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Find the number of solutions of the equations \( (\sin x-1)^{3}+(\cos x-1)^{3}+(\sin x)^{3}= \) \( (2 \sin x+\cos x-2)^{3} \) in \( [0,2 \pi] \)
2
Maths
For the given data \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} ; \boldsymbol{E}^{o}=\boldsymbol{a} \boldsymbol{v} \boldsymbol{o l} \boldsymbol{t} ; \boldsymbol{K}_{c}=\boldsymbol{K}_{1} \) \( \mathbf{2} \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}+\mathbf{2} \boldsymbol{D} ; \boldsymbol{E}^{\boldsymbol{o}}= \) \( \boldsymbol{b} \boldsymbol{v} \boldsymbol{o l} \boldsymbol{t} ; \boldsymbol{K}_{c}=\boldsymbol{K}_{2} \) Select the correct choices: This question has multiple correct options \( \mathbf{A} \cdot a=b \) В. \( K_{2}=K_{1}^{2} \) \( \mathbf{c} \cdot a \neq b \) \( \mathbf{D} \cdot b=a^{2} \)
1
Chemistry
The following acids have been arranged in the order of decreasing acid strength. Identify the correct order: CIOH (I), BrOH (II), IOH (III). A \( I>I I>I I I \) \( I \) В. \( I I>I>I I I \) c. \( I I I>I I>I \) I I \( I>I I I>I I \) \( I \)
1
Chemistry
Add an express the sum as a mixed fraction: \( \frac{-12}{5} \) and \( \frac{43}{10} \)
2
Maths
Simplify \( 3 x^{2}+5 x y-4 y^{2}+x^{2}- \) \( 8 x y-5 y^{2} \)
2
Maths
Which equation is correctly labeled oxidation or reduction? \( \mathbf{A} \cdot H_{2} S=S+2 e^{-}+2 H^{+} \) oxidation B \( \cdot S O_{2}+4 e^{-}+2 H_{2} O=S+4 O H^{-} \) oxidation \( \mathbf{C} \cdot N H_{3}+H C l=N H_{4}++C l_{2}^{-} \) oxidation D. \( N a C l+A g N O_{3}=A g C l+N a N O_{3} \) reduction \( \mathrm{E} \cdot M n^{2+}=M n O_{4} \) reduction
1
Chemistry
Ultraviolet light of \( 6.2 \mathrm{eV} \) falls on aluminium surface (work function = 4.2eV). The kinetic energy in joules of the fastest electron emitted is approximately: A \( \cdot 3 \times 10^{-21} \) B . \( 3 \times 10^{-19} \) c. \( 3 \times 10^{-17} \) D. \( 3 \times 10^{-15} \)
1
Chemistry
Coniferales and Cycadales have respectively. A. Motile sperms B. Motile and non motile sperms c. Non motile and motile sperms D. Non motile sperms
0
Biology
Let \( \vec{a}, \vec{b}, \vec{c} \) be vectors of length 3,4 and 5 respectively. Let \( \vec{a} \) be perpendicular to \( (\vec{b}+\vec{c}), \vec{b} \) to \( (\vec{c}+\vec{a}) \) and \( \vec{c} \) to \( (\vec{a}+\vec{b}) \) Find the length of the vector \( \vec{a}+\vec{b}+\vec{c} \).
2
Maths
The number of solutions for \( \sin \left(\frac{\pi x}{2}\right)=\frac{99 x}{500} \) is: \( A \cdot 3 \) B. 5 \( c \cdot 7 \) \( D \)
2
Maths
The ability of eye to focus on both near and far objects is called: A. Presbyopia B. Myopia c. Hypermetropia D. Power of accommodation
3
Physics
Which of the following is not true, if \( \mathbf{A} \) and \( B \) are two matrices each of order \( \boldsymbol{n} \times \boldsymbol{n}, \) then \( \mathbf{A} \cdot(A+B)^{T}=B^{T}+A^{T} \) \( \mathbf{B} \cdot(A-B)^{T}=A^{T}-B^{T} \) \( \mathbf{C} \cdot(A B)^{T}=A^{T} B^{T} \) \( \mathbf{D} \cdot(A B C)^{T}=C^{T} B^{T} A^{T} \)
2
Maths
Solve: \( \frac{1}{3(x-1)}-\frac{1}{4(x-2)}=1 \)
2
Maths
Fusion reaction take place at high temperature because A. atoms are ionized at high temperature B. molecules break up at high temperatures C . nuclei break up at high temperature D. kinetic energy is high enough to overcome repulsion between nuclei
3
Physics
Heavy water is: \( \mathbf{A} \cdot H_{2} O \) B. water obtained by repeated distillation \( c \cdot D_{2} O \) D. water at \( 4^{\circ} \mathrm{C} \)
1
Chemistry
Gelatin has the minimum protective powers. A. True B. False c. Ambiguous D. Data insufficient
1
Chemistry
The velocity-time graph of a body is given below. The maximum acceleration in \( m s^{-2} \) is
3
Physics
The value of the determinant \[ \left|\begin{array}{ccc} \mathbf{1} & \cos (\boldsymbol{\alpha}-\boldsymbol{\beta}) & \mathbf{c o s} \boldsymbol{\alpha} \\ \cos (\boldsymbol{\alpha}-\boldsymbol{\beta}) & \mathbf{1} & \cos \beta \\ \cos \boldsymbol{\alpha} & \cos \beta & \mathbf{1} \end{array}\right| \] A \( \cdot \alpha^{2}+\beta^{2} \) B \( \cdot \alpha^{2}-\beta^{2} \) \( c .1 \) \( D \)
2
Maths
Two thin similar convex glass pieces are joined together front to front, with its rear portion silvered such that a sharp image is formed 0.2 \( \mathrm{m} \) for an object at infinity. When the air between the glass pieces is replaced by water \( \left(\mu=\frac{4}{3}\right), \) find the position of image.
3
Physics
In the azeotropic mixture of \( H C l \) and water, the percentage of \( H C l \) is: A . 20.2\% B . 11.1\% c. 44.4\% D. 10\%
1
Chemistry
Write cell reactions in lead storage battery during discharge.
1
Chemistry
Consider the circuit below. The bulb will light up if: \( A \cdot S_{1} S_{2} \) and \( S_{3} \) are all closed \( 3 \cdot S_{1} \) is closed but \( S_{2} \) and \( S_{3} \) are open \( c \cdot s_{1} \) and \( S_{3} \) are closed but \( S_{2} \) is open D. None of thes
3
Physics
Which of the following is not a true fossil? A. Placoderm B. limulus c. Archeopteryx D. Therapsid
3
Physics
The diagram represents an atom 'X! Answer the following. Atom 'X' will lose electrons to become \( \boldsymbol{X}^{1+} \) A. True B. False
1
Chemistry
A solenoid of inductance \( 2 \mathrm{H} \) carries a current of \( 1 A . \) What is the magnetic energy stored in a solenoid? A . 2 B . 1 J c. 4 J D. 5 J
3
Physics
A teak wood log is cut first in the form of a cuboid of length \( 2.3 \mathrm{m}, \) width \( 0.75 \mathrm{m} \) and of a certain thickness. Its volume is \( 1.104 \mathrm{m}^{3} . \) How many rectangular planks of size \( 2.3 \mathrm{m} \times 0.75 \mathrm{m} \times 0.04 \mathrm{m} \) can be cut from the cuboid?
2
Maths
Radiation of wavelength 242 nm is sufficient to ionize the sodium atom. Calculate the ionization energy in \( \boldsymbol{k J} \boldsymbol{m o l}^{-1} \cdot\left(\boldsymbol{n}=\mathbf{6 . 6 2 5} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s}\right) \) A. \( 493.6 k J \) \( J \) B . \( 6.625 \times 10^{3} J \) c. \( 242 k J \) D. \( 1324 k J \)
1
Chemistry
If a parent cell has eight chromosomes, then the daughter cells following meiosis will have: A. four chromosomes B. sixteen chromosomes c. eight chromosomes D. any one of these
0
Biology
The weight of one molecule of \( C_{60} H_{122} \) is: A. \( 1.2 \times 10^{-20} g \) B . \( 5.025 \times 10^{23} g \) c. \( 1.4 \times 10^{-21} g \) D. \( 6.023 \times 10^{23} g \)
1
Chemistry
The chemical method used in the concentration of ore is also known as: A. Bleaching B. Leaching c. Roasting D. Calcination
1
Chemistry
The reaction is: \( \mathbf{A} \cdot S_{N} \) B. \( S_{N} \) ? \( \mathbf{c} \cdot E_{1} \) \( D \cdot E_{2} \)
1
Chemistry
Find out longitudinal stress and tangential stress on the given fixed block
3
Physics
A gaseous mixture contains \( 70 \% N_{2} \) and a \( 30 \% \) unknown gas, by volume. If the average molecular weight of gaseous mixture is \( 37.60, \) the molecular weight of unknown gas is: A . 42.2 B. 60 c. 40 D. 50
3
Physics
Use hund's rule to derive the electronic configuration of \( C e^{+3} \) ion, and calculate its magnetic moment on the basis of 'spin only' formula. ( For \( \mathrm{Ce}, \mathrm{Z}=58 \) )
1
Chemistry
What are ¡) Magnetic declination ii) Magnetic dip iii) Horizontal component of earth's magnetic field at a place?
3
Physics
\( \ln a \Delta A B C, I f A C>A B \) and the bisector of \( \angle A \) meets \( B C \) at \( E \), then A. \( C E>B E \) в. \( C E<B E \) c. \( C D>B E \) D. \( C D<B E \)
2
Maths
The intermediate image formed by the objective of a compound microscope is: A. real, inverted and magnified B. real, erect and magnifiedd c. virtual, erect and magnified D. virtual, inverted and magnified
3
Physics
In a multiplying the previous term by a constant. A. geometric sequence B. arithmetic sequence c. geometric series D. harmonic sequence
2
Maths
A body of mass \( 2 \mathrm{kg} \) is kept by pressing to a vertical wall by a force of \( 100 \mathrm{N} \). the coefficient of friction between wall and body is 0.3 . then the frictional force is equal to: \( A \cdot 6 N \) B. 20 N c. \( 600 \mathrm{N} \) D. 700 N
3
Physics
A sample of water has a hardness expressed as 77.5 ppm \( C a^{2+} . \) This sample is passed through an ion exchange column and \( C a^{2+} \) is replaced by \( \boldsymbol{H}^{+} . \) Select correct statement(s). This question has multiple correct options A. pH of the water after it has been so treated is 2.4 B. Every \( C a^{2+} \) ion is replaced by one \( H^{+} \) ion. C . Every \( C a^{2+} \) ion is replaced by two \( H^{+} \) ions. D. pH of the solution remains unchanged.
1
Chemistry
The purpose of exhaust system in lime kilns where the decomposition of limestone takes place is to: A. drive away, \( C O_{2} \) gas and make the reaction proceed for completion. B. reduce the temperature of the reaction c. to make the reaction attain equilibrium in less time D. all the above
1
Chemistry
Fibres would have A. Thick walled B. Thin walled C. Thickening of wall at corners D. Dense cytoplasm
0
Biology
Rusting of iron is an example of reaction. A . fast B. slow c. endothermic D. can't say
1
Chemistry
The efficiency of a surfactant towards detergency depends upon its: \( \mathbf{A} \cdot \) СМС B. Kraft temperature C. nature of hydrophilic and hydrophobic core D. all of these
1
Chemistry
Identify the mode for the following data: 12 \( \mathbf{5 6} \) 67 \begin{tabular}{r} 34 \\ \hline \end{tabular} Height(cm) Swimmers 1 1 2 A . 34 B. 56 c. 67 D. 10
2
Maths
Concentrated sulphuric acid cannot be used to prepare \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \) from \( \boldsymbol{N} \boldsymbol{a} \boldsymbol{B} \boldsymbol{r} \) because it : A. reacts slowly with \( N a B r \) B. oxidises \( H B r \) c. reduces \( H B r \) D. none of the above
1
Chemistry
How many terms are there in the sequence \( 3,6,9,12, \ldots, 111 ? \)
2
Maths
The blue zone in a LPG flame indicates A. unburnt vapours B. partial decomposition c. moderately hot D. hottest and complete combustion
1
Chemistry
Find the sum of the first (i) 75 positive integers (ii) 125 natural numbers
2
Maths
Bleaching powder gives smell of chlorine because it: A . is unstable B. gives chlorine on exposure to atmosphere c. is a mixture of chlorine and slaked lime D. contains excess of chlorine
1
Chemistry
The fissionable material used in a breeder reactor is A \( \cdot 92 \mathrm{U}^{235} \) 55 В \( \cdot \) g \( _{9} \mathrm{Pu}^{239} \) \( \mathrm{c} \cdot_{90} \mathrm{Th}^{234} \) D. \( c^{12} \)
3
Physics
Sodium cyanide is used in the: A. cleaning of silver B. creation of fires C . purification of acids D. extraction of gold
1
Chemistry
Thermoplastics are: A. linear polymers. B. soften or melt on heating C. molten polymer can be moulded in desired shape. D. All of these
1
Chemistry
\( f(x)=\cos ^{-1}\left(\frac{\sqrt{2 x^{2}+1}}{x^{2}+1}\right), \) then range of \( \boldsymbol{f}(\boldsymbol{x}) \) is \( \mathbf{A} \cdot[0, \pi] \) B \cdot \( \left(0, \frac{\pi}{4}\right. \) \( c \cdot\left(0, \frac{\pi}{3}\right. \) D \( \cdot\left[0, \frac{\pi}{2}\right) \)
2
Maths
Describe the steps involved in glycolysis (flow chart or explanation).
0
Biology
A gas has an average speed of \( 10 m / s \) and a collision frequency of \( 10 s^{-1} \) What is its mean free path? A. \( 1 m \) в. \( 2 m \) \( c .3 m \) D. \( 0.1 m \)
3
Physics
Two particles A and B perform SHM along the same straight line with the same amplitude 'a', same frequency 'f and same equilibrium position '0'. The greatest distance between them is found to be \( 3 a / 2 \). at some instant of time they have the same displacement from mean position. What is this displacement? A \( \cdot \frac{a}{\sqrt{2}} \) B. \( a \sqrt{7} / 4 \) c. \( \sqrt{7} a / 4 \) D. 3a/4
3
Physics
In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across \( 52 \mathrm{cm} \) of the potentiometer wire. If the cell is shunted by a resistance of \( 5 \Omega, \) a balance is found when the cell is connected across \( 40 \mathrm{cm} \) of the wire. Find the internal resistance of the cell. A . \( 1.5 \Omega \) B . 2\Omega \( c .2 .5 \Omega \) D. 12
3
Physics
Why bacteria and fungi are called decomposers?
0
Biology
In a step-down transformer the secondary coil has number of turns A. strength B. less c. alternating D. primary
3
Physics
How long does it stay in the air (in s)? A . 37 в. 37.1 \( c .36 \) D. 35 5
3
Physics
D is any point on AC in \( A B C . \) Now, \( \boldsymbol{P}, \boldsymbol{Q}, \boldsymbol{X}, \boldsymbol{Y} \) are the mid points of \( \mathbf{A B}, \mathbf{B C} \) AD and DC respectively. Show that \( P X= \) \( \mathrm{QY} \)
2
Maths
The displacement x of a particle moving in one dimension under the action of a constant force is related to time t by the equation \( t=\sqrt{x}+3, \) where \( x \) is in meter and \( t \) is in second. Find the displacement of the particle when its velocity is zero. A. zero в. \( 12 m \) \( c .6 m \) D. 18 т
3
Physics
In soils, PAHs are most likely to stick tightly to particles; certain PAHs move through soil to contaminate underground water A. True B. False
1
Chemistry
Find \( f \circ g \) and \( g \circ f, \) if \( f(x)=\sin ^{-1} x \) \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2} \)
2
Maths
For \( \boldsymbol{X} \rightarrow \boldsymbol{B}(\boldsymbol{n}, \boldsymbol{p}), \) if \( \boldsymbol{n}=\mathbf{2 5}, \boldsymbol{E}(\boldsymbol{x})=\mathbf{1 0} \) then \( S . D .(x)= \) A \( .2 \sqrt{6} \) B. 2.4 c. \( 2 \sqrt{10} \) D. \( \sqrt{2.4} \)
2
Maths
Let \( \boldsymbol{f}=\boldsymbol{R} \rightarrow \boldsymbol{R} \) be a continuous function defined by \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\boldsymbol{e}^{\boldsymbol{x}}+\mathbf{2} \boldsymbol{e}^{-\boldsymbol{x}}} \) Statement \( 1: f(c)=\frac{1}{3}, \) for some \( c \epsilon R \) Statement \( 2: 0<f(x) \leq \frac{1}{2 \sqrt{2}}, \) for al \( \boldsymbol{x} \epsilon \boldsymbol{R} \)
2
Maths
Evaluate \( \int(\ln x+1) d x \) \( \mathbf{A} \cdot x \ln x+c \) B. \( x^{2} \ln x+c \) c. \( x^{-2} \ln x+c \) D. \( -x \ln x+c \)
2
Maths
Assertion: The Nernst equation gives concentration dependence of EMF of the cell. Reason: In a Daniell cell current flows from cathode to anode. A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion c. Assertion is true but Reason is false D. Assertion is false but Reason is true E. Both Assertion and Reason are false
1
Chemistry
Distinguish between step-up and step down transformer.
3
Physics
Clothes of \( _{--}-_{-}-_{-}-_{-}(\text {dark, white }) \) colors absorb heat better than clothes of light colors.
3
Physics
The engulfment of food in amoeba is known as A. Excretion B. Phagocytosis c. Respiration D. All of the above
0
Biology
Lanthanoids are: A. 14 elements in the seventh period left ( atomic no. \( =90 \) to \( 103 \text { right }) \) that are filling \( 5 f \) sublevel B. 14 elements in the sixth period left ( atomic no. 58 to 71 right ) that are filling \( 4 f \) sublevel C. 14 elements in the seventh period left ( atomic no. \( =58 \) to \( 71 \text { right }) \) that are filling \( 4 f \) sublevel D. 14 elements in the sixth period left ( atomic no. 90 to \( 103 \text { right }) \) that are filling \( 4 f \) sublevel
1
Chemistry
What is the product of electrolysis of 45 grams of water? A. 40 grams of \( H_{2} \) and 45 grams of \( O_{2} \) B. 40 grams of \( O_{2} \) and 5 grams of \( H_{2} \) c. 30 grams of \( H_{2} \) and 15 grams \( O_{2} \) D. 30 grams of \( O_{2} \) and 15 grams of \( H_{2} \)
1
Chemistry
micrometer is \( 10^{-a} \) hectometer. What is value of a?
3
Physics
Which of the following is not a characteristic of good respiratory surface? A. Thin and moist B. Large surface area c. close to oxygen and gas transporttt D. Thick and dry surface
0
Biology
Find the point on the curve \( y=x^{3}- \) \( 2 x^{2}-x, \) where the tangents are parallel to \( 3 x-y+1=0 \)
2
Maths
Solve: \( \boldsymbol{x}^{2}-(\boldsymbol{3} \sqrt{\mathbf{2}}-\mathbf{2} \boldsymbol{i}) \boldsymbol{x}-\sqrt{\mathbf{2}} \boldsymbol{i}=\mathbf{0} \)
2
Maths
A broader bundle of light rays is called a A. Beam of light B. Ray of light c. Bundle of light D. None of these
3
Physics
An artificially created surface water body to recharge ground water is called as A. Dam B. well c. Percolation tank D. None of the above
0
Biology
In triangle \( A B C, D \) and \( E \) are mid-points of sides \( A B \) and \( B C \) respectively. Also, \( F \) is a point in side \( A C \) so that DF is parallel to BC. Prove that DBEF is a parallelogram. Answer: DBEF is a parallelogram, If true then enter 1 else if False enter 0
2
Maths
What is amalgam?
1
Chemistry
Describe Rutherford's atomic model and also explain its drawbacks.
1
Chemistry
\( \operatorname{Let} n(A)=n . \) Then the number of all relations on \( \boldsymbol{A} \) is \( \mathbf{A} \cdot 2^{n} \) B \( \cdot 2^{(n)} \) c. \( 2^{n^{2}} \) D. none
2
Maths
Identify the action involved when a magnet attracts a piece of iron towards ¡t. A. Pushing B. Pulling c. Flying D. Picking
3
Physics
An aromatic primary amine A with molecular formula \( C_{6} H_{7} N \) undergoes diazotisation to give B. B when the aqueous solution of \( \mathrm{B} \) is boiled it gives C. Identify \( A, B \) and \( C \)
1
Chemistry
Chlorine forms stable compounds in the presence of A. sunlight B. water \( c . \) air D. catalyst
1
Chemistry
The formula of standard deviation of a grouped frequency distribution is A \( \cdot \sqrt{\frac{\sum\left(x_{i}-\bar{x}\right)^{2}}{N}} \) в. \( \frac{\sum\left(x_{i}-\bar{x}\right)^{2} f i}{N} \) c. \( \sqrt{\frac{\sum\left(x_{i}-\bar{x}\right)^{2} f i}{N}} \) D. \( \frac{\left.\sum\left(x_{i}-\bar{x}\right)^{2}\right\} i}{f i} \)
2
Maths
Give reasons: Xenon does not form fluorides such as \( X e F_{3} \) and \( X e F_{5} \)
1
Chemistry
Find the potentials of points \( A \) and \( B: \) A \( \cdot V_{A}=+10 V ; V_{B}=0 V \) B . \( V_{A}=+7.5 V ; V_{B}=-2.5 V \) c. \( V_{A}=+2.5 V ; V_{B}=-7.5 V \) D. \( V_{A}=+0 V ; V_{B}=-10 V \)
3
Physics
Which one of the following disease is caused by Nosema bombycis in mulberry silkworm? A. Muscardine B. Pebrine c. Grasserie D. Flacherie
1
Chemistry
When you use a hair straightener, while straightening your hairs, it breaks down your hairs due to: A. Electrostatic bonds B. Hydrogen bonds c. lonic bonds D. Covalent bonds
1
Chemistry
Which of the following compounds is not coloured? A \( \cdot N a_{2}\left[C u C l_{4}\right] \) B . \( N a_{2}\left[C d C l_{2}\right] \) \( \mathbf{c} \cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{6}\right] C l_{3} \) D. all of the above
1
Chemistry
The element with \( Z=120 \) (not yet discovered) will be an/ a: A. transition metal B. inner-transition metal c. alkaline earth metal D. alkali metal
1
Chemistry
Match list (I) with List (II) List I List II a) Recoil of gun e) Newtons first law f) Newtons second law b) Acceleration in one dimension and motion in two dimensions g) Projectile motion c) Definition of force d) Measurement of force \( \mathbf{A} \cdot a \rightarrow e, b \rightarrow g, c \rightarrow h, d \rightarrow f \) В . \( a \rightarrow h, b \rightarrow g, c \rightarrow e, d \rightarrow f \) c. \( a \rightarrow e, b \rightarrow h, c \rightarrow g, d \rightarrow f \) D \( . a \rightarrow h, b \rightarrow e, c \rightarrow g, d \rightarrow f \)
3
Physics
If the color code of the carbon resistance is Red, Orange yellow, Gold. Find the value of resistance.
3
Physics
Water insoluble component of starch is: A. amylopectin B. amylose c. cellulose D. none of these
1
Chemistry
If \( \sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1, \) then \( x \) is equal to A . B. 0 \( c \cdot \frac{4}{5} \) D.
2
Maths
Show that Newton's third law of motion is contained in his second law. State and explain the principle of conservation of angular momentum
3
Physics
Time taken by a 836 Wheater to heat one litre of water from \( 10^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \) is: A. 50 s B. 100 s \( c \cdot 150 s \) D. 200
3
Physics