Question 1 1.25 / -0
The number 1 + 3 + 9 + … + 323 is divisible by exactly two numbers between 724 and 734. Find those two numbers.
Solution
Sum 1 + 3 + 9 + … + 3
23 = (3
24 - 1)/(3 - 1)
=
=
Since 3
12 + 1 is an even no. (odd + odd) therefore 2 will exactly divide 3
12 + 1.
Also other factors if this sum are (3
6 – 1), (3
6 + 1) i.e. 728 and 730.
Question 2 1.25 / -0
If the third and fifth terms of a geometric progression are 12 and 48 respectively, then the second term in it is
Solution
Fifth term of GP is 48
Third term of GP is 12
Second term of GP = ?
T
n = ar
n-1 T
5 = ar
s-1 48 = ar
4 48 = ar
2 - r
2 48 = 12 - r
2 r
2 =
= 4
r = 2
T
3 = ar
3-1 12 = ar
2 If r = 2 then ar
2 = 12
a (2)
2 = 12
a (4) = 12
a = 3
2
nd term, T
n = ar
n-1 T
2 = (3) (2)
2-1 T
2 = 3 (2)
1 T
2 = 6
Question 3 1.25 / -0
Which of the following is the solution of x +
=
?
Solution
x +
x
2 + 1 =
x
2x
2 + 2 = 5x
2x
2 - 5x + 2 = 0
2x
2 - 4x - x + 2 = 0
2x (x - 2) - (x - 2) = 0
(2x - 1) (x - 2) = 0
x =
and 2
Question 4 1.25 / -0
Let (1 + 2x)20 = a0 + a1 x + a2 x2 + ........... + a20 x20 . Then, 3a0 + 2a1 + 3a2 + 2a3 + 3a4 + 2a5 + ........ + 2a19 + 3a20 equals
Question 5 1.25 / -0
One of the factors of x2 – y2 + z2 – a2 + 2(xz + ay) is
Solution
x
2 - y
2 + z
2 - a
2 + 2(xz + ay)
(x
2 + z
2 + 2xz) - (y
2 + a
2 - 2ay)
(x + z)
2 - (y - a)
2 (x + z + y - a)(x + z - y + a)
The answer is x + z + y - a.
Question 6 1.25 / -0
A company situated at (2, 0) in the xy-plane charges Rs. 2 per km for delivery. A second company at (0, 3) charges Rs. 3 per km for delivery. The region of the plane where it is cheaper to use the first company is
Solution
Let (x, y) be any point
Using given condition 2
5x
2 + 5y
2 - 54y + 16x + 65 > 0
x
2 + y
2 - 10.8y + 3.2x + 13 > 0
It is a circle, radius =
Centre (-1.6, 5.4)
Hence region is exterior of (x + 1.6)
2 + (y - 5.4)
2 = 18.72.
Question 7 1.25 / -0
At what time between 10 o'clock and 11 o'clock are the two hands of a clock symmetric with respect to the vertical line (give the answer to the nearest second)?
Solution
Suppose after 'y' second, two hands of a clock become symmetric.
So, after 'y' second, angle made by hour hand with vertical = 60 -
and angle made by minute hand with vertical =
.
So, from the given question, angles are symmetric with vertical.
60 -
=
= 60
y = 553.8 second = 9 minutes 14 seconds
Hence, two hands of a clock are symmetric with respect to the vertical line at 10h 9m 14s.
Question 8 1.25 / -0
Given below are four equations in terms of x. Assume that 0 < r < 4. Which of the following equations has the largest solution for x?
Solution
from question
0 < r < 4
(1 + y)
x =
for largest value of x, y should be smallest
in y = Kr,
the value of k are
, 2 and 1
so smallest value of y =
r
largest value of x, when y =
r
so option 2 is correct.
Question 9 1.25 / -0
If x and y are real numbers such that then the value of (x + y)/(x - y) is
Solution
Suppose
= t
Then, from the question,
= 24
t = 9 = 3
2 = 3
2 =
Apply Componendo and Dividendo rule,
=
= 3
Question 10 1.25 / -0
A closed conical vessel is filled with water fully and is placed with its vertex down. The water is let out at a constant speed. After 21 minutes, it is found that the height of the water column is half of the original height. How much more time in minutes does it require to empty the vessel?
Solution
Rate of outflow of water =
litres in 21 minutes
i.e.
L in 21 minutes.
Hence
L in 3 minutes.
Question 11 1.25 / -0
Directions: A question is followed by data in the form of two statements labeled as I and II. You must decide whether the data given in the statements are sufficient to answer the question. What is the time taken by a train to cross a platform of length 50 metres? I. The speed of the train is 60 kmph. II. The length of the train is 30 meters.
Solution
The time taken by a train to cross a platform/station of any length is given by =
So in statement (1) we are given the speed of the train & in (2) length of the train is going & we required both the parameters.
So, both the statement are required together.
T =
=
=
hours
Question 12 1.25 / -0
The sides of a triangle are distinct positive integers in an arithmetic progression. If the smallest side is 10, the number of such triangles is
Solution
Since the sides are in A.P let the sides be x, x + d and x + 2d. Now since smallest side is 10 Therefore, x = 10 ⇒ sides are 10, 10 + d and 10 + 2d We know that sum of any two sides of a triangle is greater than the third side. ⇒ 20 + d > 10 + 2d ⇒ 10 + d > 2d Since, we know that the sign of d = + Therefore, we can subtract d. 10 > d ⇒ d Since the sides are positive integers. Therefore , d can hold the values 1, 2, 3 …, 9 Therefore, number of triangles which are possible is 9.
Question 13 1.25 / -0
Let a, b, x, y be real numbers such that a2 + b2 = 81, x2 + y2 = 121 and ax + by = 99. Then, the set of all possible values of ay - bx is
Solution
a
2 + b
2 = 81 ...... (i)
x
2 + y
2 = 121 ......(ii)
and (ax + by)
2 = (99)
2 = 9801 ......(iii)
Multiply equations (i) and (ii) and subtract equation (iii),
(a
2 + b
2 )(x
2 + y
2 ) - (ax + by)
2 = 81 × 121 - (99)
2 = 0
(ay - bx)
2 = 0
ay - bx = 0
Question 14 1.25 / -0
Let a, b, c, d be real numbers such that |a - b| = 2, |b - c| = 3, |c - d| = 4. Then, the sum of all possible values of |a - d| is
Solution
|a - b| = 2 ⇒ a - b = ±2 .....(i) |b - c| = 3 ⇒ b - c = ±3 .....(ii) |c - d| = 4 ⇒ c - d = ±4 .....(iii) From equation (i), (ii) and (iii) Possible values of a - d are ±9, ±5, ±3, ±1 So |a - d| = 9, 5, 3, 1 Hence sum of all the possible value = 18.
Question 15 1.25 / -0
A frog is presently located at the origin (0, 0) in the xy-plane. It always jumps from a point with integer coordinates to a point with integer coordinates moving a distance of 5 units in each jump. What is the minimum number of jumps required for the frog to go from (0, 0) to (0, 15)?
Solution
In the first jump, frog will go from (0, 0) to (4, 3) covering a distance of 5 metres.
In the second jump, frog will go from (4, 3) to (0, 6) covering a distance of 5 metres.
In the third jump, frog will go from (0, 6) to (0, 5) covering a distance of 5 metres.
Question 16 1.25 / -0
Consider two spherical planets of same average density. Planet 2 is 8 times as massive as planet 1. The ratio of the acceleration due to gravity of the second planet to that of the first is
Solution
(Mass = Density × Volume)
Now, g = Gm/r
2 From the given data,
g
2 /g
1 = 2
Question 17 1.25 / -0
Two balls are projected simultaneously with the same speed from the top of a tower, one vertically upwards and the other vertically downwards. They reach the ground in 9 s and 4 s, respectively. What is the height of the tower? (g = 10 m/s2 )
Solution
s = ut + (1/2) at
2 Take downward direction as positive.
For the first case:
h = (-u)9 +
× 10 × (9)
2 h = -9u + 405 ------1
For the second case:
h = (u)4 +
× 10 × (4)
2 h = 4u + 80 -------2
From equations 1 and 2,
-9u + 405 = 4u + 80 ⇒ u = 25 m/s
Substituting the value in equation 2,
h = 4 × 25 + 80 = 100 + 80
h = 180 m
Question 18 1.25 / -0
If the pressure exerted by a liquid column of height 7 m on the bottom of the container is 77,000 Nm–2 and g is taken as 10 ms- 2 , then the density of the liquid is
Solution
Pressure exerted by the liquid column, P = 77,000 Nm
–2 Depth or height, h = 7 m
Acceleration due to gravity, g = 10 ms
- 2 Pressure exerted by liquid column, P = h × d × g
77,000 = 7 × d × 10
77,000 = 70 × d
Or d = 1,100 kgm
–3
Question 19 1.25 / -0
A block of mass 'M' is at rest on a plane surface inclined at an angle
to the horizontal. The magnitude of force exerted by the plane on the block is
Solution
The magnitude of force exerted by the plane on the block will be Mg and components of force are Mg cos
and Mg sin
.
Question 20 1.25 / -0
What should be the speeds of two persons such that when they move uniformly towards each other, they get 3.0 m closer each second and when they move uniformly in the same direction with the original speeds, they get 3.0 m closer each 10 sec?
Solution
Let the velocities of the two persons be u and v When they are approaching each other u + v = 3 ...1 (As they get closer by 3 m in 1 sec) When they are moving in same direction u - v = 0.3 ...2 (As they get closer by 3 m in 10 sec) Adding 1 and 2 2u = 3.3 u = 1.65 m/s Hence v = 1.35 m/s
Question 21 1.25 / -0
atom disintegrates to
with a half-life of 10
9 years. In the process, it emits 7 alpha particles and 'n'
particles. Here, 'n' is
Solution
After balancing the equation, we get
From this, n = 4 particles.
Question 22 1.25 / -0
A block of mass M rests on a rough horizontal table. A steadily increasing horizontal force is applied such that the block starts to slide on the table without toppling. The force is continued even after sliding has started. Assume the coefficients of static and kinetic friction between the table and the block to be equal. The correct representation of the variation of the frictional force, f1 exerted by the table on the block with time t is given by:
Solution
Just before the block starts sliding, the acceleration will be zero. So, F - f
s = 0.
Friction after sliding is constant (static friction).
⇒ f
s = F
Friction before sliding is given by:
F - f
k = Ma (where f
k is kinetic friction)
So, the plot is given as follows:
Question 23 1.25 / -0
White light is split into a spectrum by a prism and it is seen on a screen. If we put another identical inverted prism behind it in contact, what will be seen on the screen?
Solution
The combination of both the prisms will behave like a full slab. So, there would not be any spectrum, but the light will be displaced literally.
Question 24 1.25 / -0
A new temperature scale uses X as a unit of temperature, where the numerical value of the temperature tx in this scale is related to the absolute temperature T by tx = 3T + 300. If the specific heat of a material using this unit is 1400 J kg-1 X-1 , its specific heat in the S.I. system of units is
Solution
Specific heat for t
x temperature is given by:
S
x =
= 1400 J kg
-1 X
-1 (given)
According to the question, t
x = 3T + 300
So,
Now, S at temp T in S.I. unit =
=
= 3 × S
x = 4200 J kg
-1 K
-1
Question 25 1.25 / -0
A small child tries to move a large rubber toy placed on the ground. The toy does not move but gets deformed under her pushing force (
) which is obliquely upward as shown. Then
Solution
Since toy is at rest, so a = 0.
According to Newton's second law of motion,
.
Resultant force acting on the toy will be zero.
Question 26 1.25 / -0
The Kirchoff's first and second law, where the symbols have their usual meanings, are respectively based on
Solution
Kirchhoff's first law states that at a junction, the sum of incoming currents and outgoing currents is always zero; this is in accordance with conservation of charge. Kirchhoff's second law states that the algebraic sum of all the potential differences in the loop is always zero; this is in accordance with the conservation of energy.
Question 27 1.25 / -0
The following three objects (1) a metal tray, (2) a block of wood, and (3) a woollen cap are left in a closed room overnight. Next day the temperature of each is recorded as T1 , T2 and T3 respectively. The likely situation is
Solution
All three objects (1) a metal tray, (2) a block of wood, and (3) a woollen cap will be in thermal equilibrium with the air of room. So, temperatures of the three will be same.
Question 28 1.25 / -0
A girl standing at point P on a beach wishes to reach a point Q in the sea as quickly as possible. She can run at 6 kmh
-1 on the beach and swim at 4 kmh
-1 in the sea. She should take the path
Solution
To travel from P to Q in minimum time, the shortest path has to be followed, which is path PCQ (using Pythagoras theorem).
Question 29 1.25 / -0
Light enters an isosceles right triangular prism at normal incidence through face AB and undergoes total internal reflection at face BC as shown below.
The minimum value of the refractive index of the prism is close to
Solution
Total internal reflection at BC will take place if
.
Here, angle of incidence i = 45°
Or minimum value of the refractive index
Question 30 1.25 / -0
A photon of energy 8 eV is incident on metal surface of threshold frequency 1.6 × 1015 Hz. The magnitude of kinetic energy of the photo electrons emitted (in eV) is (Take h = 6 × 10-34 Js)
Solution
From Einstein's photoelectric equation
E
k = hv - W
E
k =
- 8
E
k = 6 eV - 8 eV = - 2 eV
Question 31 1.25 / -0
The IUPAC name of acetic acid (CH3 COOH) is
Solution
The IUPAC name of acetic acid (CH3 COOH) is ethanoic acid.
Question 32 1.25 / -0
In the following reaction, what is X?
Solution
Ozone is used as a reagent in this reaction.
Ozonolysis of alkynes generally gives an acid anhydride or diketone product, not complete fragmentation as for alkenes.
Question 33 1.25 / -0
In which of the following states is carbon most electronegative?
Solution
Out of sp3 , sp and sp2 hybridised carbons, sp hybridised carbon is the most electronegative. The larger the 's' character of the atom, the closer the electrons are held to the nucleus. sp3 carbons are the least electronegative as the 'p' character forces the electrons to exist far away from the nucleus, thereby decreasing electronegativity.
Question 34 1.25 / -0
The symbol of the element, whose atoms have the outer most electronic configuration 2s2 , 2p3 is
Solution
Atoms have the outer most electronic configuration 2s2 , 2p3 has atomic number 7. Nitrogen is the element with atomic number 7.
Question 35 1.25 / -0
Two balloons, A and B, containing 0.2 moles and 0.1 moles, respectively, of helium at room temperature and 2.0 atm are connected. When equilibrium is established, the final pressure of He in the system is
Solution
Since pressures of the gases are the same in both the containers, therefore, the final pressure will not change.
Question 36 1.25 / -0
Which of the following are arranged in the decreasing order of dipole moment?
Solution
Dipole moment depends on the Electronegativity of the elements as it is the product of charge on one of the ions and distance between them. Dipole moment of CH3 Cl is gretaer than CH3 F due to more charge separation. CH3 Cl > CH3 F > CH3 Br > CH3 I
Question 37 1.25 / -0
Hydrogen bond is the strongest in
Solution
Hydrogen bonding is strongest in HF.
The strength of H ------ F > H ------ O
Question 38 1.25 / -0
Two cylinders containing carbon dioxide are connected together by a tube fitted with a tap. The capacity of one cylinder is 3 dm3 and that of the other cylinder is 2 dm3 ; the pressure of the first cylinder is 550 mm Hg and that of the second cylinder is 800 mm Hg. What will be the final pressure in the cylinders on opening the tap? (Temperature remains constant.)
Solution
New volume = 2 + 3 = 5 times
For the gas in the 1
st cylinder,
PV = P'V'
550
3 = P'
5
P' = 330 mm Hg
For the gas in the 2
nd cylinder,
PV = P'V'
800
2 = P'5
P'
= 320 mm Hg
Final pressure in the two cylinders = 320 + 330 = 650 mm Hg
Question 39 1.25 / -0
What are the products formed when sodium reacts with acetic acid?
Solution
Metals react with acids to form their corresponding salts accompanied by the release of hydrogen gas. Hence, the reaction of sodium (metal) with acetic acid gives sodium ethanoate and hydrogen gas.
Question 40 1.25 / -0
For reaction PCl3 (g) + Cl2 (g) ⇌ PCl5 (g), the value of KC at 250°C is 26 mole-1 litre-1 . The value of KP at this temperature will be
Solution
Use formula: Kp = Kc (RT)Δn Δn = 1 - (1 + 1) = -1 Now Kp = Kc [RT]-1 or Kp = 26 × [0.0821 × 523]-1 = 0.61 atm-1
Question 41 1.25 / -0
What is the weight of oxygen required for the complete combustion of 2.8 kg of ethylene?
Solution
required = 3 × 100 = 300
Mass of O
2 required = 300 × 32 = 9600 g = 9.6 kg
Question 42 1.25 / -0
Which of the following elements is least reactive to oxygen present in air at room temperature?
Solution
The reactivity of metals differs from metal to metal. The reactivity series of metals in which metals are arranged in decreasing order of reactivity is as follows: K > Na > Ca > Mg > Al > Zn > Fe > Pb > [H] > Cu > Hg > Ag > Au Gold has the least reactivity. So, it cannot react with oxygen present in the air at room temperature.
Question 43 1.25 / -0
Which of the following orders of hydrocarbon compounds is correct in terms of decrease in the acidic character?
Solution
The correct order of the hydrocarbon compounds in terms of the decrease in the acidic character is ethyne, ethene, ethane.
Question 44 1.25 / -0
In the following set of aromatic compounds, the correct order of reactivity towards Friedel-Crafts alkylation is
Solution
Reactivity towards Friedel-Crafts alkylation is proportional to electron density in the benzene ring. Among the given groups, -OCH3 is EDG and increases the electron density in the benzene ring, while -NO2 and -COOCH3 are EWG and decrease the electron density in the benzene ring. Since -NO2 group is more deactivating than -COOCH3 , therefore nitrobenzene is the least reactive towards Friedel Crafts reactions. Therefore, the correct order is: iv > ii > iii > i.
Question 45 1.25 / -0
The energy of second Bohr orbit of the hydrogen atom is - 328 kJ mol-1 ; hence the energy of fourth Bohr orbit would be
Solution
= - 82 kJ mol
-1
Question 46 1.25 / -0
The series of reactions, which results in the production of urea, is
Solution
The urea cycle (also known as the ornithine cycle) is a cycle of biochemical reactions that produces urea ((NH2 )2 CO) from ammonia (NH3 ). This cycle occurs in ureotelic organisms. The urea cycle converts highly toxic ammonia to urea for excretion.
Question 47 1.25 / -0
Direction of growth of roots in plants is an example of which tropic movement?
Solution
Roots show positive geotropism while stems show negative geotropism. Positive geotropism is the growth towards gravity.
Question 48 1.25 / -0
Which of the following is the cause of Kwashiorkor?
Solution
It occurs when enough protein is not in the diet.
Question 49 1.25 / -0
If tall (TT) is cross bred with short (tt), then what will be the characteristic(s) of the F1 plants?
Solution
We can show the cross between tall (TT) and short (tt) as follows:
Hence, all will appear tall because T is a dominant trait. So, option (1) is correct.
Question 50 1.25 / -0
Which one of the following pairs is wrongly matched?
Solution
Anthrax is caused by bacteria.
Question 51 1.25 / -0
What is the name of an antibiotic that works against bacteria?
Solution
Penicillin is an antibiotic that works against bacteria. Nystatin and fluconazole are anti-fungal agents whereas oseltamivir is an anti-viral drug.
Question 52 1.25 / -0
Total number of blood groups in the human body are
Solution
There are four main blood groups (types of blood) – A, B, AB and O. Your blood group is determined by the genes you inherit from your parents. Each group can be either RhD positive or RhD negative, which means in total there are eight main blood groups.
Question 53 1.25 / -0
If birds are moved from 30°C to 10°C, their body temperature
Solution
Birds are warm-blooded. Their body temperature remains the same irrespective of the temperature outside.
Question 54 1.25 / -0
Which of the following organelles has its own DNA and ribosome like mitochondria?
Solution
Stroma contains DNA, ribosomes and RNA also. Stroma is a structure of chloroplast.
Question 55 1.25 / -0
'On the origin of species, by means of Natural selection' was written by
Solution
'On the origin of species, by means of Natural selection' was written by Charles Darwin.
Question 56 1.25 / -0
A fish has evolved many features to help it survive in its environment. Which part of a fish protects the body?
Solution
Scales cover and provide protection to the body.
Question 57 1.25 / -0
What is the difference between flora and fauna?
Solution
The primary difference between flora and fauna is that flora talks about the plant life of a region or a certain period whereas fauna represents the wildlife of a region or specific period.
Question 58 1.25 / -0
Ram's uncle was suffering from 'diabetes' because his pancreas was not producing a hormone in a sufficient quantity. Identify the hormone.
Solution
Deficiency of insulin causes diabetes.
Question 59 1.25 / -0
In warmer weather, curd from milk forms faster because
Solution
The rate of bacterial multiplication increases in warm weather. Bacteria need warmth to multiply. In summers, the temperature is high which helps in the conversion of milk to curd.
Question 60 1.25 / -0
What is common among snakes, turtles and lizards? (1) Presence of scales (2) Presence of lungs (3) Presence of tough covering over the egg (4) Presence of a notochord
Solution
Snakes, lizards and turtles belong to class Reptilia. Animals of this class are cold-blooded, bear scales and breathe through lungs. Most of them have a three-chambered heart except crocodiles, which have four-chambered heart. They lay eggs with tough coverings. Notochord (chord – string) is a long flexible rod that provides support to the body. Animals with notochord are called chordates and without notochord are called non-chordates. Reptiles are chordates with a true vertebral column and internal skeleton.
Question 61 1.25 / -0
In a triangle ABC, the altitudes from B and C on to the opposite sides are not shorter than their respective opposite sides. Then, one of the angles of ABC is
Solution
Condition 1:If
= 90°, then
=
= 45°, to meet the required condition.
For another value of
and
, one of the sides, AB or AC is greater than the respective altitude.
Condition 2: If
90°
So, AB > BF and AC > CF
If AC > AB, we have AC > BF
Thus, the given situation is not met.
If AC = AB, again the situation is not met.
Hence, only possibility is in the case of an isosceles right-angled triangle.
Question 62 1.25 / -0
If area of a circle is decreased by 20%, its diameter, which is supposed to be 2r, is reduced to
Question 63 1.25 / -0
Working together, Bill and Tom painted a fence in 8 hours. Last year, Tom painted the fence by himself. The year before, Bill painted it by himself, but took 12 hours less than what Tom took. How long did Bill and Tom take (in hours) when each was painting alone?
Solution
Bill can do it in b hours, so he does
per hour. Tom does it in t hours, so he does
per hour.
Then, working together, they can do
per hour (since they took 8 hours working together).
We also know that Tom takes 12 hours longer than Bill, so t = b + 12.
We get:
16b + 96 = b
2 + 12b
b
2 - 4b - 96 = 0
(b - 12)(b + 8) = 0
Then, b = 12 and b = - 8. Now, b must be positive, so we'll ignore b = - 8.
Hence, Bill alone takes 12 hours and Tom alone takes 24 hours.
Question 64 1.25 / -0
If we have two cans of cold drinks as shown in the figure. Find out which of the two packing can hold large amount of drink.
Solution
Volume of A =
r
2 h
= 3.14 × 4 × 4 × 12
= 602.88 m
2 Volume of B =
r
2 h
= 3.14 × 6 × 6 × 8
= 904.32
Volume of B is greater.
Question 65 1.25 / -0
The sum of the first n terms of the series 1
2 + 2.2
2 + 3
2 + 2.4
2 + 5
2 + 2.6
2 + … is
when n is even. When n is odd the sum is:
Solution
When n is odd then n - 1 is even.
Then, sum of n - 1 terms =
And n
th term = n
2 So, sum of n term when n is even =
=
Question 66 1.25 / -0
A mass m is moving with a constant velocity along a line parallel to the x-axis, away from the origin. Its angular momentum with respect to the origin
Solution
Refer to Fig. The angular momentum of the mass at point P(x, y) about origin O is defined as
Now m and v are constants. Also y remains constant as the mass moves parallel to the x-axis.
Hence L remains constant. Thus the correct choice is (2).
Question 67 1.25 / -0
If equal volumes of two liquids with densities
1 and
2 are mixed, the new density will be _______.
Solution
The densities are different, i.e.
1 and
2 .
The density of a mixture is defined as the ratio of the total mass to the total volume.
Mass, m = Volume (V) × Density (
)
Hence, density of mixture
Question 68 1.25 / -0
A cylindrical copper rod has length L and resistance R. If it is melted and formed into another rod of length 2L, the resistance will be
Question 69 1.25 / -0
A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes an uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by
Solution
Let x be the compression of the spring. The kinetic energy of the block
is used
(i) imparting potential energy
to the spring and
(ii) doing work (= fx) against friction. Thus
⇒ 5000x
2 + 15x - 16 = 0
The two roots are
=
=
= 0.0551 m and - 0.0581 m
Since negative value of x is not permissible, x = 0.0551 m = 5.51 cm.
Question 70 1.25 / -0
If R1 and R2 are resistances of the filaments of 200 W and 100 W electric bulbs operating at 220 v, then
Solution
P
1 =
and P
2 =
R
1 =
, R
2 =
R
2 = 2R
1
Question 71 1.25 / -0
Grignard reagents are highly reactive organic compounds with general formula RMgX. When acetone is treated with RMgX, it produces a/an
Question 72 1.25 / -0
Consider the following sequence of reactions:
The end product C is
Question 73 1.25 / -0
How many isomers does C7 H7 Cl have?
Solution
Four position isomers of the molecular formula C
7 H
7 Cl are possible.
Question 74 1.25 / -0
A naturally occurring element Y is 80.99% 34 Y, 8.00% 35 Y and 11.01% 36 Y. What is the atomic weight of Y?
Solution
The Average atomic weight of Y = (80.99/100) × 34 + (8.00/100) × 35 + (11.01/100) × 36 = 34.29 u
Question 75 1.25 / -0
On ozonolysis, an alkene having the molecular formula C9 H18 gives 2, 2-dimethyl propanal and 2-butanone. The alkene is
Question 76 1.25 / -0
Independent assortment of Mendel was proved by __________.
Solution
Law of independent assortment was explained by dihybrid cross involving two traits.
Question 77 1.25 / -0
The primary function of DNA polymerase is to
Solution
DNA polymerase adds nucleotides to an existing nucleotide strand.
Question 78 1.25 / -0
Which of the following pairs of nitrogen bases consititues the purines of DNA?
Solution
These two nitrogen bases are the purines of DNA.
Question 79 1.25 / -0
A regular check on the unborn baby of a lady towards the end of her pregnancy showed a heart rate of 80 beats per minute. What would the doctor infer about the baby`s heart condition from this?
Solution
A normal fetal heart rate (FHR) usually ranges from 120 to 160 beats per minute (bpm) in the in utero period. It is measurable sonographically from around 6 weeks.
Question 80 1.25 / -0
What is the systolic and diastolic pressure of a normal human being respectively?
Solution
The systolic and diastolic pressure of normal human being is 120 mm Hg, 80 mm Hg respectively.