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If \( a, b \) are nonzero vectors and \( a \) is perpendicular to \( b \), then \( a \) has nonzero vector \( r \) satisfying \( r \cdot a=\alpha, \) for some scalar \( \boldsymbol{\alpha}, \boldsymbol{a} \times \boldsymbol{r}=\boldsymbol{b} \) is A \( \cdot \frac{\alpha a+(a+b)}{|a|^{2}} \) в. \( \frac{\alpha a+a \times b}{|b|^{2}} \) c. \( \frac{\alpha a-(a \times b)}{|a|^{2}} \) D. \( \frac{\alpha a-(a \times b)}{|b|^{2}} \)
2
Maths
Which of the following is not a genetic material? A. ds DNA B. ss DNA c. \( d s \) RNA D. None of the above
0
Biology
The value of \( \int_{0}^{\pi / 2} \frac{f(x) d x}{f(x)+f(\pi / 2-x)} \) is equal to A . \( \pi / 4 \) B . \( \pi / 2 \) \( c . \pi \) D. None
2
Maths
Set the following vectors in the increasing order of their magnitudes. a) \( 3 \hat{i}+4 \hat{j} \) b) \( 2 \hat{i}+4 \hat{j}+6 \hat{k} \) c) \( 2 \hat{i}+2 \hat{j}+2 \hat{k} \) \( A \cdot b, a, c \) B. \( c, a, b \) \( c \cdot a, c, b \) D. a, b, c
2
Maths
Conversion of benzene diazonium chloride to chlorobenzene is: A. Sandmeyer's reaction B. Stephen's reaction c. Gomberg reaction D. Schotten-Baumann reaction
1
Chemistry
Symbols in (I) and (II) represent standard transistors. Then A. both represents p-n-p transistors B. both represents n-p-n transistors c. (I) represents n-p-n and (II) represents \( p \) -n-p. D. (I) represents p-n-p and (II) represents n-p-n-
3
Physics
Which of the following is used as an acid bath in dyeing cotton and wool? A. Methanoic acid B. Acetic acid c. Benzoic acid D. Sulphuric acid
1
Chemistry
The quantity \( \boldsymbol{X}=\frac{\boldsymbol{\epsilon}_{0} \boldsymbol{L} \boldsymbol{V}}{\boldsymbol{t}}: \boldsymbol{\epsilon}_{0} \) is the permittivity of free space, \( \boldsymbol{L} \) is length, \( \boldsymbol{V} \) is potential difference and \( t \) is time. The dimensions of \( X \) are same as that of A . Resistance B. Charge c. voltage D. current
3
Physics
Barometric height used as a unit to express the atmospheric pressure because atmospheric pressure holds the mercury in the tube, so the height of mercury is used as a unit to express the atmospheric pressure.Type 1 for true and 0 for false
3
Physics
Compound \( A \) and \( B \) are two oxides of sulfur. Compound A is 50\% sulfur by mass, while Compound B is \( 40 \% \) sulfur by mass. Given the atomic masses of sulfur and oxygen are 32 amu and 16 am \( u \) respectively, which of the following statements is NOT a valid interpretation of these data? This question has multiple correct options A. Compound A could have the formula, \( S O_{2} \) B. Compound B could have the formula, \( S O_{2} \) C. Compound A and B illustrate Dalton's law of multiple proportions. D. Compound A could have the formula, \( S O \).
1
Chemistry
A force of \( 10 \mathrm{N} \) inclined to the horizontal at an angle of 60 acts on a body can move in horizontal direction only find its acceleration.
3
Physics
The experiment given shows that light: A. Can be reflected B. Is a form enrgy C. Travels in straight line D. Can pass through all objects
3
Physics
Find the area of the quadrilateral ABCD whose vertices are \( A(-3,-1), B(-2,-4) \) \( C(4,-1) \) and \( D(3,4) \)
2
Maths
The pressure required to liquefy a gas at the critical temperature is called A. reduced pressure B. critical pressure c. vapour pressure D. atmospheric pressure
1
Chemistry
Momentum is a measure of quantity of A. motion B. friction c. gravitation D. electric force
3
Physics
The total number of chromosomes in an organism with haploid number of 18 would be \( A \cdot 18 \) B. 16 \( c \cdot 26 \) D. 36 E. 46
0
Biology
Reabsorption of water in the nephron is controlled by ADH and aldosterone hormone. A. True B. False
0
Biology
The correct statement(s) about the oxoacids, \( H C l O_{4} \) and \( H C l O, \) is (are): This question has multiple correct options A. the central atom in both \( H C l O_{4} \) and \( H C l O \) is \( s p^{3} \) hybridized B. the conjugate base of \( H C l O_{4} \) is weaker base than \( H_{2} O \) C \( \cdot H C l O_{4} \) is formed in the reaction between \( C l_{2} \) and \( H_{2} O \) D. \( H C l O_{4} \) is more acidic than \( H C l O \) because of the resonance stabilization of its anion
1
Chemistry
Very short answer type. Name any two macronutrients and state their importance in plant nutrition.
0
Biology
A lamp is marked \( 60 \mathrm{W}, 220 \mathrm{V} \). If it operates at \( 200 \mathrm{V} \), the rate of consumption of energy will A. decrease B. increase c. remain unchanged D. first increase then decrease
3
Physics
The stable oxidation states of Cr are: \( A \cdot+3,+6 \) \( B \cdot+3,+4 \) \( c \cdot+1,+4 \) \( D \cdot+2,+5 \)
1
Chemistry
Potassium ferrocyanide is stored in dark coloured bottles and kept away from sunlight because: This question has multiple correct options A. undergoes displacement in sunlight B. dark colors of the bottles absorb a lot of energy from light c. undergoes decomposition in sunlight D. evaporates in sunlight
1
Chemistry
\( C S_{2} \) burns in excess air to produce : A. \( C O_{2} \& S O_{2} \) в. \( C O_{2} \& S O_{3} \) c. \( \cos S O_{2} \) D. \( \operatorname{co~} \& \mathrm{SO}_{3} \)
1
Chemistry
Number of pollen grains produced per pollen mother cell is gymnosperms is A . 4 B. 2 \( c \cdot 6 \) D. 10
0
Biology
What do you mean by Corrosion?
1
Chemistry
The angle between particle velocity and wave velocity in a transverse wave is: A. zero в. \( \pi / 4 \) c. \( \pi / 2 \) D.
3
Physics
If \( \cos 2 B=\frac{\cos (A+C)}{\cos (A-C)}, \) then \( \tan A, \tan B, \tan C \) are in A. \( A . P . \) в. \( G . P \) c. \( H . P \) D. None of these
2
Maths
If brakes are applied all of a sudden in a moving car, passengers automatically lean forward is an example of inertia in motion: Type 1 for true and 0 for false
3
Physics
The principal is Rs. \( 1000, \) so if you pay off Rs. \( 500, \) the remaining Rs. 500 left to repay is also called the A. interest B. Ioan c. principal D. rate
2
Maths
The inductive reactance of a choke coil of \( 1 / 4 \pi m H \) in an \( A C \) circuit of \( 50 H z \) will be A. 25 ohm B. 0.25 ohm c. 0.025 ohm D. 2.5 ohm
3
Physics
Which one of the following is a matching pair? A. Lub-sharp closure of AV valves at the begining of ventricular systole B. Dup-sudden opening of semilunar valves at the begining of ventricular diastole C. Pulsation of the radial artery-valves in the blood vessels D. Initiation of the heart beat-Purkinje fibres
0
Biology
Find the total number of possible structural isomers of the compound \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} C l_{4}\right] \)
1
Chemistry
If three sides of a triangle are respectively equal to three sides of another triangle, then the triangles are: A. unequal B. equilateral c. congruent D. none of these
2
Maths
The valency of an atom is equal to its combining capacity. A. True B. False
1
Chemistry
In the middle of the depletion layer of a reverse biased \( p-n \) junction, the A. Potential is zero B. Potential is maximum c. Electric field is maximum D. Electric field is zero
3
Physics
In which stage DNA replication takes place? A. Metaphase B. \( G_{1} \) -phase c. \( S \) - phase D. \( G_{2} \) -phase
0
Biology
A heavy block of length \( b \) and height \( h \) is placed at rest on a rough inclined plane of inclination \( \theta \) with the horizontal, as shown in figure. (a) The normal reaction from the surface cannot pass through the centre mass.Why? (b) If \( \mu \) is the coefficient of friction between the block and the inclined plane, then discuss the conditions of translational and rational equilibrium of the block. A heavy block is placed at rest on a rough inclined plane.
3
Physics
Rod-shaped elongated sclereids found in the seed coats of pulses are known as A. Astrosclereids B. Macrosclereids c. Trichosclereids D. Brachysclereids
0
Biology
\( C_{2} H_{4}+H_{2} \stackrel{N i / P d}{\longrightarrow} C_{2} H_{6} \) name of this reaction is: A. substitution B. hydrogenation c. alkanes formation D. dehydrohalogenation
1
Chemistry
If \( x \) and \( y \) are complex numbers, then system of equations \( (1+i) x+(1- \) \( \boldsymbol{i}) \boldsymbol{y}=1,2 i \boldsymbol{x}+2 \boldsymbol{y}=1+\boldsymbol{i} \) has A. unique solution B. no solution c. infinite numbers of solution D. none of these
2
Maths
Is it possible to define the matrix \( A+B \) when A has 3 rows and \( \mathrm{B} \) has 2 columns
2
Maths
All the organism uses oxygen to produce energy except A. Humans B. Mango tree c. clostridium D. Pseudomonas
0
Biology
What will be \( \angle X O Y \) if arc \( A B= \) arc \( X Y \) and \( \angle A O B=60^{\circ} ? \) \( A \cdot 30^{\circ} \) B. \( 45^{\circ} \) \( c \cdot 50^{\circ} \) D. 60
2
Maths
Materials which allow only larger currents to flow through them are A. Insulators B. Semi-conductors c. conductors D. Alloys
3
Physics
Which type of rain can cause soil pollution? A. Acid rain B. Tropical rain c. Temperate rain D. All of these
1
Chemistry
Molar heat capacity of water in equilibrium with ice at constant pressure is: A. zero B. \( \infty \) c. \( 40.45 k J K^{-1} \) mol\( ^{-1} \) D. \( 75.48 J K^{-1} \mathrm{mol}^{-1} \)
1
Chemistry
The area included between the parabolas \( y^{2}=4 x \) and \( x^{2}=4 y \) is A \( \cdot \frac{8}{3} \) sq unit B. 8 sq unit c. \( \frac{16}{3} \) sq unit D. 12 sq unit
2
Maths
The temperature at which molecular energy is minimum on Kelvin temperature scale is called: A. Absolute Zero Temperature B. Zero Energy Temperature c. Absolute Temperature D. None of These
3
Physics
Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.
2
Maths
Which of the following values corresponds to the value of energy required to remove the second electron from the ground state of helium atom? A. 27.2 ev B. 13.6 ev c. 6.8 ev D. 54.4 ev
1
Chemistry
The rate of a chemical reaction generally increases rapidly even for small temperature increase because of a rapid increase in: A. Collision frequency B. Fraction of molecules with energies in excess of the activation energy c. Activation energy D. Average kinetic energy of molecules
1
Chemistry
Correct order of excretory organs in cockroach, earthworm and rabbits are respectively A. Skin, malpighian tubules, kidney B. Malpighian tubules, nephridia, kidney c. Nephridia, malpighian tubules, kidney D. Nephridia, kidney, green gland
0
Biology
Which of the following letters will be seem without any change in a plane mirror? A. B. T \( c \cdot L \) D.
3
Physics
Balance the following equation by ion electron method. \( Z n+B r O_{4}^{-}+O H^{-}+H_{2} O \rightarrow \) \( \left[\boldsymbol{Z n}(\boldsymbol{O H})_{4}\right]^{2-}+\boldsymbol{B r}^{-} \)
1
Chemistry
The inner lining of the kidney tubules has A. Cuboidal epithelium B. Columnar epithelium c. Squamous epithelium D. None of the above
0
Biology
Complete the following reaction: \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{O}_{3} \longrightarrow ? \)
1
Chemistry
Which of the following will give \( \boldsymbol{H}_{2} \) gas with dilute \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} ? \) A. \( M g \) в. \( Z n \) c. \( C u \) D. \( H g \)
1
Chemistry
The density of \( 85 \% \) Phosphoric acid is \( 1.70 g c m^{-3} . \) What is the volume of a solution that contains \( 17 g m \) Phosphoric acid?
1
Chemistry
Mixture of ice and water is form a A. closed system B. open system C. isolated system D. heterogeneous system
1
Chemistry
Solve the differential equation: \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{y} \tan \boldsymbol{x}=\mathbf{0} \)
2
Maths
In a \( \triangle A B C, \) let \( P \) and \( Q \) are points on \( A B \) and \( A C \) respectively sucvh that \( P Q \mid B C . \) Prove that the median \( A D \) bisects \( \boldsymbol{P} \boldsymbol{Q} \)
2
Maths
Area bounded by the lines \( y=x, x= \) \( -1, x=2 \) and \( x \) -axis is A \( \cdot \frac{5}{2} \) sq. units B. \( \frac{3}{2} \) squnits c. \( \frac{1}{2} s q \) units D. None of these
2
Maths
For the reaction of one-mole zinc dust with one more sulphuric acid in a bomb calorimeter, \( \Delta U \) and \( w \) correspond to: [Hint: In bomb calorimeter, \( \boldsymbol{w}= \) \( \mathbf{0}, \mathbf{\Delta} \boldsymbol{U}=\boldsymbol{q}(-\boldsymbol{v} e)] \) A. \( \Delta U, 0, W=0 \) в. \( \Delta U<0, W<0 \) c. \( \Delta U>0, W=0 \) D. \( \Delta U>0, W>0 \)
1
Chemistry
Which of the following is a chemical compound? A. Salt B. Iron c. oxygen D. Diamond
1
Chemistry
Fill in the blanks: \( \frac{-\mathbf{7}}{\mathbf{9}}+\ldots \ldots=3 . \) Hence find the sum of the numerator and denominator so obtained.
2
Maths
In dicot root showing secondary growth, cork is found A. External to primary cortex B. Inner to epidermis and outer to pericycle C. Outer to endodermis and inner to primary cortex D. Inner to endodermis and external to primary phloem
0
Biology
Which contains hydrogen bonds? \( \mathbf{A} \cdot H F \) в. \( H C l \) \( \mathbf{c} \cdot H B r \) D. \( H I \)
1
Chemistry
Unit of power is \( A \cdot H p \) B. Kilowatt hour c. watt D. None
3
Physics
If \( (x-1) \) divides \( m x^{3}-2 x^{2}+25 x- \) 26 with remainder \( 0, \) find the value of \( m \)
2
Maths
The rate of growth of population is proportional to the number present. If the population doubled in the last 25 years and the present population is 1 lac, when will the city have population \( 4,00,000 ? \)
2
Maths
A body of mass \( 5 k g \) is whirled in vertical circle by a string \( 1 \mathrm{m} \) long. Calculate velocity at top of the circle for just looping the vertical loop. A. \( 3.1 m / s \) в. \( 7 m / s \) \( \mathrm{c} \cdot 9 \mathrm{m} / \mathrm{s} \) D. \( 7.3 \mathrm{m} / \mathrm{s} \)
3
Physics
During every financial year, the value of a machine depreciates by \( 10 \% \). Find the original value (cost) of a machine which depreciates by Rs. 2,250 during the second year.
2
Maths
A particle starts from rest with acceleration \( 2 m s^{2}, \) The distance moved by particle in 5 sec is: A . \( 22 \mathrm{m} \) B. 28 m c. \( 25 \mathrm{m} \) D. 13 \( m \)
3
Physics
Predict the correct product when \( C l_{2} \) passed through \( \boldsymbol{H}--\boldsymbol{0}^{\mathbf{8}}--\boldsymbol{0}^{18}--\boldsymbol{H} \) solution. A \( \left.\cdot H^{+} C l^{-}+O_{2} \text { (both oxygen having } 18\right) \) B. HOCl and \( H C l O_{2} \) (all oxygen having 18 ) c. \( H C l O_{4} \) and \( H C \) ( all oxygen having 18 ) D. \( C l_{2} O \) and \( H_{2} O \) (all oxygen having 18
1
Chemistry
If a stock has \( 2 n=48 \) and scion microspore cell has \( 2 n=24 \) then root cell and the microspores will have how many chromosomes respectively? \( A \cdot 12,48 \) B. 48, 12 c. \( 24, \) 12 D. 24, 96
0
Biology
Without actual division, check whether \( \frac{47}{14} \) is terminating or not.
2
Maths
Which of the following is not a redox reaction? A. Burning of candle B. Rusting of iron c. Dissolving a saltin water D. Dissolving Zn in dil. \( H_{2} S O_{4} \)
1
Chemistry
The amplitude of vibrations measured on the Richter's scale increase by steps of about A . 10 B. 20 \( c . \) 30 D. 40
3
Physics
Give the balanced equation to prepare Nitric oxide. Which type of oxide is Nitric oxide?
1
Chemistry
During \( \beta \) -decay, the mass of atomic nucleus: A. decreases by 1 unit B. increases by 1 unitt c. decreases by 2 units D. remains unaffected
1
Chemistry
A substance of mass \( 49.53 g \) occupies \( 1.5 \mathrm{cm}^{3} \) of volume. The density of the substance (in \( g c m^{-3} \) ) with correct number of significant figures is : A. 3.3 B. 3.302 c. 3.30 D. 3.300
3
Physics
A string of length \( 0.4 \mathrm{m} \& \operatorname{mass} 10^{2} \mathrm{kg} \) is tightly clamped at its ends. The tension in the string is 1.6 N. Identical wave pulses are produced at one end at equal intervals of time, \( \Delta \) t. The minimum value of \( \Delta t \) which allows constructive interference between successive pulses is: A . \( 0.05 \mathrm{s} \) B. 0.10 s c. \( 0.20 \mathrm{s} \) D. 0.40 s
3
Physics
Which pair is not correct for the instrument used in the laboratory and their uses from the following? Instrument uses To measure the electric \( \begin{array}{ll}\text { (A) } & \text { Voltmeter }\end{array} \quad \) potential difference To measure the electric (B) \( \quad \) Ammeter \( \quad \) current To detect the presence (C) Galvanometer of current To supply the electric (D) \( \quad \) Resistor \( \quad \) energy to circuit \( A \cdot A \) B. B \( c \cdot c \) \( D \cdot D \)
3
Physics
Earth's magnetic field inside a closed iron box, as compared to that outside is A. same B. less c. more D. zero
3
Physics
The vapour pressure of two pure liquids \( A \) and \( B \) which from an ideal solution are 500 and 800 torr respectively at \( 300 K . \) A liquid solution \( A \) and \( B \) for which the mole fraction of \( A \) is 0.60 is contained in a cylinder closed by a piston on which the pressure can be varied. What will be the pressure when 1 mol of the mixture has been vaporized?
1
Chemistry
Rust forms on: A. Tin B. copper c. Iron D. Lead
1
Chemistry
Classify the following into monosaccharides and disaccharides. Ribose, 2-deoxyribose, maltose, galactose, fructose and lactose.
1
Chemistry
What is the maximum value of binding energy per nucleon? \( A \cdot 8 \mathrm{MeV} \) B. 8.8 MeV c. 7.6 Mev D. 1.1 Mev
3
Physics
Write the structural formula of the two isomers of butane.
1
Chemistry
When a wave travels through medium A. particles are transferred from one place to another B. energy is transferred in a periodic manner C. energy is transferred at a constant speed D. none of the above statements is applicable
3
Physics
the diagram shows the propagation of a wave. Which points are in same phase? \( A \cdot F \) and \( G \) B. \( C \) and \( E \) \( \mathrm{C} \cdot \mathrm{B} \) and \( \mathrm{G} \) D. \( B \) and \( F \)
3
Physics
Ammonium nitrate \( \left(N H_{4} N O_{3}\right. \) phosphorus as \( P_{2} O_{5} \) and potassium as \( K_{2} O \) is called : A . organic manure B. mixed fertilizers c. insecticides D. pesticides
1
Chemistry
The sum to \( n \) terms of the services \( \frac{3}{1^{2}}+ \) \( \frac{5}{1^{2}+2^{2}}+\frac{7}{1^{2}+2^{2}+3^{2}}+\dots \dots \) is A \( \cdot \frac{3 n}{n+1} \) В. \( \frac{6 n}{n+1} \) c. \( \frac{g n}{n+1} \) D. \( \frac{12 n}{n+1} \)
2
Maths
A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes 71 time to decrease the height of water to \( \frac{H}{\eta}(\eta> \) 1) and \( T_{2} \) time to take out the rest of 11 water. If \( T_{1}=T_{2} \) then the value of \( \eta \) is \( A \cdot 2 \) B. 4 \( c \cdot 6 \) D. 8
3
Physics
Find the differential equation of family of circles of all of radius \( 5, \) with their centres on the y-axis.
2
Maths
A reversible engine takes heat from a reservoir at \( 527^{\circ} \mathrm{C} \) and gives out heat to \( a \sin k \) at \( 127^{\circ} \) C. How many Joules/s must it take from the reservoir to perform useful mechanical work at the rate of \( 750 W ? \) A . 257.14 B. 1500 c. 457.14 D. 557.14
3
Physics
What is the maximum number of \( \boldsymbol{O}_{2} \) molecules which one haemoglobin molecule can carry?
0
Biology
Which one of the following exceeds octet rule? A \( \cdot \mathrm{NCl}_{3} \) в. PCls c. \( \mathrm{PCl}_{5} \) D. NH
1
Chemistry
Expansion of \( (3 x+2)^{3} \) is \( 27 x^{3}+8+ \) \( 18 x(3 x+2) \) A. True B. False
2
Maths
The electric and magnetic field differ in that : A. the electric lines of force are closed curves, while magnetic field lines are not B. the magnetic field lines are closed, while electric lines are not C. the electric lines can give direction of electric field, while magnetic lines cannot D. the magnetic lines can give direction of magnetic field, while electric lines cannot
3
Physics