylicum acid
(C) Aspergillus r Acetic acid Por Is niger (iii) tC acid dot
(D) Lactobacillus \( \quad \) (iv) Butyric ric acid
\( \mathbf{A} \)
\( A-(i i), B-(i), C-(i i i), D-(i v) \)
B. A-(iii), B-(ii), C-(i), D-(iv)
C \( . A-(\text { iii) }, B-(i v), C-(i), D-(i i) \)
D. \( A-(\text { iv }), B-(\text { iii) }, C-(i i), D-(i) \)


In a rhombus PQRS, PR = 24 cm and QS
\( =18 \mathrm{cm} . \) Find the perimeter of the rhombus.


Three distinct numbers, \( x, y, z \) form a geometric progression in that order,
and the numbers \( \boldsymbol{x}+\boldsymbol{y}, \boldsymbol{y}+\boldsymbol{z}, \boldsymbol{z}+\boldsymbol{x} \)
form an arithmetic progression in that
order. Find the common ratio of the
geometric progression.


Discuss the chemistry of Lassaignes
test.


The Savanna type of climate is characterised by
A. Humid summers and humid winters
B. Humid summers and dry winters
c. Humid winters and dry summers
D. Humid throughout the year


Which of the following contains maximum number of atoms?
A. \( 0.16 g \) СН\( _{3} \)
В. \( 0.28 g N_{2} \)
\( \mathbf{c} \cdot 0.36 g C_{6} H_{12} O_{6} \)
D. \( 1.1 g C O_{2} \)


Two spheres each of mass \( 10^{5} \mathrm{kg} \) and
radius \( 10 \mathrm{m} \) are kept in contact. Find the force of gravitation acting between them?


Assertion
The number of real solution of the
equation \( \sin (\cos x)=\cos (\sin x) \) is
zero
Reason
\( \sin x>0, \) then \( 2 n \pi<x< \)
\( (2 n+1) \pi, n \epsilon I \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion false but Reason is true


If \( 2 x+3 y=\sin y, \) find \( \frac{d y}{d x} \)


Marie Curie is credited to the
development of which of the following element?
A. Thorium
B. cesium
c. Radium
D. carbon


Find the ratio in which YZ-plane divides the line joining \( A(2,4,5) \) and \( B(3,5,-4) . \) Also find the point of
intersection.


A uniform rod of length \( l \) is placed
symmetrically on two walls as shown in figure. The rod is in equilibrium. If
\( N_{1} \) and \( N_{2} \) are the normal forces
exerted by the walls on the rod then:
\( \mathbf{A} \cdot N_{1}>N_{2} \)
В. \( N_{1}<N_{2} \)
\( \mathbf{c} \cdot N_{1}=N_{2} \)
D. \( N_{1} \) and \( N_{2} \) would be in the vertical directions


Match the points on the curve \( 2 y^{2}= \)
\( x+1 \) with the slope of normals at those
points and choose
the correct answer.
A \( . i-b, i i-d, i i i-c, i v-a \)
B . \( i-b, i i-a, i i i-d, i v-c \)
c. \( i-b, i i-c, i i i-d, i v-a \)
D. \( i-b, i i-d, i i i-a, i v-c \)


Arrange in ascending order:
\( \mathbf{2 5 6 . 3 6}, \mathbf{2 5 6 . 5 6}, \mathbf{2 5 6 . 2 6}, \mathbf{2 5 6 . 4 6} \)
A . 256.36,256.56,256.26,256.46
B . 256.26,256.56,256.36,256.46
c. 256.36,256.46,256.26,256.56
D. 256.26,256.36,256.46,256.56


A black body of mass 34.38 gm and surface area \( 19.2 \mathrm{cm}^{2} \) is at an initial
temperature of \( 400 \mathrm{K} \). It is allowed to cool inside an evacuated enclosure
kept at constant temperature \( 300 \mathrm{K} \)
The rate of cooling is \( 0.04^{\circ} \mathrm{C} \) per second. The specific heat of the body in \( J k g^{-1} K^{-1} \) is (Stefan's constant \( \sigma= \) \( \left.5.73 \times 10^{-8} W m^{-2} K^{-4}\right) \)
A. 2800
в. 2100
\( c \cdot 1400 \)
D. 1200


What is an AC generator? Obtain an expression for the sinusoidal emf induced in the coil of ac generator,
rotating with a uniform angular speed in a uniform magnetic field.


In bryophytes, which part of archegonium encloses egg?
A. Neck
B. Cover cell
c. venter
D. Neck canal cell


A particle performs SHM with a period \( \boldsymbol{T} \)
and amplitude \( a \). The mean velocity of
particle over the time interval during which it travels a distance \( a / 2 \) from the extreme position is:
\( ^{A} \cdot \frac{6 a}{T} \)
в. \( \frac{2 a}{T} \)
\( c \cdot \frac{3 a}{T} \)
D. None


toppr
Q Type your question
This oscillation is finally transmitted to the fluid filled in inner portion of the ear
termed as inner ear, the motion of the
fluid disturbs hair calls within the inner
ear which transmit nerve impulses to the brain with information that a sound
is present. The three bones present in the middle ear are named as hammer, anvil and stirrup. Out of these the stirrup is the smallest one and this only connects the middle ear to inner ear as
shown in the figure below. The area of stirrup and its extent of connection with
the inner ear limits the sensitivity of the human ear. Consider a person's eat whose moving part of the eardrum has
an area of about \( 43 \mathrm{mm}^{2} \) and the area of
stirrup is about \( 3.2 \mathrm{mm}^{2} . \) The mass of
ossicles is negligible. As a result, force exerted by sound wave in air on eardrum and ossicles is same as the
force exerted by ossicles on the inner ear. Consider a sound wave having maximum pressure fluctuation of \( 3 x \)
\( 10^{-2} \) Pa from its normal equilibrium
pressure value which is wqual to \( 10^{5} \) Pa Frequency of sound wave is \( 1200 \mathrm{Hz} \) Data: Velocity of sound wave in air is \( 332 \mathrm{m} / \mathrm{s} \). Velocity of sound wave in fluid (present in inner ear) is \( 1500 \mathrm{m} / \mathrm{s} \). Bulk
modulus of air is \( 1.42 \times 10^{5} \) Pa. Bulk
modulus of fluid is \( 2.18 \times 10^{9} \) Pa.
Find the pressure amplitude of given sound wave in the fluid of inner ear.
A. 0.03 Pa
B. \( 0.04 \mathrm{Pa} \)
c. \( 0.3 \mathrm{Pa} \)
D. \( 0.4 \mathrm{Pa} \)


Using remainder theorem, find the
remainder when \( 3 x^{2}+x+7 \) is divided
by \( \boldsymbol{x}+\mathbf{2} \)
A . 17
B. -23
c. 13
D. -29


The common passage for bile and pancreatic juice is
A. Ampulla of vater
B. Ductus choledochus
c. Duct of Warsung
D. Duct of Santorini


The following table shows the electronic configuration of the elements \( \boldsymbol{W}, \boldsymbol{X}, \boldsymbol{Y}, \boldsymbol{Z} \)
\[
\begin{array}{lllll}
\text { Element } & \mathrm{w} & \mathrm{x} & \mathrm{Y} & \mathrm{z} \\
\begin{array}{l}
\text { Electronic } \\
\text { configuration }
\end{array} & \begin{array}{l}
2, \\
8,1
\end{array} & \begin{array}{l}
2, \\
8,
\end{array} & \begin{array}{l}
2, \\
7
\end{array} & 5
\end{array}
\]
Answer the following questions based on the table above:
(i) What type of Bond is formed between
1. \( W \) and \( X \)
2. \( Y \) and \( Z \)
(ii) What is the formula of the
compound formed between:
1. \( X \) and \( Z \)
2. \( W \) and \( X \)


Which of the following is a redox reaction?
A \( \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( H_{2}+C l_{2} \rightarrow 2 H C l \)
\( \mathrm{c} \cdot \mathrm{CaO}+2 \mathrm{HCl} \rightarrow \mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O} \)
D. \( N a O H+H C l \rightarrow N a C l+H_{2} O \)


Which of the following exists as associated molecules due to hydrogen bonding? This question has multiple correct options
A \( \cdot N H_{3} \)
в. \( H_{2} O \)
c. \( H F \)
D. \( H C l \)


E. Negative temperature
A. Hole \( \quad \) coefficient of resistance
B. Copper
F. Energy vacancy
G. Positive temperature coefficient
C. Doping \( \quad \) of resistance
H. Addition of impurity to increase
D. \( \quad \) the conductivity Germanium
Charges are holes and electrons
Match the above lists:
\( A \cdot A-H, I B-E C-F D-G \)
B. A-E B-F,I C-G D-H
C \( . \) A-F B-G C-H D-E,
D. A-G,I B-H C-E D-F


Find \( \frac{1}{2}\left(A+A^{T}\right) \) and \( \frac{1}{2}\left(A-A^{T}\right) \)
when \( A=\left[\begin{array}{ccc}0 & a b \\ -a & 0 & c \\ -b-c 0\end{array}\right] \)


Nucleon contains:
A . only protons
B. only neutrons
C. both protons and neutrons
D. electrons, protons, and neutrons


The magnetic field at the center of a
long circular coil carrying current will
be:
A. parabolic lines
B. circular lines
c. parallel straight lines
D. perpendicular straight lines


If the freezing point of a 0.01 mola aqueous solution of a cobalt(III) chloride-ammonia complex (which behaves as a strong electrolyte) is
\( -0.0558^{\circ} C, \) the number of chloride(s)
in the coordination sphere of the
complex is:
\( \left[K_{f} \text { of water }=1.86 K k g m o l^{-1}\right] \)


The sex hormone which controls the
development and maintenance of
pregnancy is:
A. Cortisone
B. Thyroxine
c. Progesterone
D. Estrone


The \( n^{t h} \) term of the sequence
\( \frac{1}{100}, \frac{1}{10000}, \frac{1}{1000000}, \dots \dots \) is
A \( \cdot(1000)^{n} \)
B. \( 10^{2 n} \)
\( c \cdot 10^{-2 n} \)
D. \( 10^{-n} \)


When borax is dissolved in water:
\( \mathbf{A} \cdot B(O H)_{3} \) is formed only
\( \mathbf{B} \cdot\left[B(O H)_{4}\right]^{-} \) is formed only
\( \mathbf{c} \cdot \operatorname{Both} B(O H)_{3} \) and \( \left[B(O H)_{4}\right]^{-} \) are formed
D. \( \left[B_{3} O_{3}(O H)_{4}\right]^{-} \) is formed only


Statement-1: When two vibrating tuning
forks having frequencies 256 Hz and 512
Hz are held near each other, beats
cannot be heard.
Statement-2: The principle of
superposition is valid only if the
frequencies of the oscillations are
nearly equal.
A. Both the statements are true and statement- 2 is the correct explanation of statement-
B. Both the statements are true but statement-2 is not the correct explanation of statement-
c. Statement-1 is true and statement-2 is false
D. Statement-1 is false and statement-2 is true


Let \( S_{n} \) denote the sum of first \( n \) terms of
an \( A P \) and \( 3 S_{n}=S_{2 n} . \) What is \( S_{3 n}: S_{n} \)
equal to?
A . 4: 1
B. 6: 1
c. 8: 1
D. 10: 1


A ball is thrown up at a speed of \( 4 \mathrm{m} / \mathrm{s} \) with constant acceleration. Find the
maximum height reached by the ball. Take \( g=10 m s^{-2} \)
A. \( 0.4 \mathrm{m} \)
B. \( 0.8 \mathrm{m} \)
c. \( 1.0 \mathrm{m} \)
D. 1.4 \( m \)


The simplest form of the expression \( \frac{10-\sqrt{-12}}{1-\sqrt{-27}} \) is
\( A \cdot-\frac{2}{7} \)
в. \( \frac{28}{3} \)
c. \( -\frac{2}{7}+i \sqrt{3} \)
D. \( 1+i \sqrt{3} \)


The position versus time graph for
certain particle moving along the \( x \) -axis
is shown in the figure. Find the average
velocity in the time intervals \( (a) 0 \) to \( 2 s \)
\( (b) 2 s t 04 s, \) and \( (c) 4 s t o 7 s \)


Units of rate constant of a first order
reaction is :
A . mole.lit"
B. lit.mole
c. mole.sec \( ^{-1} \)
D. \( \sec ^{-1} \)


Choose the correct statements from the
following
This question has multiple correct options
A. Evaporation takes place from the surface of a liquid at all temperatures.
B. The rate of evaporation depends upon the area of the exposed surface of the liquid, nature of the liquid and its temperature.
C. The rate of evaporation depends on the pressure to which the liquid is subjected.
D. The cooling produced in evaporation is a consequence of the fact that a liquid has latent heat.


If one root of the quadratic equation
\( 2 x^{2}+k x-6=0 \) is \( 2, \) find the value of
k. Also, find the other root.


Name the steps in the manufacture of
common sugar from sugarcane and
explain the first step.


Give the structure of pyrosulphuric
acid. How would you prepare it? What would you observe, when colourless \( H I \)
is added to sulphuric acid?


(a) In a metre bridge [Fig.], the balance point is found to be at \( 39.5 \mathrm{cm} \) from the
end \( A, \) when the resistor \( Y \) is of \( 12.5 \Omega \)
Determine the resistance of X. Why are the connections between resistors in a
Wheat stone or meter bridge made of thick copper strips?(b) Determine the balance point of the bridge above if \( \mathbf{X} \)
and \( Y \) are interchanged.(c) What
happens if the galvanometer and cell
are interchanged at the balance point of the bridge? Would the galvanometer show any current?


Which type of isomerism is shown by
But-1-yne and cyclobutene?
A. Ring chain isomerism
B. Chain isomerism
c. Position isomerism
D. Metamerism


The rate constant of a certain first order
reaction is \( 200 s^{-1} \) What is its half life
period?


The area of the region lying between the
line \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{2}=\mathbf{0} \) and the curve \( \boldsymbol{x}= \)
\( \sqrt{\boldsymbol{y}} \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. \( \frac{9}{2} \)
c. \( \frac{10}{3} \)
D. none


An apple falling from a tree is an example of motion
A . Rectilinear
B. Oscillatory
c. Periodic
D. Rotational


In a current voltage plot of a \( \mathrm{p}-\mathrm{n} \)
junction, find out the correct statement
from the following?
A. A p-njunction is essentially nonconducting when it is forward biased and highly conducting when it is reverse biased
B. A p-njunction is highly conducting when it is forward biased and essentially nonconducting when it is reverse biased
C. A p-njunction is highly conducting when it is forward biased as well as when it is reverse biased
D. A p-njunction is essectially nonconducting when it is forward biased as well as when it is reverse biased


Why bee strings are treated by alkaline
solutions?
A. Because it is basic in nature.
B. Because it is acidic in nature.
C. Because it is treatable by only alkaline solution.
D. None of these.


What are
(i) methanogens (ii) Halophiles (iii) thermoacidophiles?


About \( _{\text {tho }} \) axis in the following fig,
the moment of inertia of the rectangular
lamina is the maximum


Van Helmont concluded that plants get their food from
A. Air
B. water
c. Humus
D. Air and \( H_{2} O \)


Peeling of ozone umbrella is due to
A. CFCs
B. PAN
\( c \cdot C O_{2} \)
D. Coal burning


\( \int \sin ^{3} x \cos ^{2} x d x \) is equal to


\( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{A l}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \) is called:
A. Potassium alumino oxalate
B. Potassium trioxalatoaluminate(III)
C. Potassium aluminium(III) oxalate
D. Potassium trioxalato aluminate(VI)


The potential of the cell containing two hydrogen electrodes as represented below, is:
\( \boldsymbol{P t}, \boldsymbol{H}_{2(g)}\left|\boldsymbol{H}^{+}\left(\mathbf{1 0}^{-6} \boldsymbol{M}\right) \| \boldsymbol{H}^{+}\left(\mathbf{1 0}^{-4} \boldsymbol{M}\right)\right| \boldsymbol{H} \)
\( \operatorname{at} 298 K \)
A. \( -0.118 V \)
B . \( -0.0591 V \)
c. \( 0.118 V \)
D. \( 0.0591 V \)


What is oxidation number of \( C r \) in
\( C r O_{5} \) or \( C r O\left(O_{2}\right)_{2} ? \)


The function of sedimentation tank in
sewage treatment is to:
A. disinfect the sewage
B. aerate the sewage
c. remove water content
D. remove suspended solids


Ethylene on combustion gives carbon dioxide and water. Its heat of
combustion is \( 1410.0 \mathrm{kJ} \). \( \mathrm{mol}^{-1} \). If the
heat of formation of \( C O_{2} \) and \( H_{2} O \) are
\( 393.3 k J \) and \( 286.2 k J, \) respectively
Calculate the heat of formation of
ethylene.
\( \mathbf{A} \cdot \Delta_{f} H=51.0 k J m o l^{-1} \)
B . \( \Delta_{f} H=102.0 k J m o l^{-1} \)
C \( . \Delta_{f} H=25.0 k J m o l^{-1} \)
D. None of these


The number of positive integers which can be formed by using any number of digits from 0,1,2,3,4,5 without repetition
A . 1200
в. 1500
c. 1600
D. 1630


\( \boldsymbol{C H}_{3} \boldsymbol{B r}+\boldsymbol{M} \boldsymbol{g} \stackrel{\text {Ether}}{\longrightarrow} \boldsymbol{A} \stackrel{\boldsymbol{H C H O}}{\longrightarrow} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{H O H}}{\longrightarrow} \boldsymbol{C} \)
Compound \( \boldsymbol{C} \) is:
A. acetic acid
B. acetaldehyde
c. ethyl alcohol
D. formic acid


In the five-kingdom system of classification, which single kingdom out of the following can include bluegreen algae, nitrogen fixing bacteria and methanogenic Archaebacteria?
A. Monera
B. Fungi
c. Plantae
D. Protista


How many 3 -digit number can be formed from the digit 1,2,3,4 and 5 assuming that
(i) repetition of the digit is allowed?
(ii) repetition of the digits is not allowed?


\( \boldsymbol{C} \boldsymbol{a}_{\boldsymbol{4}}\left(\boldsymbol{P} \boldsymbol{O}_{\boldsymbol{4}}\right)_{2} \boldsymbol{O} \) is:
This question has multiple correct options
A. thomas slag
B. formed in manufacturing of steel iron
C. used in manufacture of phosphorus fertilizer
D. used as a refractory material


Heat is supplied to a diatomic gas at constant pressure. The ratio of \( \Delta Q: \Delta U \)
\( \Delta \) W is:
A . 5: 3: 2
B. 7:5:
c. 2: 3: 5
D. 2:5:


What are possible speeds of two objects, if they move uniformly towards each other, they get \( 4 m \) closer in each second and if they move uniformly in the same direction with the original
speeds they get \( 4.0 m \) closer in each \( 10 s \)
A. \( 2.8 m / s \) and \( 1.2 m / s \)
B. \( 5.2 m / s \) and \( 4.6 m / s \)
c. \( 3.2 m / s \) and \( 1.2 m / s \)
D. \( 2.2 m / s \) and \( 1.8 m / s \)


If the resultant of all the external forces
acting on a system of particles is zero, then from an inertial frame,one can
surely say that :
A. linear momentum of the system does not change in time
B. kinetic energy of the system does not change in time
c. angular momentum of the system does not change in time
D. potential energy of the system does not change in time


Q Type your question
surface as shown in the figure. The bottom of the container is square shaped of side \( \sqrt{3} m \) and its top is open
There is a very small hole in the vertical wall of the container near the bottom. A
small cap closes the hole. The hole gets opened when pressure near the bottom becomes more than \( 4 \times 10^{4} \) pascal.
(a) What minimum acceleration can be
given to the container in the positive
\( x- \) direction so that the cap will came
out of the hole? Assume water dose not
spill out of container when the
container accelerates.
(b) Find the velocity of efflux as soon as
the container starts moving with the
acceleration calculate in part (a) of the
question.


Which of these is true about
Hydrocarbons?
A. Small hydrocarbons with only a few carbon atoms have low boiling points and are gases.
B. Hydrocarbons with between five and 12 carbon atoms a re usually liquids.
C. Large hydrocarbons with many carbon atoms have high boiling points and are solids.
D. All of the above.


Write in brief about 'acid rain'.


Find a and
b, if \( 2\left[\begin{array}{ll}5 & a \\ 3 & 4\end{array}\right]+\left[\begin{array}{ll}0 & 1 \\ 1 & b\end{array}\right]= \)
\( \left[\begin{array}{cc}10 & 5 \\ 7 & 0\end{array}\right] \)


Taking chromium and arsenic, which
are toxic, out of pressure-treated wood, and using new less toxic chemicals for
bleaching paper, are examples of
A. Green chemistry
B. Green revolution
c. revolution resource recovery
D. waste management


Simplify the following into their lowest form: \( \frac{6 x^{2}+9 x}{3 x^{2}-12 x} \)
A \( \cdot \frac{2 x+3}{x-4} \)
в. \( \frac{2 x-3}{x-4} \)
c. \( \frac{2 x+3}{x+4} \)
D. None of these


A copper wire of length \( 2.4 m \) and a steel
wire of length \( 1.6 m, \) both the diameter
\( 3 m m, \) are connected end to end. When
stretched by a load, the net elongation is found to be \( 0.7 m m \). The load applied
is
\( \left(\boldsymbol{Y}_{\text {copper}}=\mathbf{1 . 2} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} \quad \boldsymbol{m}^{-2}, \boldsymbol{Y}_{\text {steel}}=\right. \)
A . \( 1.2 \times 10^{2} N \)
B. \( 1.8 \times 10^{2} N \)
c. \( 2.4 \times 10^{2} N \)
D. \( 3.2 \times 10^{2} N \)


The figure show a series LCR circuit with \( L=5.0 H, C=80 \mu F, R=40 \Omega \)
connected to variable frequency 240 source. Calculate
(i)The angular frequency of the source which driver the circuit at resonance
(ii) The current at the frequency.
(iii)The rms potential drop across the capacitor at resonance


Loop of Henle is meant for absorption of
A. Potassium
B. Glucose
c. water
D. \( C O_{2} \)


As compared to seral communities, the number of niches in climax
communities would be
A. Same
B. Fewer and generalised
c. More and specialised
D. None of the above


In a reversible reaction, a catalyst:
A. increases the rate of the forward reaction only
B. increases the rate of forward reaction to a greater extent then that of the backward reaction
C. increases the rate of the forward reaction and decreases that of the backward reaction to different
extent
D. increases the rate of the forward and backward reaction equally


A series of fast-moving still pictures
can create an illusion of movement
because:
A. The eye can focus on very rapidly changing pictures
B. Eye is quicker than the brain
C. Eye can separate two images only when the interval of separation between them is one-tenth of a second
D. The otical cortex can see through the rapidly moving images


Draw the number line and represent the following rational numbers on it:
\( \frac{-5}{8} \)


A 250 -Turn rectangular coil of length \( 2.1 \mathrm{cm} \) and width \( 1.25 \mathrm{cmcarries} \) a
current of \( 85 \mu A \) and subjected to a
magnetic field of strength 0.85T. Work
done for rotating the coil by \( 180^{\circ} \)
against the torque is:
B. \( 9.1 \mu J \)
c. \( 4.55 \mu \) J
D. \( 23 \mu J \)


What is the difference between
polarised light and unpolarised light?


Write down the names of parts of the
eye in the blank spaces shown in Fig
16.10


The orbitals of oxygen used for bonding
to hydrogen in water are
A. p-orbitals
B. sp-hybridised orbitals
c. \( s p^{2} \) -hybridised orbitals
D. \( s p^{3} \) -hybridized orbitals


Set up an equation in the following
cases:
Irfan says that he has 7 marbles more than five times the marbles Pramit has.
Irfan has 37 marbles. (Let \( m \) to be the
number of Pramit's marbles.)


The wavelength of a certain line in Balmer series is observed to be \( 4341 \dot{A} \).
To what value of ' \( n \) ' does this
correspond? \( \left(R_{H}=109678 \mathrm{cm}^{-1}\right) \)


Draw a velocity-time graph for an object
in uniform motion show that the area
under the velocity-time graph gives the displacement of the object in the given time interval.


Sum of infinity the following series:
\( \mathbf{1}+\mathbf{4} \boldsymbol{x}^{\mathbf{2}}+\mathbf{7} \boldsymbol{x}^{\mathbf{4}}+\mathbf{1 0} \boldsymbol{x}^{\mathbf{6}}+\ldots,|\boldsymbol{x}|<\mathbf{1} \)


A tank is filled with two immiscible
liquids of densities \( 2 \rho \) and \( \rho \) each of height \( h \). Two holes are made to the side wall at \( \frac{h}{2} \) and \( \frac{3 h}{2} \) from upper surface of the liquid, then the ratio of velocity of efflux of the liquids through the holes
A \( \frac{\sqrt{2}}{3} \)
в. \( \frac{\sqrt{3}}{1} \)
c. \( \frac{3}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{2}} \)


Find the area of the triangle formed by joining the mid points of the sides of the triangle, whose vertices are (0,1)\( ;(2,1) \) and \( (0,3) . \) Find the ratio of this area to the area of the given triangle


In a first order reaction, the
concentration of the reactant decreases
from \( 0.8 ~ M \) to 0.4 in 15 minutes. The
time taken for the concentration to
change from \( 0.1 \mathrm{M} \) to \( 0.025 \mathrm{M} \) is:
A. 30 min
B. 40 min
\( c .35 \) min
D. 25 min


Give the hybridization of carbon in
currect showing
A \( \cdot C O_{3}^{2-} S P^{3} d \)
B. Diamond \( S P^{3} \)
C . Graphite \( S P^{3} \)
D. Fullerene \( S P^{3} \)


If a string attached to a fixed pulley of radius R moves through a distance \( x \) and the pulley rolls without slipping
through an angle \( \theta, x \) and \( \theta \) are related
by
\( A \cdot x>R \theta \)
B. \( x=R \theta \)
\( c \cdot x<R \theta \)
D. 2R \( \theta \)


A wire is in the form of an equilateral triangle with area \( \sqrt{3} m^{2} \). If it is changed into a circle, the radius will be:


Farmers in a particular region were
concerned that premature yellowing of leaves of a pulse crop might cause decrease in the yield. Which treatment could be most beneficial to obtain
maximum seed yield?
A. Removal of all yellow leaves and spraying the remaining green leaves with 2,4,5 - trichlorophenoxy acetic acid
B. Application of iron and magnesium to promote synthesis of chlorophyll.
c. Frequent irrigaion of the crop
D. Treatment of the plants with cytokinins along with a small dose of nitrogenous fertilizer.


A \( 15 \mathrm{m} \) long ladder reached a window 12
m high from the ground on placing it
against a wall at a distance a. Find the distance of the foot of the ladder from
the wall.


Solve the following pair of equations:
\( \frac{\mathbf{9}}{\boldsymbol{x}}-\frac{\mathbf{4}}{\boldsymbol{y}}=\mathbf{8}, \frac{\mathbf{1 3}}{\boldsymbol{x}}+\frac{\mathbf{7}}{\boldsymbol{y}}=\mathbf{1 0 1} \)
A \( \cdot x=\frac{2}{3} ; y=\frac{4}{3} \)
B. \( x=\frac{1}{4} ; y=\frac{1}{7} \)
c. \( x=\frac{5}{4} ; y=\frac{2}{5} \)
D. \( x=\frac{3}{2} ; y=\frac{6}{5} \)


Which of the following vitamins is oil soluble?
\( A \cdot A \)
B. B 6
\( c \cdot B_{12} \)
D. B \( _{1} \)


A father holds his child on his shoulders
during a parade. The father does no work during the parade because:
A. No force acts on the child
B. The momentum of the child is constant
c. The potential energy of the child is varying
D. The child's kinetic energy is constant
E. The child's distance from the gro


\( \frac{-}{\infty} \)
\( \frac{\sigma}{\infty} \)
\( \sigma \)


Solve the simultaneous equations by
substitution method.
\( -\boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{0} ; \mathbf{1 0} \boldsymbol{x}+\mathbf{1 5} \boldsymbol{y}=\mathbf{1 0 5} \)


When phenol is treated with \( B r_{2} \) -water,
the product is:
A. \( \sigma \) -and p-bromophenol
B. 2, 3,4-tribromophenol
c. 2,4,6 - tribromophenol
D. none of these


The value of \( \lim _{n \rightarrow \infty} \frac{1}{n} \Sigma_{r=0}^{n-1} 4 \cdot \frac{r}{n}=? \)
\( ^{\mathrm{A}} \cdot \int_{1}^{5} 4 d x \)
в. \( \int_{0}^{4} 5 d x \)
\( ^{\mathrm{c}} \int_{0}^{1} 4 x d x \)
D. \( \int_{0}^{1} 4 d x \)


Identify the incorrect statement in
respect of two square matrices \( A \) and \( B \) conformable for sum and product
A \( \cdot t_{r}(A+B)=t_{r}(A)+t_{r}(B) \)
B . \( t_{r}(\alpha A)=\alpha t_{r}(A), \quad \alpha \epsilon R \)
\( \mathbf{c} \cdot t_{r}\left(A^{T}\right)=t_{r}(A) \)
D. none of these


toppr
Q Type your question.
stationary by applying a force P parallel to the plane is taken to be positive. As P is varied from \( \boldsymbol{P}_{1}=\boldsymbol{m} \boldsymbol{g}(\sin \boldsymbol{\theta}-\boldsymbol{\mu} \cos \boldsymbol{\theta}) \)
to \( P_{2}=m g(\sin \theta+\mu \cos \theta), \) the
frictional force f verses P graph will look
like
\( \mathbf{A} \)
3
\( c \)
\( D \)


Identify Pyridinium chlorochromate from the following.
\( A \)
0
в.
c.
O \( N^{*}-H \cdot C_{r} \circ_{2}, C l \)
D.
O \( v^{\prime}-H_{2} \cdot \operatorname{cog}_{C l} \)


Identify the odd one out:
Magnet, Solenoid, Compass needle, Oven.


The bisectors of the angles of a
parallelogram enclose a:
A. Rhombus
B. Rectangle
c. square
D. Kitt


Evaluate: \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{4} ; \mathbf{2} \boldsymbol{x}-\mathbf{5} \boldsymbol{y}=\mathbf{1} \)


The ages of ten students of a group are
given below. The ages have been recorded in years and months:
\( 8-6,9-0,8-4,9-3,7-8,8- \)
\( \mathbf{1 1}, \mathbf{8}-\mathbf{7}, \mathbf{9}-\mathbf{2}, \mathbf{7}-\mathbf{1 0}, \mathbf{8}-\mathbf{8} \)
What is the lowest age?
What is the highest age? Determine the range?


Assertion
A particle in \( x-y \) plane is related by
\( \boldsymbol{x}=\boldsymbol{a} \sin \omega \boldsymbol{t} \) and \( \boldsymbol{y}=\boldsymbol{a}(\mathbf{1}-\cos \boldsymbol{\omega} \boldsymbol{t}) \)
where \( a \) and \( \omega \) constants, then the
particle will have parabolic motion.
Reason

A particle under the influence of two perpendicular velocities has parabolic
motion.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the mean deviation about the median
of the numbers \( a, 2 a, \ldots ., 50 a \) is \( 50, \) then
\( |a| \) equals:-
A .4
B. 5
\( c \cdot 2 \)
D. 3


the number of electric field lines
emerged out of 1 C charge is
A . infinite
B. 1.13*10^11
\( c \cdot 885 \)
D. \( 1.13^{*} 10^{\wedge} 12 \)


Assertion
The electromagnetic wave is transverse
in nature.
Reason
Electromagnetic wave propagates
parallel to the direction of electric and
magnetic fields.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The liquids shown in fig. in the two arms
are mercury (specific gravity \( =\mathbf{1 3 . 6} \) )
and water. If the difference of heights of
the mercury columns is \( 2 \mathrm{cm} \), find the
height h of the water column
\( A \cdot 27 c m \)
В. \( 30 \mathrm{cm} \)
\( c .35 c m \)
D. \( 440 \mathrm{cm} \)


Writer the mechanism of acid
dehydration of ethanol to yield ethene.


A circular disc rotates in a vertical
plane about a fixed horizontal axis which passes through a point \( X \) on the circumference of disc. When the centre
of the disc moves with speed \( v \), the
speed of the opposite end of the
diameter through \( \boldsymbol{X} \) is
A \( .2 v \)
B. \( \sqrt{2} v \)
\( c \)
D. \( v / 2 \)


What are known as conventional
sources of energy?
A. The sources which have been used for quite a long time and they are getting depleted
B. The sources which have been used for quite a long time and they are not getting depleted
C. The sources which have been used recently and they are getting depleted
D. The sources which are not used from ancient time and are renewable.


Dynamo produces:
A. Charge
B. Electromotive force
C . Electric field
D. Magnetic field


n Fig 3.13
line \( D E \| \) line \( G F \) ray \( E G \) and ray \( F G \)
are bisectors of \( \angle D E F \) and \( \angle D F M \)
respectively. Prove that.
(i) \( \angle D E G=\frac{1}{2} \angle E D F \)
(ii) \( \boldsymbol{E} \boldsymbol{F}=\boldsymbol{F} \boldsymbol{G} \)


The system of equation \( 3 x-4 y=12 \) and \( 6 x \) \( 8 y=48 \)
A. 2 solution
B. 1 solution
c. infinite number of solutions
D. no solutuion


A family has two children. What is the
probability that both the children are boys given that at least one of them is a boy?


Which of the following statements is not correct about physisorption?
A . It is a reversible process.
B. It requires less heat of adsorption.
c. It requires activation energy.
D. It takes place at low temperature


The vapour pressure of a pure liquid \( \mathbf{A} \) is \( 40 \mathrm{mm} \) of \( \mathrm{Hg} \) at \( 310 \mathrm{K} \). The vapour pressure of this liquid in a solution with liquid B is 32 mm of Hg. The mole fraction of \( A \) in the solution, if it obey's Raoult's law, is?
A . 0.8
B. 0.5
\( c \cdot 0.2 \)
D. 0.4


A drunkard is walking along a straight
road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1 \( \mathrm{m} \) long and takes 1 s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit
after:
A . 21 s
B. 29 s
c. \( 31 s \)
D. 37 s


A loop carrying a current \( i \), lying in the
plane of the paper, is in the field of a
long straight wire with current \( \boldsymbol{i}_{0} \) (inward) as shown in figure. If the
torque acting on the loop is given by
\( \tau=\frac{\mu_{0} i i_{0}}{x \pi r}[\sin \theta](b-a) . \) Find \( x \)


Heat is flowing through two cylindrical rods made of same materials whose
ends are maintained at similar
temperatures. If diameters of the rods are in ratio 1: 2 and lengths in the ratio \( 2: 1, \) then the ratio of thermal current
through in steady state is:
A \( \cdot 1: 8 \)
B. 1: 4
\( c \cdot 1: 6 \)
D. 4: 1


The area of the region bounded by the parabola \( (\boldsymbol{y}-\mathbf{2})^{2}=(\boldsymbol{x}-\mathbf{1}), \) the
tangent to the parabola at the point (2,3) and the X-axis is?
\( A \cdot 3 \)
B. 6
\( c .9 \)
D. 12


Fungi differ from slime moulds in lacking
A. flagellated spores
B. zygospores
c. ascospores
D. basidiospores


Study the bar graph representing the number of persons in various age
groups in a town shown in above fig.
Observe the bar graph and answer the
following questions:
What is the total number of persons
living in the town in the age-groups 50
\( 55 ? \)


Why did Shyam refuse to accept the
items in polythene bags?


The coil of the moving coil galvanometer is wound over an aluminium frame
A. because aluminium is a good conductor
B. because aluminium is very light.
c. because aluminium is comparatively cheaper
D. to provide electro-magnetic damping.


Find the domain and range of the following real functions:
\( \boldsymbol{f}(\boldsymbol{x})=-|\boldsymbol{x}| \)


For a reaction following first-order kinetics, which of the following statements is/are correct?
A. The time taken for the completion of \( 50 \% \) of the reaction is \( t_{1 / 2} \)
B. A plot of the reciprocal of the concentration of the reactants against time gives a straight line.
c. The degree of dissociation is equal to \( 1-e^{-k t} \)
D. A plot of \( [A]_{0} /[A] \) versus time gives a straight line


Who developed the conversion between mechanical energy and heat.
A. celsius
B. Kelvin.
c. Joule.
D. Newton.
E. watt


Why is detergent better than soap in
cleaning action?


The value of \( \frac{2}{3} \times \frac{3}{\frac{5}{6} \div \frac{2}{3} \text { of } 1 \frac{1}{4}} \) is :
\( A \cdot 2 \)
B.
\( c \cdot \frac{1}{2} \)
D.


Electrolytes include which of the following types of compounds?
A. Acids
B. Bases
c. Salts
D. All of the above


Which of the following is a secondary amine?
A. Aniline
B. Diphenyl amine
c. sec. butyl amine
D. Tert. butyl amine


Which of the following is incorrect?
A. Phosphate is covalently bonded to nitrogenous base
B. Sugar is covalently bonded to nitrogenous base
C. Nitrogenous bases are hydrogen bonded to each other
D. Sugar and nitrogenous bases from peptide bonds


The IUPAC name for
\( \left[\boldsymbol{N} \boldsymbol{i}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{N} \boldsymbol{i} \boldsymbol{C l}_{4}\right] \) is :
A. Tetrachloridonickel(II)-tetraamminenickel(II)
B. Tetraamminenickel(II)-tetrachloridonickel(II)
C. Tetraamminenickel(II)-tetrachloronickelate(II)
D. Tetrachloridonickel(II)-tetraamminenickelate(II)


A ray is incident at an angle of incidence on one surface of a prism of
small angle \( A \) and emerges normally from the opposite surface. If the refractive index of the material of the
prism is \( \mu, \) the angle of incidence \( i \) is
nearly equal to :
\( A \cdot A / \mu \)
в. \( A / 2 \mu \)
c. \( \mu / A \)
D. \( \mu A \)


The solution of the equation \( |z| z=1+2 i \)
is
A \( \cdot \frac{-2}{5^{0.25}}+\frac{4}{5^{0.25}} \)
B. \( \frac{1}{5^{0.25}}+\frac{2}{5^{0.25}} \)
c. \( \frac{0.5}{5^{0.25}}-\frac{1}{5^{0.25}} \)
D. \( \frac{0.25}{5^{0.25}}-\frac{0.5}{5^{0.25}} \)


Hydrogen exhibits:
A. electropositive character
B. elctronegative character
C. Both A and B
D. None of the above


Match column I with column II and
select the correct option from the given codes.
Column I Column I I
(i) Vegetation which modifies its
A. Pioneers \( \quad \) own environment and thus causing its own replacement
B.
(ii) Replacement of existing Autogenic community by external conditions successic
c.
(iii) Establishment of organisms in Allogenic an area into which they have come by dispersal or migration
D. Ecesis
(iv) Primary colonizers
A. A-(iv), B-(i), C-(ii), D-(iii)
B. A-(i), B-(ii), C-(iii), D-(iv)
c. A-(ii), B-(i), C-(iv), D-(iii)
D. A-(i), B-(iv), C-(iii) D-(ii)


The area bounded by the curves \( x=y^{2} \)
and \( x=3-2 y^{2} \) is:


Metals react differently with water. The more vigorous is the reaction, the more
is the bubble formation. The following
diagram illustrates the reaction of sodium, magnesium and copper with
water.
What can be concluded from this
diagram?
A. Magnesium reacts more vigorously with water than sodium and copper
B. Sodium reacts more vigorously with water than magnesium and copper.
c. Sodium reacts more vigorously than copper but less vigorously than magnesium.
D. copper reacts more vigorously with water than sodium and magnesium.


Draw the structure of \( \boldsymbol{P}_{4} \boldsymbol{O}_{10} \)


What is the length of the alimentary canal in human beings? List out the
parts of the gastro-intestinal tract in the correct sequential order based on the passage of food.


The end product of the decay of \( _{90} T h^{232} \) is \( _{32} P b^{208} \). The number of cc and fa-
particles emitted are respectively
\( A \cdot 6,4 \)
B. 3,3
\( c \cdot 4,6 \)
D. 6,0


The pair of amphoteric hydroxides is:
A \( \cdot \operatorname{Be}(O H)_{2} \) and \( Z n(O H)_{2} \)
B \( \cdot \operatorname{Al}(O H)_{3} \) and \( L i O H \)
c. \( _{B}(O H)_{3} \) and \( B e(O H)_{2} \)
D. \( B e(O H)_{2} \) and \( M g(O H) \)


Which of the following is a correct way
by which we can take care of our eyes?
A. Reading the books by bringing as near as possible
B. Washing our eyes frequently
C. Using as much light as possible while studying
D. Looking directly at sun every morning


Draw the structure of the simplest
ketone.


The adjacent sides of a parallelogram \( \operatorname{are} 2 i+4 \bar{j}-5 \bar{k} \) and \( i+2 \bar{j}+3 \bar{k} \) then
the unitvector parallel to a diagonal is
A \( \cdot \frac{-i+2 j+8 k}{\sqrt{69}} \)
B. \( \frac{3 i+6 \bar{j}-2 \bar{k}}{7} \)
C. \( \frac{-i+2 \bar{j}-8 \bar{k}}{\sqrt{69}} \)
D. \( \frac{-i-2 \bar{j}+8 \bar{k}}{\sqrt{69}} \)


In deep fresh water ponds, different layers of water with different temperatures are noticed. This is known
as
A. Thermal stratification
B. Surface tension
c. water equilibrium
D. Thermal equilibrium


A light spiral spring supports a 200 g weight at its lower end. It oscillates up and down with a period of 1 sec. How much weight (gram) must be removed from the lower end to reduce the period
to 0.5 sec.?
A . 200
B. 50
\( c .53 \)
D. 100


A man throws a ball at height of \( 10 \mathrm{m} \) at
an angle of \( 35^{\circ} \) from horizontal. If mass
of ball is \( 0.5 \mathrm{kg} \) and its initial speed is \( 30 \mathrm{m} / \mathrm{s} \)
\( \boldsymbol{g}=-\mathbf{9 . 8} \frac{\boldsymbol{m}}{s^{2}} \)
How long is the ball in the air?
A . \( 2.26 s \)
B. 4.02s
\( c \cdot 1.76 s \)
D. 5.05s
E. 1.12 s


Top surface of a raised platform is in the shape of a rectangular octagon as
shown in the figure. Find the area of the
octagon surface.


ff \( y=\tan ^{-1} \frac{1}{x^{2}+x+1}+ \)
\( \tan ^{-1} \frac{1}{x^{2}+3 x+3}+ \)
\( \tan ^{-1} \frac{1}{x^{2}+5 x+7}+\ldots . \) to \( n \) terms
then
A \( \cdot \frac{d y}{d x}=\frac{1}{1+(x+n)^{2}}-\frac{1}{1+x^{2}} \)
B. \( \frac{d y}{d x}=\frac{1}{(x+n)^{2}}-\frac{1}{1+x^{2}} \)
c. \( \frac{d y}{d x}=\frac{1}{1+(x+n)^{2}}+\frac{1}{1+x^{2}} \)
D. None of these


Which of the following compounds give a ketone with grignard reagent?
A. Formaldehyde
B. Ethyl alcohol
c. Methyl cyanide
D. Methyl iodide


The velocity of any particle at maximum
height is equal to


An object is weighed at the North pole by a beam balance and a spring
balance, giving readings of \( W_{B} \) and \( W_{S} \)
respectively. It is again weighed in the same manner at the equator, giving
readings of \( W_{B}^{\prime} \) and \( W_{S}^{\prime} \) respectively. Assume that the acceleration due to
gravity is the same everywhere and that the balances are quite sensitive. This question has multiple correct options
A \( . W_{B}=W_{S} \)
В. \( W_{B}^{\prime}=W_{S}^{\prime} \)
\( \mathbf{c} \cdot W_{B}=W_{B}^{\prime} \)
D. \( W_{S}^{\prime}=W_{S} \)


A stone is dropped into a lake from a
tower 500 metre high. The sound of splash will be heard by the man approximately after:
A. 11.5 sec
B. 21 sec
c. 10 sec
D. 14 sec


An oscillator consists of a block
attached to spring \( (\mathrm{K}=1,1,400 \mathrm{l}, \mathrm{N} / \mathrm{m}), \mathrm{At} \)
some time \( t, \) the position (measured from the system's equilibrium location), velocity and acceleration of
the block are \( \boldsymbol{x}=\mathbf{0 . 1 0 0 m}, \boldsymbol{v}= \)
\( -15.0 m / s, \) and \( a=-90 m / s^{2} . \) The
amplitude of the motion and the mass of the block are :
A. \( 0.2 m, 0.84 k g \)
\( g \)
в. \( 0.3 m, 0.76 k g \)
\( \mathrm{c} .0 .4 m, 0.54 \mathrm{kg} \)
D. \( 0.5 m, 0.44 k g \)


A travelling wave is represented by the equation \( \boldsymbol{y}=20 \sin (20 \pi t-5 x) . \) The
angular frequency of the wave is
\( A \cdot 100 \mathrm{rad} / \mathrm{s} \)
B. 20 rad/s
c. \( 10 \mathrm{rad} / \mathrm{s} \)
D. 5 rad/s


The principal cation in alkaline soil is
A . Na
B. \( \kappa^{-} \)
\( c \cdot c a^{2} \)
D. Any of the above


A ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and each of these equal to 3/4th of the angle of the prism. The angle of deviation is
A . 45
B. 39
\( c \cdot 20 \)
D. \( 30^{\circ} \)


Convert each part of the ratio to
percentage:
\( \mathbf{3}: \mathbf{1} \)


Contrapositive of the statement 'If two
number are not equal, then their squares are not equal', is:


fin a binomial distribution the mean is
20, standard deviation is \( \sqrt{15}, \) then \( p= \)
A \( \cdot \frac{3}{4} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D.


If \( \boldsymbol{I}=\int_{0}^{a} \sqrt{\frac{\boldsymbol{a}-\boldsymbol{x}}{\boldsymbol{a}+\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{a}>\mathbf{0}, \) then \( \boldsymbol{I} \)
equals
A \( \cdot \frac{1}{2}\left(a-\frac{\pi}{2}\right) \)
B \( \cdot \frac{a}{2}(\pi-1) \)
c. \( \frac{1}{\sqrt{2}} a(\pi-1) \)
D. \( a\left(\frac{\pi}{2}-1\right) \)


A red coloured mixed oxide \( (X) \) on
treatment with conc. \( H N O_{3} \) gives a
compound (Y). (Y) with HCl produces a chloride compound (Z) which can also be produced by treating (X) with cone.
HCl. Compounds \( (X),(Y) \) and \( (Z) \) will be :
This question has multiple correct options
A. \( M n_{3} O_{4}, M n O_{2}, M n C l_{2} \)
в. \( P b_{3} O_{4}, P b O_{2}, P b C l_{2} \)
\( \mathrm{c} \cdot F e_{3} O_{4}, F e_{2} O_{3}, F e C l_{2} \)
D. \( F e_{3} O_{4}, F e_{2} O_{3}, F e C l_{3} \)


What is the ratio of mass for \( \alpha \) and
neutron particles?
A .1: 16
B. 16: 1
\( c \cdot 4: \)
D. 1: 4


Long-sightedness is caused by the eyeball being too short. It can be
corrected by the use of a :
A. convergent lens
B. plane mirror
c. divergent lens
D. concave mirror


The frequency of a wave is 5 Hz. Then the wave is a/an (type of wave)
A . ultrasonic wave
B. microwaves wave
c. infrasonics wave
D. radio wave


The effective capacitance between the
point \( P \) and \( Q \) of the arrangement shown in the figure is:


Solve this \( \left|\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{b}-\boldsymbol{c} & \boldsymbol{2} \boldsymbol{a} & \boldsymbol{2} \boldsymbol{a} \\ \boldsymbol{2} \boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c}-\boldsymbol{a} & \boldsymbol{2} \boldsymbol{b} \\ \boldsymbol{2} \boldsymbol{c} & \boldsymbol{2} \boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a}-\boldsymbol{b}\end{array}\right| \)


Angiosperms have dominates the land
flora, primarily because of their
A. Power of adaptability in diverse habitat
B. Property of producing large number of seeds
c. Nature of same pollination
D. Domestication by man


Dental formula for the monophyodont teeth of human is
A \( \cdot \frac{0021}{0021} \)
В. \( \frac{0003}{0003} \)
c. \( \frac{2120}{2120} \)
D. \( \frac{2102}{2102} \)


Mention any three characteristics of
Neanderthal man that lived in Near East
and Central Asia.


If a matrix is of order \( 2 \times 3 \), then the
number of elements in the matrix is
A. 5
B. 6
\( c \cdot 2 \)
D. 3


Using triangle inequality theorem check whether the given side lengths
\( \boldsymbol{a}=\mathbf{4}, \boldsymbol{b}=\mathbf{5} \) and \( \boldsymbol{c}=\mathbf{8} \) will form a
triangle or not


The density of water and ethanol at room temperature is \( 1.0 \mathrm{g} / \mathrm{mL} \) and \( 0.789 g / \) mL respectively. What volume
of ethanol contains the same number of
molecules as are present in \( 100 \mathrm{mL} \) of
water?
A. \( 307.8 \mathrm{mL} \)
B . \( 168.7 \mathrm{mL} \)
c. \( 323.9 \mathrm{mL} \)
D. \( 253.3 \mathrm{mL} \)


\( A B C D \) is a quadrilateral. Forces \( \overrightarrow{B A}, \overrightarrow{B C}, \overrightarrow{C D} \) and \( \overrightarrow{D A} \) act at a point. Their resultant is:
A \( \cdot 2 A B \)
B. \( 2 D A \)
c. zero vector
D. \( 2 \overrightarrow{B A} \)


An athlete runs for a certain distance
before taking long jump, Why?


How many different signals can be made by 5 flags from 8 flags of different
colours?


If \( \vec{A}=2 \hat{i}+7 \hat{j}+3 \hat{k} \) and \( \vec{B}=3 \hat{i}+2 \hat{j}+ \)
\( \mathbf{5} \hat{k}, \) then find the projection of \( \overrightarrow{\boldsymbol{a}} \) on \( \overrightarrow{\boldsymbol{b}} \)


The cost of a scooter depreciates every year by \( 15 \% \) of its value at beginning of
the year. If the present cost of the scooter is Rs. 8,\( 000 ; \) find its cost (in
Rs.) after 2 years.
\( A \cdot 5780 \)
B. 6690
c. 7200
D. 7530


The efficiency of any ecosystem is best depicted by pyramid of
A. Energy
B. Number
c. Biomass
D. volume


An arrangement for YDSE is shown in
figure. S is a light source then find the
position of central maxima from point 0
on screen B.
A. \( 5 \mathrm{mm} \) below
B. \( 5 \mathrm{mm} \) above 0
c. \( 30 \mathrm{mm} \) below
\( D \cdot \alpha \)


\( P \cup Q \) and \( P \cap Q \)


Neutron has a \( _{-1-} \) charge
A \( \cdot \) tve
B. -ve
c. zero
D. None of these


Find the sum of atomicity of nitrogen and phosphorous.


Three balanced coins are tossed
simultaneously. If \( X \) denotes the
number of heads, find probability
distribution of \( \boldsymbol{X} \)


Find the slope of the line passing through the following pairs:
\( (0,-\sqrt{3}) \) and (3,0)
A. \( -\frac{\sqrt{3}}{3} \)
B. \( \frac{3}{\sqrt{3}} \)
c. \( -\frac{3}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{3} \)


If \( \boldsymbol{\alpha}=\mathbf{1} / \mathbf{4} \) and \( \boldsymbol{P}_{\boldsymbol{n}} \) denotes the
perimeter of the nth square then \( \sum_{n=1}^{\infty} P_{n} \) equals
A \( \cdot \frac{8}{3}(4+\sqrt{10}) \)
B. \( \frac{8}{3} \)
\( c \cdot \frac{16}{3} \)
D. None of these


A cord is wrapped around the rim of a
flywheel \( 0.5 m \) in radius and a steady
pull of \( 50 N \) in applied on the cord as shown in the figure. The wheel is mounted on a frictionless bearing on the horizontal shaft through its centre.
The moment of inertia of the wheel is
\( 4 k g m^{2} \)
(a) Compute angular acceleration of the whee
(b) If a mass having a weight \( 50 N \) hangs from the cord as shown in the figure. Compute the angular acceleration of the wheel. Why is this not the same as in part (a)?


The EMF of a galvanic cell is determined
by using a:
A. voltmeter
B. potentiometer
c. coulometer
D. ammeter


If \( y=\log _{x^{2}+4}\left(7 x^{2}-5 x+1\right), \) then
\( \frac{d y}{d x}= \)
A \( \cdot \frac{1}{\log _{e}\left(x^{2}+4\right)}\left(\frac{14 x-5}{7 x^{2}-5 x+1}-\frac{2 x y}{x^{2}+4}\right) \)
В \( \cdot \frac{1}{\log _{e}\left(x^{2}+4\right)}\left(\frac{14 x-5}{7 x^{2}-5 x+1}+\frac{2 x y}{x^{2}+4}\right) \)
c. \( -\frac{1}{\log _{e}\left(x^{2}+4\right)}\left(\frac{14 x-5}{7 x^{2}-5 x+1}-\frac{2 x y}{x^{2}+4}\right) \)
D. None of these


Use Euclid's division algorithm to find
the \( H C F \) of 196 and 38220


Assertion
Carbon monoxide is considered a
compound but carbon and oxygen as elements.
Reason
A chemical element is a pure chemical substance consisting of a single type of atom distinguished by its atomic number, which is the number of protons in its atomic nucleus. While the
compound is composed of two or more separate elements.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A square plate of edge 'a' and a circular
disc of the same diameter are placed touching each other at the midpoint of
an edge of the plate as shown in the figure. If mass per unit area for the two
plates are same then find the distance
of the center of mass of the system from
the center of the disc.


If angle of minimum deviation of a
prism is equal to refracting angle of the prism, then refractive index \( \mu \) of
material of prism satisfies
A. \( 1<\mu<\sqrt{2} \)
в. \( 2<\mu<3 \)
c. \( \sqrt{2}<\mu<2 \)
D. \( 1<\mu<\sqrt{3} \)


The path of beam of light becomes in a colloidal solution.
A . visible
B. invisible
c. white
D. dispersed


In the equation of motion, \( \boldsymbol{S}=\boldsymbol{u} \boldsymbol{t}+ \)
\( 1 / 2 a t^{2}, \) S stands for
A. displacement in t seconds
B. maximum height reached
C. displacement in the \( t^{t h} \) second
D. none of these


At the instant when the current in an
inductor is increasing at a rate of \( \mathbf{0 . 0 6 4 0} \boldsymbol{A} / \boldsymbol{s}, \) the magnitude of the self-
induced emf is \( 0.0160 V . \) If the inductor
is a solenoid with 400 turns, what is the
average magnetic flux through each turn when the current is \( 0.720 A ? \)


is used in submarines
to see objects above the water surfaces.
A. Kaleidoscope
B. Periscope
c. мR।
D. None of the above


Which of the following is diamagnetic?
A \( \cdot H_{2}^{+} \)
в. \( O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( H_{2}^{-} \)


In \( \triangle A B C, \) if \( A D \perp B C \) and \( A D^{2}= \)
\( B D \times D C, \) prove that \( \angle B A C=90^{0} \)


Types of hardness of water is :
A. temporary and semi-permanent
B. permanent and temporary
C. permanent and partially permanent
D. none of the above


The smallest and largest numbers in
the data are 21 and 60 respectively. Find
the range of the data.


The correct IUPAC name of the following
compound is:
A. 1,1 -diformyl propanal
B. 3-formyl butanedial
C . 2-formyl butanedial
D. 1,1,2 -ethane tricarbaldehyde


Find the area of the sector of a circle
bounded by the circle \( x^{2}+y^{2}=16 \) and
the line \( y=x \) in the first quadrant.


Choose the correct answer from the
alternatives given. Thyroid-stimulating hormone (TSH) is secreted by:
A. hypothalamus
B. anterior pituitary
c. posterior pituitary
D. thyroid


Heating of ammonium dichromate produces all these compounds except:
\( A \cdot N H_{3} \)
B. \( \mathrm{H}_{2} \mathrm{O} \)
\( c \cdot N_{2} \)
D. \( \operatorname{cr}_{2} \), 3 s


\( \mathbf{5 8 0 0} \boldsymbol{A}=\mathbf{5 . 8} \times \mathbf{1 0}^{-\boldsymbol{x}} \boldsymbol{m} . \) Find the value
of \( \boldsymbol{x} \)


The same force acting on a smaller area exerts a larger pressure, and a smaller pressure on a larger area.
A. True
B. False
c. Ambiguous
D. Data insufficient


A magnet is pulled away from a conducting coil in a circuit. The direction of the induced emf in the coil
can be found from.....................
A. Faraday's law of electromagnetic induction
B. Joule's law
c. Lenz's law
D. Fleming's left hand rule


Two large vertical and parallel metal
plates having a separation of \( 1 \mathrm{cm} \) are
connected to a DC voltage source of potential difference \( X . \) A proton is
released at rest midway between the two plates. It is found to move at 45 to
the vertical JUST after release. Then X is
nearly
\( \mathbf{A} \cdot 1 \times 10^{-5} V \)
B . \( 1 \times 10^{-7} V \)
C . \( 1 \times 10^{-9} V \)
D. \( 1 \times 10^{-10} V \)


In which of the following the final image
is erect?
A. simple microscope
B. Compound microscope
C. Astronomical telescope
D. none of these


Speed of electromagnetic waves is the
same:
A. for all wavelengths
B. in all media
c. for all intensities
D. for all frequencies


In which one of the following pairs, the two items mean the same thing?
A. Malleus - anvil
B. SA node - pacemaker
c. Leucocytes - Iymphocytes
D. Haemophilia - blood cancer


What is electronegativity, and how it is related to the type of bond formed?


Solve:\( \int \frac{x}{\sqrt{4-x^{2}}} d x \)


Calculate the ratio of \( H C O O^{-} \) and \( F^{-} \)
in a mixture of \( 0.2 M \) HCOOH \( \left(K_{a}=\right. \)
\( \left.2 \times 10^{-4}\right) \) and \( 0.1 M H F\left(K_{a}=6.6 \times\right. \)
\( \left.10^{-4}\right) \)
A .1: 6.6
B. 1: 3.3
c. 2: 3.3
D. 3.3 : 2


What should be added to \( 1+2 x-3 x^{2} \)
to get \( x^{2}-x-1 ? \)


The surface tension of soap solution is \( 0.03 N / m . \) The work done in blowing to
from a soap bubble of surface area
\( 40 c m^{2},(\text { in } J), \) is
A \( \cdot 1.2 \times 10^{-4} \)
B. \( 2.4 \times 10^{-4} \)
c. \( 12 \times 10^{-4} \)
D. \( 24 \times 10^{-4} \)


NaOH cannot be stored in the vessel
made of \( Z n \) or \( A l \) or \( B e \).

Answer whether the above statement is
true or false.
A . True
B. False
c. Cannot be determined
D. None of the above


One litre of \( 2 M \) acetic acid and one litre
of \( 3 M \) ethyl alcohol were mixed. The
esterification takes place according to the reaction:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \rightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}+\boldsymbol{H}_{2} \boldsymbol{O} \)
If each solution is diluted by one litre water, the rate would become:
A. 4 times
B. 2 times
c. 0.5 times
D. 0.25 times


The horizontal distance between two
trees of different height is 60 m. the angle of depression of the top of the first
tree when seen from the top of the
second tree is \( 45^{0} . \) If the height of the
second tree is \( 80 \mathrm{m} \), find the length of
the tree


What is used as a catalyst in manufacture of sulphuric acid by
contact process?
A. \( A l_{2} O_{3} \)
в. \( K_{2} \) о
\( c \cdot V_{2} O_{5} \)
D. \( F e \)


Oxidising agent(s) is/are:
This question has multiple correct options
A. \( X e F_{2} \)
в. \( X e F_{4} \)
c. \( X e F_{6} \)
D. \( X e O F_{4} \)


An electron beam passes through a
magnetic field of \( 2 \times 10^{-3} W b / m^{2} \) and
an electric field of \( 1.0 \times 10^{4} V / m \) both
acting simultaneously. The path of electron remains undeviating. The speed of electron if the electric field is removed, and the radius of electron path will be respectively.
A \( \cdot 10 \times 10^{6} m / s, 2.43 \)
В. \( 2.5 \times 10^{6} \mathrm{m} / \mathrm{s}, 0.43 \)
c. \( 5 \times 10^{6} \mathrm{m} / \mathrm{s}, 1.43 \)
D. None of these


Which of the following pairs are
coordination isomers?
\( \mathbf{A} \)
\( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Br}\right] \mathrm{SO}_{4} \) and \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{SO}_{4}\right] \mathrm{Br} \)
B. \( \left[\mathrm{Co}(\mathrm{en})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}\right] \mathrm{Cl}_{2} \) and \( \left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}\right] \mathrm{Cl} . \mathrm{H}_{2} \mathrm{O} \)
\( \mathbf{c} \)
\( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]\left[\mathrm{Cr}(\mathrm{CN})_{6}\right] \) and \( \left[\mathrm{CO}(\mathrm{CN})_{6}\right]\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \)
\( D \)
\( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{NO}_{2}\right)\right] \mathrm{Cl}_{2} \) and \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}(\mathrm{ONO})\right] \mathrm{Cl}_{2} \)


The area bounded by the curves \( y= \) \( \sin x, y=\cos x \) and the \( y \) -axis and the
first point of intersection is:
A \( \cdot \sqrt{2} \) sq,units
B. \( \sqrt{2}-1 \) sq. units
c. \( 2+\sqrt{2} \) sq. units
D. 0 sq, units


Through what potential difference must an electron pass to have a wavelength of \( \mathbf{5 0 0} \boldsymbol{A} ? \)
A \( \cdot 6.03 \times 10^{-3} \) ev
В. \( 3.01 \times 10^{-4} \mathrm{ev} \)
\( c \cdot 6.03 \times 10^{-5} \mathrm{ev} \)
\( v \)
D. \( 3.01 \times 10^{-5} \mathrm{ev} \)


Which definition is correct and uses
only quantities rather than units?
A. Density is mass per cubic metre
B. Potential difference is energy per unit current
c. Pressure is force per unit area
D. speed is distance traveled per second


Heat can be transferred to the inside
surface of the walls of the container by
which of the above?
A. I only
B. I and II only
C. I and III only
D. II only
E. I, II, and III only


Assertion
\( P(n)=n^{2}+n+1 \) is an odd natural
number \( \forall n \in N \)
Reason
If 1 is added to an even number then it
becomes an odd number
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
c. (A)is true but (R) is false
D. (A)is false but (R) is true


\( \boldsymbol{C}_{7} \boldsymbol{H}_{8} \stackrel{3 C l_{2} / \text {heat}}{\rightarrow} \boldsymbol{A} \stackrel{\boldsymbol{F} e / B r}{\rightarrow} \boldsymbol{B} \stackrel{Z \boldsymbol{n} / H C l}{\rightarrow} \boldsymbol{C} \)
Here, the compound C is:
A. 3 -bromo 2,4,6 -trichlorotoluene
B. o-bromotoluene
c. P-bromotoluene
D. m-bromotoluene


Where should be the centre of gravity of a body?
A. It must lie within the body
B. It may be near but not essentially within the body
c. It changes its position from time to time
D. It must be outside the body


A thermodynamic system is taken through the cycle abcda, find the total heat rejected by the gas during the
process-
\( \mathbf{A} \cdot 10 J \)
B . \( 20 J \)
\( c .30 J \)
D. \( 40 J \)


If \( z_{1}, z_{2} \) are the complex numbers such
that \( \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right| \) then arg \( z_{1}- \)
\( \arg z_{2} \) is
A . \( -\pi \)
в. \( \frac{-\pi}{2} \)
\( c \cdot 0 \)
D.


A stone is dropped by a person from the top of a tower, which is \( 200 \mathrm{m} \) tall. At
the same time another stone is thrown
upwards, with a velocity of \( 50 m s^{-1} \) by
a person standing at the foot of the
tower. Find the time after which two
stones meet.
A . \( 4 s \)
B. 5 s
\( c .8 s \)
D. 10 s


\( \ln S c^{3+}, T i^{2+}, T i^{3+}, V^{2+}, \) increasing
order of spin only magnetic moment is:
A. \( S c^{3+}<T i^{2+}<T i^{3+}<V^{2+} \)
B. \( S c^{3+}<T i^{3+}<T i^{2+}<V^{2+} \)
c. \( T i^{2+}<S c^{3+}<T i^{3+}<V^{2+} \)
D. \( S c^{3+}<T i^{2+}<V^{2+}<T i^{3+} \)


Let \( [x] \) be the greatest integar function. Then the equation \( \sin x=[1+\sin x]+[1- \)
\( \cos x] \) has
A . one solution in \( \left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
B. one solution in \( \left[\frac{\pi}{2}, \pi\right] \)
c. one solution in R
D. no solution in R


Which is not a correct advantage of parallel combination in domestic
circuit?
A. Same voltage of the mains is available for all electrical appliances.
B. Switching on or off of one switch has no effect on the other
C. If one appliance stops working, other appliances keep on working
D. none


The sum of circumference and the
radius of a circle is \( 51 \mathrm{cm} \), find the radius of the circle.


A car moving with a constant acceleration covers the distance
between two points \( 180 m \) apart in \( 6 s \)
If its speed as it passes the second
point is \( 45 \mathrm{ms}^{-1}, \) its speed at the first
point is
A \( \cdot 10 m s^{-1} \)
В \( \cdot 15 \mathrm{ms}^{-1} \)
c. \( 30 m s^{-1} \)
D. \( 45 \mathrm{ms}^{-1} \)


Growing more trees helps to
A \( \cdot \) reduce \( O_{2} \) in the environment
B. increase \( C O_{2} \) in the environment
C. reduce \( C O_{2} \) only in the environment
D. reduce \( C O_{2} \) and increase \( O_{2} \) in the environment


What happens when the current
passing through the circuit is too
weak?
A. The filament does not get heated sufficiently and the bulb does not glow.
B. The filament gets heated but the bulb does not glow
c. The filament does not get heated but the bulb glows
D. The filament gets heated and the bulb glows


Find the intervals in which the following function is (a) increasing (b)
decreasing \( f(x)=x^{4}-8 x^{3}+22 x^{2}-24 x+21 \)


Which of the following is a coloured
compound?
A. Nitrogen dioxide
B. Nitrous oxide
c. Nitric oxide
D. Ammonia


Which of the following molecules has two lone pairs and bond angle (need not
be all bond angles) \( <109.5^{\circ} ? \)
\( \mathbf{A} \cdot S F_{2} \)
в. \( K r F_{4} \)
\( \mathbf{c} \cdot I O I_{4}^{-} \)
D. All of the above


Keeping the banking angle same to increase the maximum speed with
which a vehicle can travel on the curved
road by \( 10 \%, \) the radius of curvature of the road has to be changed from \( 20 m \)
to-
A. \( 16 m \)
в. 18 т
c. \( 24.2 m \)
D. 30.5 \( m \)


\( \int e^{x}\left(\frac{x^{4}+x^{2}+1}{x^{2}+x+1}\right) d x= \)
A \( \cdot e^{x}\left(x^{4}+x^{2}+1\right)+c \)
B \( \cdot e^{x}\left(x^{2}+x+1\right)+c \)
c. \( e^{x}\left(x^{2}-3 x+4\right)+c \)
D. \( e^{x}\left(x^{2}-4 x+5\right)+c \)


Very short answer type. Name the monomer(s) of the following dimers/polymers starch


Metallic lustre exhibited by sodium is
due to:
A. diffusion of sodium ion
B. oscillation of loose electron
c. escalation of free protons
D. existence of lattice structure


The radio nuclide \( ^{11} \boldsymbol{C} \) decays according
to
\( _{6}^{11} C \rightarrow_{5}^{11} B+e^{+}+\nu: T_{1 / 2}= \)
20.3 min
The maximum energy of the emitted positron is \( 0.960 \mathrm{MeV} \)
Given the mass values:
\( \boldsymbol{m}\left(_{6}^{11} \boldsymbol{C}\right)=\mathbf{1 1 . 0 1 1 4 3 4} \boldsymbol{u} \) and
\( \boldsymbol{m}\left(_{6}^{11} \boldsymbol{B}\right)=\mathbf{1 1 . 0 0 9 3 0 5} \boldsymbol{u} \)
Calculate \( Q \) and compare it with the
maximum energy of the positron emitted.


The area bounded by the curve \( y=e^{x} \)
and the lines \( y=|x-1|, x=2 \) is given
by:
\( \mathbf{A} \cdot e^{2}+1 \)
B \( \cdot e^{2}-1 \)
c. \( e^{2}-2 \)
D. \( e-2 \)


Give two ways in which we can all helps to reduce global warming. Write a catchy slogan to create awareness about it.


An element has six electrons in its
outermost shell, then its valency can be
\( A \cdot 6 \)
B. 2
\( c \cdot 4 \)
D. All of the above


The ratio of lowering of vapour pressure of \( 0.1 ~ M \) aqueous solutions of \( K C l \)
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \& \boldsymbol{N a}_{2} \boldsymbol{S O}_{4} \) is:
A. 1: 2: 3
B. 2: 2: 3
\( \mathrm{c} \cdot 1: 1: 1 \)
D. 3: 2: 1


What is half life period of a reaction?
Calculate the half life period of a first
order reaction?


The principal quantum number and
azimuthal quantum number values for the differentiating electron of 'd' block
elements are and


Select the correct option: \( \ln (\mathrm{i}) \)
protoxylem lies towards periphery and metaxylem lies towards centre. Such an
arrangement of primary xylem is called \( \operatorname{as}(i i) \)
(i) 1 (ii)
stems ems endrach
exarch stems \( \mathrm{h} \)
roots endrach \( \mathrm{ch} \)
roots exarch A
A. A-stems,B-endrach
B. A-stems, B-exarch
C. A-roots, B-endrach
D. A-roots, B-exarch


What is the length of the other sides of
the rectangle as shown in the figure, if
side \( A B=10 \) and \( B C=7 ? \)
\( A \cdot C D=10 \) and \( A D=5 \)
B. \( C D=10 \) and \( A D=7 \)
\( c \cdot C D=7 \) and \( A D=7 \)
D. \( C D=7 \) and \( A D=10 \)
0


The initial pressure inside the flask is:
A. near zero (vacuum)
В. 27 тт Н\( g \)
c. 760 mm \( H g \)
D. \( (760-27) \) mm \( H g \)


Carbonic anhydrase is found in
A. wвс
в. RВС
c. Blood plasma
D. All of the above


The heat of combustion of \( C, S \) and \( C S_{2} \)
are \( -393.3 \mathrm{kJ},-293.7 \mathrm{kJ} \) and \( -1108.76 \mathrm{kJ} \)
What will be the heat of formation of
\( \boldsymbol{C} \boldsymbol{S}_{2} ? \)
A . -128.02 kJ
в. +970 kJ
c. \( +1108.7 k J \)
D . +12 kJ


Which of the following families have the largest geographical distribution?
A. Malvaceae
B. Leguminosae
c. solanaceae
D. compositae


A priest of temple collected dried garlands. holy old books and some statues. He asked his son to throw in
the river. But instead of throwing. he buried them in the soil.
a. In the situation above who wins your
support: the priest or the sonJustify your answer by giving two reasons.
b. What are the values reflected in the
behaviour of son?


Solve:
\( \lim _{x \rightarrow 0} \frac{\sqrt[3]{1+x}-\sqrt[3]{1-x}}{x} \)


The density of 3 M solution of NaCl is 1.2 \( \mathrm{g} m L^{-1} . \) The molality of the solution is?
A. 2.79 \( \mathrm{m} \)
B. 1.79 \( m \)
c. \( 3.5 \mathrm{m} \)
D. 5.58 m


Which of them decomposes \( S O_{3} \) to \( S O_{2} \)
?
A \( . S O C l_{2} \)
в. \( S C l \)
c. \( S C l_{2} \)
D. \( N a O H \)


When \( S O_{2} \) gas is passed into aqueous
\( N a_{2} C O_{3} \) the product(s) formed is (are):
A \( . \) NaHSO \( _{4} \)
B. \( N a_{2} S O_{4} \)
\( \mathbf{c} \cdot \operatorname{NaH} S O_{3} \)
D. \( N a_{2} S O_{3} \) and \( N a H S O_{3} \)
E. \( N a H S O_{4} \) and \( N a_{2} S O_{4} \)


If pressure at the half depth of a lake is equal to \( \frac{3}{4} \) times the pressure at its
bottom, then find the depth of the lake.
[Take \( \left.g=10 m / s^{2}\right] \)
A. \( \frac{P_{0}}{\rho g} \)
в. \( \frac{2 P_{0}}{\rho g} \)
c. \( \frac{P_{0}}{2 \rho g g} \)
D. \( \frac{3 P_{0}}{\rho g} \)


Identical metal plates are located in air at equal distance \( d \) from one another
The area of each plate is equal to \( A \). If
the capacitance of the system between \( P \) and \( Q \) if the plates are interconnected
as shown in the figure is given as \( \frac{x}{2} \varepsilon_{0} \frac{A}{d} \) Find \( x: \)


On heating with bleaching powder, ethyl alcohol is converted into:
A. \( C H_{3} \) СООН
в. \( C H_{3} C H O \)
c. \( C H_{3} C O C H_{3} \)
D. \( C H C l_{3} \)


The functional group in methanol and methanal respectively are :
\( A \cdot-0 H,-C H O \)
в. -сно, -ОН
c. -он,-соон
D. -сно, -соон


The incorrect configuration is:
A. \( K=[A r] 4 s^{1} \)
B. \( C r=[A r] 3 d^{5}, 4 s^{1} \)
c. \( C r=[A r] 3 d^{4}, 4 s^{2} \)
D. \( C u=[A r] 3 d^{10}, 4 s^{1} \)


Which of the following solution has the highest boiling point?
A. \( 1 \% \) glucose
B . \( 1 \% \) NaCl
c. \( 1 \% \) sucrose
D. \( 1 \% \) CaCl\( _{2} \),


Saline hydrides:
A. are dehydrating agents
B. are formed by transition metals
C . are very poor reducing agents
D. are stable towards water and alcohol


Focal length of eye lens is changes by
A. Pupil
B. Iriss
c. cornea
D. Ciliary body


One litre of a sample of hard water \( (d=1 \)
\( g / m L \) contains 136 mg of \( C a S O_{4} \) and
\( 190 \mathrm{mg} \) of \( M g C l_{2} . \) What is the total
hardness of water in terms of \( C a C O_{3} ? \)
A. 100 ppm
B. 200 ppm
c. 300 ppm
D. None of the above


How many times more acidic will be the
aqueous solution having 2 pH compared to that having 4 pH.


The boiling point of phenols are higher than the hydrocarbons of comparable
masses due to:
A. more polarising power
B. presence of hydrogen bonding
c. resonance stabilisation
D. acidic character


State de Broglie hypothesis.


Prove that "In a trapezium, the line
joining the mid points of non-parallel
sides is
(i) parallel to the parallel sides and
(ii) Half of the sum of the parallel sides"


Assertion
Certain drugs are called enzyme inhibitors
Reason
Drugs block the binding site of the
enzyme and prevent the binding of
Substrate.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


The depressions in freezing point for \( 1 \mathrm{m} \) urea, \( 1 \mathrm{m} \) glucose and \( 1 \mathrm{m} \) NaCl are in
the ratio:
A .1: 2: 3
B. 3:2:2
c. 1: 1: 2
D. None of these


Which component of the cooked food should not be disposed off into the
drain?
A. Dry vegetables
B. Oil/ghee
c. Supernatent liquid
D. None of the above


Among the ones given below, the salt which dissolves in water upon
hydrolysis is:
A. Nacı
в. \( N H_{4} C l \)
c. кс।
D. \( N a_{2} S O_{4} \)


The main reason for larger number of
oxidation states exhibited by the
actinoids than the corresponding
lanthanoids, is:
A. the lesser energy difference between \( 5 f \) and \( 6 d \) orbitals than between \( 4 f \) and \( 5 d \) orbitals
B. more energy difference between 5 fand 6 d orbitals than between \( 4 f \) and \( 5 d \) orbitals
C . greater reactive nature of the actinoids than the lanthanoids
D. larger atomic size of actinoids than the lanthanoids


Find the area of a quadrant of a circle whose circumference is \( 44 \mathrm{cm} \)


A balloon is rising vertically with a velocity of \( 9.8 m / s . \) A packet is dropped
from it when it is at a height of \( 39.2 \mathrm{m} \) Time taken by the packet to reach the ground is (Given \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \) )
A . \( 1 s \)
B . \( 2 s \)
\( c \cdot 3 s \)
D. \( 4 s \)


\( 50 \mathrm{ml} \) of \( 2 \mathrm{N} \) acetic acid mixed with 10
\( \mathrm{ml} \) of \( 1 \mathrm{N} \) sodium acetate solution will
have an approximate \( \boldsymbol{p} \boldsymbol{H}\left(\boldsymbol{K}_{a}=\mathbf{1 0}^{-5}\right) \)
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
\( D \)


Initially the reactions in the containers a and b are at equilibrium when the products and reactants are put together in a container \( c \) than at the equilibrium the total number of different chemical
compounds are?
A. 5
B. 7
\( c \cdot 6 \)
\( D \)


An integrating factor of the differential
equation \( x d y-y d x+x^{2} e^{x} d x=0 \) is
A \( \cdot \frac{1}{x} \)
B. \( \log \sqrt{1+x^{2}} \)
c. \( \sqrt{1+x^{2}} \)
D.
E \( \frac{1}{1+x^{2}} \)


The stress strain curve for two metals \( A \)
and \( \mathrm{B} \) are as shown in the figure. then
A. A is ductile while B is brittle
B. A is brittle while B is ductile
c. Both \( A \) and \( B \) are ductile
D. Both A and B are brittle


The reactance of a circuit is zero. It is
possible that the circuit contains This question has multiple correct options
A. an inductor and a capacitor
B. an inductor but no capacitor
c. a capacitor but no inductor
D. neither an inductor nor a capacitor


An ebonite rod held in hand can be
charged by rubbing with flannel but a copper rod cannot be charged like this. Why?


A body moves through a distance of 'm' in the following different ways, the work done is minimum when the body is :
A. pushed over an inclined plane
B. lifted vertically upward
c. pushed over smooth rollers
D. pushed over a wedge


Solve the following linear equations. \( \boldsymbol{x}-\boldsymbol{y}=\mathbf{3} ; \mathbf{4} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{0} \)


You throw a ball which a launch velocity of \( \overrightarrow{\boldsymbol{v}}=(\mathbf{3} \hat{\boldsymbol{i}}+\mathbf{4} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} \) the maximum
height attaind by the body is?
A. \( 0.8 m \)
в. \( 0.2 m \)
\( \mathrm{c} .2 .3 \mathrm{m} \)
D. \( 5.3 \mathrm{m} \)


toppr )
Q Type your question
the rigure. the alstance \( \boldsymbol{a} \) Is \( \mathbf{U} . \mathbf{I} \boldsymbol{Z} \mathbf{U} \boldsymbol{m} \)
When the two charges are at the
locations as shown in the figure, what
are the magnitude and direction of the
net magnetic field they produce at point
\( \boldsymbol{P ?} \)
(Take \( \boldsymbol{v}=\mathbf{4 . 5 0} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m} \boldsymbol{s}^{-1} \) and \( \boldsymbol{v}^{\prime}= \)
\( \left.9.00 \times 10^{6} m s^{-1}\right) \)
A \( .4 .38 \times 10^{-4} T, \) into the page
B. \( 4.38 \times 10^{-4} T \), out of the page
\( c: \quad 10^{-4} T, \) into the page
D. \( 2.9 \times 10^{-9} T, \) out of the page


Draw the Lewis dot structure of \( S N F_{3} \)
consistent with \( V \) SEPR.


A charged particle begins to move from the origin in a region which has a
uniform magnetic field in the \( x- \)
direction and a uniform electric field in
the \( y- \) direction. Its speed is \( v \) when it
reaches the point \( (x, y, z) . \) Then, \( v \) will
depend
A. only on \( x \)
B. only on \( y \)
c. on both \( x \) and \( y \), but not \( z \)
D. on \( x, y \) and \( z \)


The matrix of hyaline cartilage contains
A. Collagen
B. Chondroitin sulfate
c. ossein
D. Both A and B


Prevention of pregnancy is called
A. Contraception
B. conception
C. Abortion
D. Sterilization


The total number of structural isomers
possible for an amine with molecular
formula \( \boldsymbol{C}_{\mathbf{4}} \boldsymbol{H}_{\mathbf{1 1}} \boldsymbol{N} \) is :
A. 5
B. 6
\( c \cdot 7 \)
D. 8


Which is not a method of genetic recombination in bacteria?
A. Transformation
B. Transduction
c. Translation
D. conjugation


In aqueous solution of Urea is \( 20 \% \) by mass of solution. molarity of the solution when the density of the solution is 1.2 gram per ml is
\( A \cdot 4 M \)
B. 3.5 M
\( c \cdot 5 M \)
D. none of these


The most significant end point of polycyclic aromatic hydrocarbon is :
A. cancer
B. fever
c. tubercolosis
D. jaundice


The band structure determines the
behaviour of a solid
A. chemical
B. electrical
c. mechanical
D. molecular


A parallelogram has diagonals expressed as \( \vec{A}=5 \hat{i}-4 \hat{j}+3 \hat{k} \) and \( \vec{B}=3 \hat{i}+2 \hat{j}-\hat{k} \)
Area of parallelogram is:
A. \( \sqrt{117} \) units
B. \( \sqrt{171} \) units
c. \( \sqrt{711} \) units
D. \( \sqrt{107} \) units


As shown in the figure \( \boldsymbol{A C}= \)
\( \boldsymbol{C D}, \angle \boldsymbol{C A B}-\angle \boldsymbol{A B C}=\mathbf{3 0}^{\circ} . \) Then
\( \angle B A D \) has a measure of:
A \( \cdot 15^{\circ} \)
B. 30
\( c \cdot 20 \)
\( \left(22 \frac{1}{2}\right)^{\circ} \)


Who confirmed communities with more
species tend to be more stable than those with less species?
A. Alexander von Humboldt
B. David Tilman
c. Paul Ehrlich
D. Edward Wilson


Define principal axis of a lens.


Find the derivative of \( \left(x^{2}+\cos x\right) \)
\( \mathbf{A} \cdot 2 x+\sin x \)
B. \( 2 x^{2}+\sin x \)
\( \mathbf{c} \cdot 2 x-\sin x \)
D. \( 2 x-\cos x \)


Area bounded by the curves \( y=x^{2} \) and
\( y=2-x^{2} \) is
A \( \cdot \frac{8}{3} \) sq. units
B. \( \frac{3}{8} \) sq. units
c. \( _{-5 \text {funits }}^{\text {s }} \)
D. None of these


In two construction companies \( A \) and \( B \)
the average weekly wages in rupees and the standard deviations are as
follows:
\( \begin{array}{lll}\text { Company } & \begin{array}{l}\text { Average of } \\ \text { wages }(\text { in } \mathrm{Rs})\end{array} & \begin{array}{l}\text { S.D of wages } \\ \text { in }(\mathrm{Rs})\end{array} \\ A & 3450 & 6.21 \\ B & 2850 & 4.56\end{array} \)
Determine which factory has greater variability in individual wages?


The volume of a sphere is \( 38808 \mathrm{cm}^{3} \)
Find its radius and surface area.


Which of the following statement is correct with respect to the property of elements in carbon family? With an increase in their atomic
number their:
A. atomic size decreases
B. ionization energy increases
c. metallic character decreases
D. stability of +2 oxidation state increases


If the equilibrium constant for the
reaction \( 2 X Y \rightleftharpoons X_{2}+Y_{2} \) is 81
what is the value of equilibrium constant for the reaction?
\( \boldsymbol{X} \boldsymbol{Y} \rightleftharpoons \frac{1}{2} \boldsymbol{X}_{2}+\frac{1}{2} \boldsymbol{Y}_{2} \)
\( \mathbf{A} \cdot 81 \)
B. 9
\( c .6561 \)
D. 40.5


Which of the following metal can be reduced by carbon reduction as well as
self reduction?
\( A \cdot F e \)
B. Al
\( c \cdot P b \)
D. None of these


If the coefficient of \( (2 r+4)^{t h} \) term and
\( (r-2)^{t h} \) term in the expansion of \( (1+ \)
\( x)^{18} \) are equal then \( r \)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 4
\( c .6 \)
D. 3


An urn contains 5 red and 5 black balls
A ball is drawn at random, its colour is noted and is returned to the urn.
Moreover, 2 additional balls of the
colour drawn are put in the urn and then a ball is drawn at random. What is the
probability that the second ball is red?


Product of photorespiration is
A. Phosphoglycerate
B. Erythrose 4-phosphate
c. Dihydroxy acetone 3-phosphate
D. All of the above


Animal fibres are made of :
A. cellulose
B. protein
c. fats
D. animal cells


Find the value of: \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{x}^{2} & \boldsymbol{y}^{2} & \boldsymbol{z}^{2} \\ \boldsymbol{x}^{3} & \boldsymbol{y}^{3} & \boldsymbol{z}^{3}\end{array}\right| \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( (x-y)(y-z)(z-x)(x y+y z+z x) \)
C. \( (x+y x+z x)(x+y)(y+z)(z+x) \)
D. \( (x+y+z) \)


Non-cyclic photophosphorylation
involves
A. PS-I and PS-II
B. PS-I only
c. PS-II only
D. Stroma matrix


Eutrophication leads to death of fish
due to
A. Increased \( O_{2} \) concentration
B. Decreased \( O_{2} \) concentration
c. Increased algal contents
D. Decreased algal contents


Which of the following is an electrica conductor?
A. Silver
B. Rubber Cork
c. Silver-coloured plastic sheet
D. woodd


Butene when treated with chlorine at
about \( 500^{\circ} \mathrm{C} \) forms:
A \( \cdot \) МесН \( _{2} \) СНС। \( -\mathrm{cH}_{2} \mathrm{c} \)
B. Месн(С)-СН=СН \( _{2} \)
\( \mathrm{c} \cdot \mathrm{CICH}_{2} \mathrm{CH}_{2} \mathrm{CH}=\mathrm{CH}_{2} \)
D. \( \operatorname{Me} \mathrm{C}\left(\mathrm{Cl}_{2}\right) \mathrm{CH}=\mathrm{CH}_{2} \)


\( \lim _{\boldsymbol{y} \rightarrow 0} \frac{\sqrt{1+\sqrt{1+\boldsymbol{y}^{4}}}-\sqrt{\mathbf{2}}}{\boldsymbol{y}^{4}} \)
A \( \cdot \) Exists and equals \( \frac{1}{4 \sqrt{2}} \)
B. Does not exist
C - Exist and equals \( \frac{1}{2 \sqrt{2}} \)
D. Exists and equals \( \frac{1}{2 \sqrt{2}(\sqrt{2}+1)} \)


Solution of the different equation,
\( y d x-x d y+x y^{2} d x=0 \) can be
A \( \cdot 2 x+x^{2} y=\lambda y \)
в. \( 2 y+y^{2} x=\lambda y \)
c. \( 2 y-y^{2} x=\lambda y \)
D. none of these


Deepest algae in sea are
A. Red algae
B. Brown algae
c. Green algae
D. Golden algae


A ring of diameter dis rotated in a uniform electric field until be position of maximum electric flux is found. The
flux is found to be \( \phi \). If the electric field
strength is \( \boldsymbol{E}=\frac{\boldsymbol{X} \boldsymbol{\phi}}{\pi d^{2}} . \) Find out \( \boldsymbol{X} \) ?


The number of sides of two regular
polygons \( A \) and \( B \) are in the ratio 1: 3.1
each interior angle of polygon \( \mathrm{B} \) is \( 168^{\circ} \) find each interior angle of polygon \( \boldsymbol{A} \)
A \( .144^{\circ} \)
B. 124
\( c \cdot 134^{\circ} \)
D. none of the above


The mean momentum of a nucleon in a
nucleus with mass number \( A \) varies as
\( \mathbf{A} \cdot A^{3} \)
B. \( A^{2} \)
\( c \cdot \frac{2}{3} \)
D.
E \( \cdot \frac{1}{3} \)


During the discharge of a lead storage
battery, the density of sulphuric acid
fell from 1.294 to \( 1.139 g m l^{-1} \)
Sulphuric acid of density \( 1.294 g m l^{-1} \)
is \( 39 \% \) by weight and that of density \( 1.139 g m l^{-1} \) is \( 20 \% \) by weight. The battery holds 3.5 L of the acid and the volume remained practically constant during the discharge. Find the number of ampere-hours for which the battery must has been used.

The charging and discharging reactions are as follows:
\( P b+S O_{4}^{2-} \rightarrow P b S O_{4}+2 e^{-}(\text {charging }) \)
\( P b O_{2}+4 H^{\oplus}+S O_{4}^{2-}+2 e^{-} \rightarrow P b S O_{4}+ \)
\( 2 H_{2} O(\text { discharging }) \)


Which liquid oxide of nitrogen is blue?
A. Nitrous oxide
B. Dinitrogen trioxide
c. Nitrogen dioxide
D. Nitrogen pentaoxide


A balloon filled with methane \( C H_{4} \) is
pricked with a sharp point and quickly plunged into a tank of hydrogen at the same pressure. After sometime the balloon will have?
A. Enlarged
B. collapsed
c. Remained unchanged in size
D. Ethylene \( \left(C_{2} H_{4}\right) \) inside it


A problem in statistics is given to solve to three students independently. Their
chances of solving problem are \( \frac{1}{3}, \frac{1}{4}, \frac{1}{5} \) respectively. Find the probability that the problem is solved


A Cylindrical vassel of volume \( 25 \frac{1}{7} \) cubic metres, which is open at the top
is to be manufactured from a sheet of
metal. Find the dimensions of the vessel
so that the amount of sheet used in
manufacturing it is the least possible.
\( \mathbf{A} \cdot r=h=2 \)
В. \( r=1, h=8 \)
c. \( r=2 \sqrt{2}, h=1 \)
D. \( r=2, h=1 \)


LEDs have the following advantages over conventional incandescent low
power lamps:
A. Long life and ruggedness
B. Low operational voltage and less power
c. Fast on-off switching capability,
D. All of the above


Which of the following IUPAC names is
not correctly matched?
\( A \)
cì
B . \( \left(C H_{3}\right)_{2} C=C H C O O H: 3 \) - Methylbut- 2 -enoic acid
c. \( P h C H_{2} C H_{2} C O O H: \) 3-Phenylpropanoic acid
\( D \)
Trinitr


Analyze the Photoelectron Spectra.
What is the identity of the element?
\( A \cdot H \)
в. \( H e \)
\( c \cdot L i \)
D. \( B e \)


Which objects use the reflection of light?
This question has multiple correct options
A. sun glasses
B. Periscope
c. Mirror
D. side mirror of a car


The radius of a sphere is \( 2 r, \) then find its
volume


Assertion
When small amount of an acid or base
is added to pure water its pH undergoes a change.
Reason
Addition of an acid or a base increases
the degree of ionisation of water.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A circular flower bed is surmounted by
a path \( 5 \mathrm{m} \) wide as shown in fig.The
diameter of the flowerbed is \( 60 \mathrm{m} \). What
is the area of this path?
\( \mathbf{A} \cdot 735 \pi c m^{2} \)
В. \( 325 \pi c m^{2} \)
\( \mathbf{c} \cdot 635 \pi c m^{2} \)
D. None of these


Assertion
Prickles of last have a single role of
protection of plant
Reason
They are superficial in origin.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Three long straight wires \( A, B \) and \( C \) are carrying currents as shown in figure.
Then the resultant force on B is directed
A. perpendicular to the plane of the paper and outward
B. perpendicular to the plane of the paper and inward
c. towards \( A \)
D. towards


The depression in freezing point for \( 1 \mathrm{M} \) urea, 1 M glucose and 1 M \( N a C l \) are in
the ratio:
A. 1: 2: 3
B. 3: 2: 2
\( \mathrm{c} \cdot 1: 1: 2 \)
D. 2: 3: 2


Write a value of
\( \int \sqrt{x^{2}-9} d x \)


are drawn on light rays to show the direction in which light travels.
A. RAYS
B. ARROWS
c. LINES
D. LINE SEGMENTS


In the quadrilateral (3) given below,
\( A B|| D C, E \) and \( F \) are mid point of of
non-parallel sides \( A D \) and \( B C \) respectively. Calculate \( \boldsymbol{E F} \) if \( \boldsymbol{A B}=\boldsymbol{6 c m} \) and \( \boldsymbol{D C}=\boldsymbol{4 c m} \)


Let the image of the point \( \boldsymbol{P}(\mathbf{1}, \mathbf{0}, \mathbf{0}) \) in
the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}+\mathbf{1}}{-\mathbf{3}}=\frac{\boldsymbol{z}+\mathbf{1 0}}{\mathbf{8}} \) be \( \boldsymbol{R} \)
\( (x, y,-z) . \) Find \( x+y+z ? \)


Find the ratio in which the \( y \) -axis
divides the line segment joining the points \( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{4}) \) and \( \boldsymbol{B}(-\boldsymbol{2}, \mathbf{1}) . \) Also, find
the point of intersection.
A \( \cdot 3: 2,\left(0, \frac{11}{5}\right) \)
в. \( _{1: 2,\left(0, \frac{13}{5}\right)} \)
c. \( _{1: 2,\left(0, \frac{3}{5}\right)} \)
D. \( 3: 4,\left(0, \frac{13}{5}\right) \)


The mass of body is \( 10 \mathrm{kg} \) at a place
where \( g=9.8 m / s^{2} . \) Find its weight.


Which of the following statements
about the transmission of the nerve
impulse is incorrect?
A. Nerve impulse travels from dendritic end towards axonal end.
B. At the dendritic end, electrical impulses bring about the release of some chemicals which generate an electrical impulse at the axonal end of another neuron.
C. The chemicals released from the axonal end of one
neuron cross the synapse and generate a similar electrical impulse in a dendrite of another neuron.
D. A neuron transmits electrical impulses not only to another neuron but also to muscle and gland cells.


Which of the following methods can be
used to prepare propanoic acid?
\( \mathbf{A} \)
B.
\( \mathrm{CH}_{2}=\mathrm{CH}_{2}+\mathrm{CO}+\underset{(\text { Steam })}{\mathrm{H}_{2} \mathrm{O}}-\frac{\text { High pressure }}{570-670 \mathrm{K}} \)
C. Reaction of \( E t M g B r \) with dry ice followed by the acidification with diL \( H C l \)
D. Sodium ethoxide is heated with \( C O \) under pressure followed by the acidification with dil, \( H C l \)


The light ray which comes out from the surface after reflection is called:
A. incident ray
B. reflected ray
c. normal ray
D. emergent ray


Which gas law relates the volume of a gas to the number of molecules of the
gas?
A. Gay-Lussac's Law
B. Avogadro's Law
c. Boyle's Law
D. charle's Law


An ellipse having foci at (3,1) and
(1,1) passes through the point (1,3)
Its eccentricity is:
A \( \cdot \sqrt{2}-1 \)
B. \( \sqrt{3}-1 \)
c. \( \frac{1}{2}(\sqrt{2}-1) \)
D. \( \frac{1}{2}(\sqrt{3}-1) \)


In the given figure, \( P A \) and \( P B \) are two
tangents drawn from an external point
\( P \) to a circle with centre \( O \). Prove that
OP is the right bisector of line segment
\( A B \)


When environmental change occurs, multiple new niches become available Organisms in this changing environment will undergo rapid change to fill these new niches.
This process is known as
A. Diversifying selection
B. Allopatric speciation
c. Adaptive radiation
D. Directional selection
E. Convergent evolution


Which of the following order for bond angles is correct?
A. \( B F_{3}<N F_{3}<C l F_{3}<P F_{3} \)
B. \( B F_{3}<N F_{3}<P F_{3}<C l F_{3} \)
c. \( C l F_{3}<P F_{3}<N F_{3}<B F_{3} \)
D. \( B F_{3} \approx N F_{3}<P F_{3}<C l F_{3} \)


\( \frac{d}{d x}\left\{\cos ^{-1} x+\sin ^{-1} \sqrt{1-x^{2}}\right\}= \)
A .
B.
c. \( \frac{2}{\sqrt{1-x^{2}}} \)
D. \( \frac{-2}{\sqrt{1-x^{2}}} \)


In pair annihilation the least number of
\( \gamma \) - ray photons produced is :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Why are sacred groves highly protected?


Real gases do not react as expected :
A. noble gas
B. inert gas
c. ideal gas
D. non-ideal gas


Q Type your question
velocity \( v \) out of a region of uniform
magnetic field whose magnitude is \( \boldsymbol{B} \)
The plane of loop and the velocity are both perpendicular to \( \vec{B} \). Then the electrical power in the circular loop at the instant when the arc (of circular
loop) outside the region of magnetic field subtends an angle \( \frac{\pi}{3} \) at centre of
the loop is
\( ^{\mathrm{A}} \cdot \frac{B^{2} a^{2} v^{2}}{R} \)
B. \( \frac{2 B^{2} a^{2} v^{2}}{R} \)
c. \( \frac{B^{2} a^{2} v^{2}}{2 R} \)
D. None of thes


Catalytic poisoners act by:
A. coagulating the catalyst
B. getting adsorbed on the active centres on the surface of catalyst
C. chemical combination with any one of the reactants
D. none of the above