Solution
Solution
5401CMD303031250002 MD
PHYSICS
2) Bottom end of a ladder leaning against a wall is 3 m away from the foot of the wall as shown in
(1) 8m
(2) 5m
(3) 4m
(4) 6m
3)
(1) 30°
(2) 135°
(3) 60°
(4) 120°
(1) x = 3
(2)
(3)
(4) x = 2
(1) 10
(2) 13
(3) 6
(4) 3
(1) –18
(2) 3
(3) –3
(4) 18
9) =
(4)
sin (5x – 3) + c
10)
If m indicate slope of a straight line then for the given lines A and B the value of is equal to :
(1)
(2) 3
(3)
(4)
11)
(3)
loge (4t + 3) + c
(4)
–
(1)
(2)
(3)
(4)
(1) 170
(2) 150
(3) 200
(4) 120
(1)
(2)
(3)
(4)
17) =
(1)
(2)
+C
(3)
+C
(4)
+C
Statement-I: if y is minimum
Statement-II: If is maximum
(1)
(2)
(3)
20) =?
(1)
(2)
(3)
(4)
Column I Column II
A. P.
B. Q.
C. R.
D. S. –e–x + C
23) Given figures show regular hexagon, the charges are placed at the vertices. In which of the
(1) IV
(2) III
(3) I
(4) II
24) Two objects are rubbed against each other, the nature of electric force, when they are placed at
some distance is :
(1) Attractive
(2) Repulsive
(3) Both (1) and (2)
(4) Either (1) or (2)
25) Three point charges 4q, Q and q are placed in a straight line of length l at points
O, and along x-axis respectively. The net force on charge q is zero. The value of Q is :-
(1)
(2) –q
(3) –2q
(4) –4q
26) Two charges are 10 mC and 20 mC placed at a distance 1m apart . Find the ratio of magnitudes
of electric force acting on each other is :
(1) 2 : 5
(2) 5 : 2
(3) 1 : 1
(4) 10 : 20
27) A point charge q is situated at a distance d from one end of a thin non - conducting rod of length
L having a charge Q(uniformly distributed along its length) as shown in fig. Then the magnitude of
(1)
(2)
(3)
(4)
28)
Two point charges +3µC and +8µC repel each other with a force of 40 N. If a charge of -5µC is a
added to each of them, then the force between them will become
(1) -10 N
(2) + 10 N
(3) + 20 N
(4) - 20 N
29) A charged particle of mass 2 mili gram remains freely in air in an electric field of strength 4 N/C
directed upward. Calculate the charge and determine its nature (g = 10 m/s2).
(1) 5 × 10–6 C
(2) 6 × 10–6 C
(3) 4 × 10–6 C
(4) 3 × 10–6 C
30) Two charges are placed as shown in figure. Where should be a third charge be placed so that it
(1) 30 cm from 9 e
(2) 40 cm from 16 e
(3) 40 cm from 9 e
(4) (1) or (2)
31) Three charges each of magnitude 'q' are placed at the corners of an equilateral triangle, the
electrostatic force on the charge 'q' placed at the center is (each side of triangle is ℓ) :-
(1) Zero
(2)
(3)
(4)
32) Consider the following suspended charged ball system. If α > β then at eqilibrium which of the
33) Two metal spheres of same mass are suspended from a common point by a light insulating
string. The length of each string is same. The spheres are given electric charges +q on one end and
+4q on the other. Which of the following diagrams best show the resulting positions of spheres ?
(1)
(2)
(3)
(4)
34) Net electric field at centre of uniform pentagon as shown. If Q is a +ve charge.
(1)
upward
(2)
downward
(3) Zero
(4) None
35) Two charges 4q and q are placed at 30 cm apart from each other. Electric field intensity will be
zero.
36) Two charges +5µC and +10µC are placed 20 cm apart. The net electric field at the mid-point
between the two charges is.
37) The electric field strength due to a ring of radius R at a distance x from its centre on the axis of
ring carrying charge Q is given by At what distance from the centre will the
electric field be maximum -
(1) x = R
(2) x = R/2
x = R/
(3)
(4) x = R
38) A semi circular arc of radius a is charged uniformly and the charge per unit length is . The
electric field at the centre is:
(1)
(2)
(3)
(4) None
39) A thin glass rod is bent into a semicircle of radius r. A charge +q is uniformly distributed along
the upper half and a charge –q is uniformly distributed along the lower half, as shown in the figure.
The magnitude and direction of the electric field produced at P, the centre of the circle will be :
(1) 0
(2)
perpendicular to the line OP and directed downward
(3)
perpendicular to the line OP and directed downward
(4)
along the axis OP
40) In the given diagrams the direction of electric field at point O is given in list-II (O is
circumcenter of the given regular polygon). Charge Q is positive. Match the direction of electric field
for the given arrangement:-
Code :-
P Q R S
(1) 2 1 4 3
(2) 3 1 2 4
(3) 3 2 1 4
(4) 1 4 3 2
(1) 1
(2) 2
(3) 3
(4) 4
41) Find the variation of electric field on the line joining the two charges -
(1)
(2)
(3)
(4)
42) Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of
radii R/2, R and 2R respectively, as shown in figure. If magnitudes of the electric fields at point P at
a distance R from the centre of spheres 1, 2 and 3 are E1 E2 and E3 respectively, then
43) A proton and an electron are placed in uniform electric field which of the following is correct :
44)
Charge 16 Q is placed at point A and another charge 25Q is placed at point B calculate at origin.
(1)
(2)
(3) 2kQ
(4)
45) For the given figure the direction of electric field at A will be :
(1) towards AL
(2) towards AY
(3) towards AX
(4) towards AZ
CHEMISTRY
1) The reaction, 2C + O2 → 2CO2 is carried out by taking 24 g carbon and 96 g O2. Which one is
limiting reagent:
(1) C
(2) O2
(3) CO2
(4) None of these
2) Match the mass of elements given in Colum-I with the number of moles given in Column-II and
mark the appropriate choice. Choose the correct codes form he options given below :
Column-I Column-II
(1) CH2
(2) CH3
(3) C2H5
(4) CH4
(1)
mol
(2)
mol
(3) 20 mol
(4) 10 mol
6) 6.02 × 1022 molecules NaOH are removed from 20g NaOH. How many moles of NaOH are
remaining?
7) A gaseous mixture contains CO2 (g) and N2O (g) in a 2 : 5 ratio by mass. The ratio of the number
of molecules of CO2 (g) and N2O (g) is
(1) 5 : 2
(2) 2 : 5
(3) 1 : 2
(4) 5 : 4
8) A compound contains 10–2 % of phosphorous. If atomic mass of phosphorus is 31, the molecular
mass of the compound having one phosphorus atom per molecule is :–
(1) 31
(2) 3.1 × 103
(3) 3.1 × 105
(4) 3.1 × 104
(1) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1
Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for
(2)
statement-1
(3) Statement-1 is true, statement-2 is false
(4) Statement-1 is false, statement-2 is true
10) The molecular formula of a compound is X4O9. If the compound contains 40% X by mass, then
what is the atomic mass of X?
(1) 24
(2) 12
(3) 26
(4) 13
11) Which has the maximum number of molecules among the following ?
(1) 64 g SO2
(2) 44 g CO2
(3) 48 g O3
(4) 8 g H2
13) Correct relationship between molecular weight and vapour density is (H2 gas is it taken as
standard)
(2)
Molecular weight = Vapour density
(3)
Molecular weight = Vapour density
(4)
Molecular weight = Vapour density
14) 5 L of an alkane requires 25 L of oxygen for its complete combustion. If all volumes are
measured at constant temperature and pressure, the alkane is :
(1) Isobutane
(2) Ethane
(3) Butane
(4) Propane
15) How many moles of Ca3(PO4)2 will contain 0.04 mol of oxygen atoms?
(1) 0.5
(2) 0.05
(3) 0.005
(4) 1
16) Which of the following statements are correct regarding a mixture containing 64.0 gm H2 and
64.0 g O2 is ignited so that water is formed as follows :-
I. H2 is the limiting Reagent
II. O2 is the limiting Reagent
III. Reaction mixture contains 72.0 gm H2O and 56.0 gm unreacted H2.
IV. The reaction mixture contains 56.0 gm H2O and 72 gm unreacted H2.
(1) I and IV
(2) II and IV
(3) II and III
(4) I and III
17) An element belongs to 6th period & 15th group its electronic configuration is :-
2 13
(1) 54[xe] 6s 4f
2 14 13
(2) 54[xe] 6s 4f 5d
2 14 10 3
(3) 54[xe] 6s 4f 5d 6p
14 1
(4) 54[xe] 4f 6s
18)
In above graph correct position of transition metal elements.
(1) A
(2) B
(3) C
(4) D
19) If each orbital can hold max. 2 electron, than total no. of elements in 8th period would be :
(1) 75
(2) 50
(3) 100
(4) 25
(1)
(2)
(3)
(4)
21)
(1)
(2)
(3)
(4)
22)
(1) Cu > Zn
(2) Cl > F
(3) P > S
(4) Sc > Ti
23) The increasing order of the ionic radii of the given isoelectronic species is–
(1) 2nd
(2) 6th
(3) 8th
(4) 10th
26) In modern periodic table, the element with atomic number Z = 118 will be:
27)
28) Which of the following set of atomic numbers represent representative elements ?
29) If total 100 elements are present in periodic table then how many of them contain e– in 4d
subshell.
(1) 60
(2) 62
(3) 64
(4) 80
30) Which two elements are in same period as well as same group of modern periodic table ?
(1) 12, 3
(2) 6, 3
(3) 3, 3
(4) 12, 12
(1) 22σ, 7π
(2) 16σ, 7π
(3) 26σ, 7π
(4) 24σ, 7π
34) How many and bonds are present in the following molecule respectively ?
(1) 10, 2
(2) 12, 2
(3) 8, 3
(4) 10, 2
35)
(1) sp3–sp3
(2) sp2–sp2
(3) sp3–sp
(4) sp–sp2
36) Find out total number σ and π bonds respectively in following compound.
(1) 14, 2
(2) 15,3
(3) 9, 3
(4) 12, 2
(1) 8 σ and 4 π
(2) 10 σ and 5 π
(3) 8 σ and 3 π
(4) 9 σ and 4 π
(1) 6
(2) 10
(3) 8
(4) 2
39) Find out the number of 1°, 2°, 3° carbon in given compound ?
(1) 2, 6, 2
(2) 3, 5, 1
(3) 3, 6, 1
(4) 3, 5, 2
(1) 3, 14, 1
(2) 3, 14, 2
(3) 3, 12, 3
(4) 3, 12, 2
41) The number of 1°, 2°, 3° H-atom respectively in the given compound ?
(1) 1, 2, 3
(2) 8, 3, 1
(3) 6, 4, 2
(4) 8, 2, 2
(1)
(2)
(3)
(4)
43) Which of the following compound is having only one type of hydrogen atom :-
(1) Benzene
(2) Nephthalene
(3) Biphenyl
(4) All
Column-I Column-II
(S)
(T)
(1) A → Q, T ; B → P, R ; C → S
(2) A → R, T ; B → Q ; C → R, S
(3) A → Q, T ; B → P ; C → R, S
(4) A → T ; B → P, Q, R ; C → S
BIOLOGY
1) Trilamellar model proposed by :-
(1) 75 nm
(2) 7.5 nm
(3) 150 nm
(4) 1.0 nm
3) S.J. singer and G.L. Nicolson's model of plasma membrane differs from sandwitch's model in the:-
6) Who study different type of animal cells and reported that cells had a thin outer layer as the
plasma membrane :-
(1) M. Schleiden
(2) T. Schwann
(3) Leeuwenhock
(4) Rudolf virchow
7) As the polar molecules cannot pass through the non polar I , they requires II of the
membrane to facilitate their transport across the membrane.
Choose the correct word for I and II :-
I II
(1) Cholesterol Carbohydrate
(2) Protein Lipid
(3) Carbohydrate Protein
(4) Lipid bilayer Protei
(1) 1
(2) 2
(3) 3
(4) 4
(1) The tail is non polar hydrocarbon and should present within an aqueous environment.
(2) The tail is polar hydrocarbon and so is protected from aqueous environment
The nonpolar or hydrophobic hydrocarbon tails of lipid, being on inner side ensures their
(3)
protection from aqueous environment.
(4) The tail is hydrophilic so it tends to be located in the aqueous inner side of membrane
Column-I Column-II
Various types of cell and organism Size
(1) Any thing less than a complete structure of a cell does not ensure independent living
(2) Anton Von Leeuwenhock first saw and described a living cell
(3) Robert Brown discovered cell
(4) Cell is the basic unit of structure and function of all organisms
15) Which of the following is common to facilitated diffusion and active transport ?
16) The quasifluid nature (A) enables (B) movement of proteins within the overall bilayer
of plasma membrane.
17) which of the following was a germen botanist, examined a large number of plants and observed
that all plants are composed of different kinds of cells which form the tissues of plant cell.
(1) Schleiden
(2) Schleiden & Schwann
(3) Schwann
(4) Virchow
20) Cell theory which was given by Schleiden and Schwann, did not explain as to how the new cells
are formed. Who modified the hypothesis of cell theory to give it a final shape ?
(1) R. Hooke
(2) R. Virchow
(3) Mendel
(4) C.P. Swanson
23) Find out the correct match from the following table:-
24) G.N. RAMACHANDRAN received a Ph.D. from Cambridge University in 1949, while at
Cambridge, he met —— and was deeply influenced by his publications on models of the a-helix and
b-sheet structures that directed his attention to solving the structure of collagen. -
25) Nucleus as a "cell organelle" was first described by.....as early as........
26) Read the following statement (A-D). How many statement are correct
(A) All living organisms are composed of cells and products of cells.
(B) All cells arise from pre existing cells
(C) According to Schleiden, all plants are composed of different kinds of cells. Which form the
tissues of the plants.
(D) According to Schwann animal cells had a thin outer layer which is known as cell wall
(1) One
(2) Three
(3) Two
(4) Four
27) Given below is the digramatic sketch of cell membrane. Identity the parts labelled A,B,C,D,E and
(1) Four
(2) One
(3) Two
(4) Three
29) The following diagram shows of the structures in a plant cell (A-G) identify the structures.
(I to VII) with their respective parts :- (I) The structure replicates during
mitosis and genrates the spindle.
(II) Major site for systhesis of lipid.
(III) Power house of the cell.
(IV) Store house of digestive enzyme.
(V) Increases the surface area for the absorption of materials.
(VI) Site of Glycolysis
(VII) Site for active ribosomal RNA synthesis
The correct option is :-
I II III IV V VI VII
(1) B E H G E D C
(2) H B G E J C D
(3) H B E G J D C
(4) H B G E D J C
(1) 1
(2) 2
(3) 3
(4) 4
31) Substance 'A' is a polar molecule with higher concentration inside the cell than outside. How
might this substance enter the cell ?
(1) Nucleus
(2) Plasma membrane
(3) Mitochondrian
(4) Cytoplasm
35) Regarding differences between animal & plant cells, which of the following statement is correct?
(1) Animal cells contain centrioles & cell wall, plant cells do not
(2) Animal cells contain centrioles & plant cells contain plastids, cell wall and large central vacuole
(3) Animal cells do not contain centrioles plant cells contain
(4) Animal cells contain plastids, while plants cells do not contain
36) According to the fluid mosaic model of the cell membrane, the proteins are located :-
(1) In a continous layer over the outer surface of the membrane only
(2) In a continuous layer over the inner surface only
In discontinuous arrangement both on the surface (as peripheral proteins) and in the interior of
(3)
the membrane (as integral proteins)
(4) In the middle of the membrane, between the lipid bilayer
(1) Phosphoprotein
(2) Protein and lipids
(3) Phospholipids
(4) Hemicellulose
39) Identify the labelled organelles A, B and C with their correct function :
40) Keeping in view the "fluid mosaic model" for the structure of cell membrane, which one of the
following statements is correct with respect to the movement of lipids and proteins from one lipid
monolayer to the other (described as flipflop movement) ?
42) Fill in the blanks correctly in following paragraph with the help of given options :-
Many molecules can move briefly across plasma membrane without any requirement of energy and
this is called the __________. Neutral solutes may move across the membrane by the process of
_______ along the concentration gradient.
43) Carbohydrates which are present in the bio membrane in the form of :-
(1) Cellulose
(2) Glycolipid
(3) Glycoprotein
(4) Both (2) and (3)
44) Protein which are present in cell membrane are differentiated on the basis.
Column-I Column-II
(1) It is multilayered
(2) Limited role in secretion and absorption
(3) They cover the dry surface of the skin like epidermis
(4) Found in inner lining of blood vessels and lymph vessels
(1) 1
(2) 2
(3) 3
(4) 4
53)
(2)
Found in Small Intestine
(3)
Bowman's capsule
(4)
Found in blood vessel
55) Which of the following secretions are related with exocrine glands ?
(a) Mucus (b) Ear wax
(c) Saliva (d) Oil
(e) Insulin (f) Milk
56) Read the statement(s) carefully and fill the blanks with correct option -
Tendons, which attach ___A___ are example of ___B___.
A - bones to muscles,
(1)
B - specialised connective tissue
A - bones to muscles
(2)
B - dense regular connective tissue
A - one bone to another
(3)
B - dense regular connective tissue
A - one bone to another
(4)
B - dense irregular connective tissue
Column-I Column-II
A B C D
(1) ii i iii iv
(2) iii ii iv i
(3) iv iii i ii
(4) i iv ii iii
(1) 1
(2) 2
(3) 3
(4) 4
59) Given below is the diagrammatic sketch of a certain type of connective tissue. Identify the parts
labelled A,B,C and D, and select the right option
60)
(1) Periosteum
(2) Perimysium
(3) Endomysium
(4) Renal capsule
61) Assertion :- All cells in epithelium are held together with little intercellular material.
Reason :- All animal tissue specialised junctions provide both structural and functional links
between its individual cell.
(1) Both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
(2) Both Assertion & Reason are True but Reason is not a correct explanation of the Assertion.
(3) Assertion is True but the Reason is False.
(4) Both Assertion & Reason are False.
62) Statement-I: Ciliated epithelium is mainly present in the inner surface of hollow organs.
Statement-II: Function of ciliated epithelium is to move particles or mucus in specific direction.
(1) Fibroblasts
(2) Macrophages
(3) Mast cell
(4) All of the above
(1) a, b
(2) b, c, d only
(3) only d
(4) a, b, c
(1) Melanin
(2) Keratin
(3) Collagen
(4) Myosin
(1) Areolar C. T.
(2) Mucoid C. T.
(3) Fibrous C. T.
(4) Adipose C. T.
Facilitate communication between adjoining cells by connecting the cytoplasm for rapid transfer
(1)
of ions, small molecules and some large molecules.
(2) Separate two cells from each other.
(3) Stop substance from leaking across a tissue.
(4) Performing cementing to keep neighbouring cells together.
(1) If both assertion & reason are true & the reason is a correct explanation of the assertion.
(2) If both assertion & reason are true but reason is not a correct explanation of the assertion.
(3) If assertion is true but the reason is false.
(4) If both assertion & reason are false
75) Identify the organism, the body is divided into head, thorax and abdomen having bitting and
chewing mouth parts.
(1) Pigeon
(2) Fish
(3) Earthworm
(4) Cockroach
76) A ring of A blind tubules called B is present at the junction of foregut and mid gut Which secrete
digestive juice. At junction of midgut and hind gut is present another ring of C filamentous D :-
A B C D
Malpighian Hepatic
1 6-8 100-150
tubules caecae
Malpighian Hepatic
2 100-150 6-8
tubules caecae
Malpighian
3 100-150 Hepatic caecae 6-8
tubules
Malpighian
4 6-8 Hepatic caecae 100-150
tubules
1
(1)
(2) 2
(3) 3
(4) 4
(1) Sternum
(2) Tergum
(3) Articular or Arthrodial membrane
(4) Peritrophic membrane
78) In the following diagram, identify and label the structures A, B, C and D :
(1) Elytra
(2) Metathoracic wings
(3) Tegmina
(4) Both (1) and (3)
80)
Structures which help in distinguishing a male cockroach from a female cockroach are-
81) Nocturnal, omniovorus, resident of human homes, serious pest, vector of several diseases, live in
damp place, chitinous exoskeleton, piercing and sucking mouth parts.
How many of above characters are applicable to Periplaneta americana :-
(1) 8
(2) 7
(3) 4
(4) 2
82) The dorsal plate of skeleton found on the abdomen of cockroach is called :
(1) Pleuron
(2) Sternum
(3) Tergum
(4) Vertex
(1) By cuticle
(2) By mucous membrane
(3) By endoepithelium
(4) By peritrophic membrane
89) A ring of 6-8 blind tubules present at the junction of foregut and midgut and are called:-
90) With the help of several ommatidia, a cockroach can receive several images of an object. This
kind of vision is caled :-
PHYSICS
Q. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A. 2 2 2 1 2 3 4 1 4 1 3 2 2 1 4 4 2 3 3 2
Q. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
A. 1 1 2 1 2 3 4 1 1 4 1 3 1 2 1 1 3 1 2 2
Q. 41 42 43 44 45
A. 3 3 2 1 2
CHEMISTRY
Q. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
A. 1 4 1 4 2 4 2 3 4 1 4 4 4 4 3 3 3 3 2 3
Q. 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
A. 1 1 2 4 3 3 4 4 2 2 1 3 2 2 4 2 1 3 2 3
Q. 86 87 88 89 90
A. 2 4 4 1 3
BIOLOGY
Q. 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110
A. 2 2 3 3 2 2 4 3 1 3 3 4 4 3 4 2 1 2 3 2
Q. 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
A. 2 1 1 3 2 2 3 4 3 3 1 1 2 4 2 3 3 4 2 4
Q. 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150
A. 4 3 4 1 4 3 1 1 4 3 3 4 3 3 3 2 1 3 3 4
Q. 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
A. 2 2 2 4 4 4 3 4 4 2 1 3 1 3 4 4 3 2 4 1
Q. 171 172 173 174 175 176 177 178 179 180
A. 2 3 4 3 1 2 3 3 4 2
SOLUTIONS
PHYSICS
1)
Concept:
The relevant trigonometric identities are the sum and difference formulas:
• sin(A + B) = sin A cos B + cos A sin B
• cos(A + B) = cos A cos B - sin A sin B (Note the minus sign)
• sin(A - B) = sin A cos B - cos A sin B
• cos(A - B) = cos A cos B + sin A sin B
Mathematical Calculation:
We compare each given option with the correct formulas:
• Option 1 (sin(A+B)): sin(A+B) = sin A cos B + cos A sin B - This is correct.
• Option 2 (cos(A+B)): The question states cos(A+B) = cos A cos B + sin A sin B. This is
incorrect. The correct formula has a minus sign between the terms.
• Option 3 (sin(A-B)): sin(A - B) = sin A cos B - cos A sin B - This is correct.
• Option 4 (cos(A-B)): cos(A - B) = cos A cos B + sin A sin B - This is correct.
Final Answer:
The incorrect trigonometric identity is: cos(A+B) = cos A cos B + sin A sin B. The correct
identity is cos(A+B) = cos A cos B - sin A sin B.
Question Level: Easy
4)
8)
y = 2x2 – 12x
= 4x – 12 = 0 ⇒ x = +3
=4>0
so, minimum value of y = 2(3)2 – 12 × 3 = –18
10) Because slope m = tanθ
This is the integral of the gravitational force over a radial distance r, where G is the
gravitational constnat, M and m are masses, and r is the variable of integration.
Concept : Definite Integration
Formula :
We are using the power rule of integration. The power rule for integrating a function xn is:
Calculation:
1. Set up the integral:
2. Integrate r–2:
4. Rearrange terms:
15)
= 120
16)
17)
we know that
So +C
= +C
For y to be maximum.
23)
Due to symmetry of charge distribution in III the net electric field is zero.
24)
When two objects are rubbed against each other, they undergo triboelectric charging, where :
One object gains electrons – becomes negatively charged (– q)
The other object loses electrons – becomes positively charged (+ q)
Since they acquire opposite charges, they will experience an attractive force due to
electrostatic interaction.
According Coulomb's Law, the electrostatic force between two point charges is
F=
where :
k is Coulomb's constant,
q1 and q2 are the charges on the objects,
r is the separation distance.
since q1 and q2 are of opposite signs, the force is attractive.
As per given condition, one object is positively charged and the other is negatively charged.
Opposite charges always attract, meaning the nature of the force is attractive.
Correct Answer is 1
25)
Given F1 + F2 = 0
∴
or q2 = –qQ ⇒ Q = –q
26) Coulomb's law is analogus to newton's third law.
27) F = qE = q
q = × 10–5 = 5 × 10–6 C
Nature of charge will be positive
30)
for eqm condition
3(70 – x) = 4x
7x = 210
x = 30 cm
31)
32)
Concept Based:
• Electrostatic Force: The repulsive force between two charged bodies due to their charges.
• Tension in the Strings: The force exerted by the strings the balls, which has both
horizontal vertical components.
• Equilibrium of Forces: Conditions for horizontal vertical forces to balance in a static
system.
Formula :
• Horizontal equilibrium:
The electrostatic force Fe must balance the horizontal Component of tension:
Vertical equilibrium:
The vertical forces (gravitational forces) are balanced by the vertical components of the
tension:
m1 = T1cos (α) for ball 1 and m2g cos(ß) for ball 2
Calculation:
• Horizontal equilibrium:
Since a > b this implies sin (a) > sin (b), so the tension T1 in the string of ball 1 must be than
the tension T2 in the string of ball 2. Therefore, We have:
T1 < T2
This means that the tension in the string of ball 1 is less than the tension in the string of ball 2.
• Vertical equilibrium:
Since T1 < T2 and cos(a) < cos(ß), it follows that the mass m1 of ball 1 must be less than the
mass of m2 of ball 2.
Hence:
m 1 < m2
• Relating the charges:
The greater horizontal displacement of ball 1 implies that the electrostatic force on ball 1 is
larger. This can only happen if q1 ≥ q2 (the charge on ball 1 is greater than to the charge on
ball 2).
From the analysis, we conclude the correct answer is Option 3: q1 > q2 & m1 < m2
40) Apply superposition of electric field using the fact that electric field is radially outwards.
41) Electric field will be infinite near both charges. Since 2Q is the bigger charge hence
electric field will be zero near the smaller charge.
42) E1 =
E2 = ⇒ E2 =
E3 = ⇒ E3 =
E3 < E1 < E2
CHEMISTRY
70)
72)
Explanation -
The question asks to identify the element whose electronic configuration places it in a
different block of the periodic table compared to the others.
Solution -
2 2 6 2 6
The electronic configuration 1s 2s 2p 3s 3p (Argon) belongs to the p-block. The other three
configurations belong to the d-block.
73) Only s & p-block elements except noble gas, d-block, f-block.
Total σ-bonds : 26
Total π-bonds : 7
78)
83)
Key Concept:
Carbon atom attached to two carbon is called as 2º/secondary carbon.
Solution/Explanation/Calculation:
Conclusion:
Hence, option (3) is correct.
89)
(P)
(Q)
All atom of cyclic same so Homocylcic
(R)
90)
having 3°C also but there is no hydrogen so no 3°H.
BIOLOGY
115)
Concept:
A. Robert Brown is credited with the discovery and detailed description of the nucleus.
Solution:
A. Robert Brown observed and described the nucleus in plant cells in 1831.
122)
127)
135)
NCERT Page # 93
136)
138)
139)
NCERT Pg # 102
140)
148)
154) Module
158)
162)
169)
170)
172)
The tergum is the dorsal plate of the exoskeleton in each abdominal segment of a
cockroach. It provides structural support and protection to the dorsal side of the
body.
A. Pleuron: Refers to the lateral (side) plates of each segment.
B. Sternum: Refers to the ventral (bottom) plate of each segment. Vertex: Refers to the
top of the head, not the abdomen.
173)
While cockroach wings have various functions, their primary use is in finding a mate. They use
their wings to fly short distances.
Answer - 4
174)
175)