NSEJS 2018 18th Nov Question Paper

A tiny ball of mass $$m$$ is initially at rest at height $$H$$ above a cake of uniform thickness $$h$$. At some moment the particle falls freely, touches the cake surface and then penetrates in it at such a constant rate that its speed becomes zero on just reaching the ground at the bottom of the cake. Speed of the ball at the instant it touches the cake surface and its retardation inside the cake are respectively

Two sound waves in air have wavelengths differing by $$2\ \text{m}$$ at a certain temperature $$T$$. Their notes have musical interval $$1.4$$. Period of the lower pitch note is $$20\ \text{ms}$$. Then, speed of sound in air at this temperature $$T$$ is

Two plane mirrors $$M_1$$ and $$M_2$$ have their reflecting faces inclined at $$\theta$$. Mirror $$M_1$$ receives a ray $$AB$$, reflects it at $$B$$ and sends it as $$BC$$. It is now reflected by mirror $$M_2$$ along $$CD$$, as shown in the figure. Total angular deviation $$\delta$$ suffered by the incident ray $$AB$$ is

In the adjacent figure, line $$AB$$ is parallel to screen $$S$$. A linear obstacle $$PQ$$ between the two is also parallel to both. $$AB$$, $$PQ$$ and screen $$S$$ are coplanar. A point source is carried from $$A$$ to $$B$$, along the line $$AB$$. What will happen to the size of the shadow of $$PQ$$ cast due to the point source on the screen $$S$$

Two particles $$P_1$$ and $$P_2$$ move towards origin $$O$$, along the $$X$$ and $$Y$$ axes at constant speeds $$u_1$$ and $$u_2$$ respectively as shown in the figure. At $$t=0$$, the particles $$P_1$$ and $$P_2$$ are at distances $$a$$ and $$b$$ respectively from $$O$$. Then the instantaneous distance $$s$$ between the two particles is given by the relation

An electric generator consumes some oil fuel and generates output of 25 kW. Calorific
value (amount of heat released per unit mass) of the oil fuel is 17200 kcal/kg and efficiency
(output to input ratio) of the generator is 0.25. Then, mass of the fuel consumed per hour
and electric energy generated per ton of fuel burnt are respectively

Image is obtained on a screen by keeping an object at $$25\ \text{cm}$$ and at $$40\ \text{cm}$$ in front of a concave mirror. Image in the former case is four times bigger than in the latter. Focal length of the mirror must be

A glass cube of refractive index $$1.5$$ and edge $$1\ \text{cm}$$ has a tiny black spot at its center. A circular dark sheet is to be kept symmetrically on the top surface so that the central spot is not visible from the top. Minimum radius of the circular sheet should be. Given $$\frac{1}{\sqrt2}=0.707$$, $$\frac{1}{\sqrt3}=0.577$$, $$\frac{1}{\sqrt5}=0.447$$

A metal rod of length $$L$$ at temperature $$T$$, when heated to temperature $$T'$$, expands to new length $$L'$$. These quantities are related as $$L'=L(1+\alpha[T'-T])$$ where $$\alpha$$ is a constant for that material and called as coefficient of linear expansion. Correct SI unit of $$\alpha$$ is

A paramedical staff nurse improvises a second's pendulum with time period $$2\ \text{s}$$ by fixing one end of a string of length $$L$$ to a ceiling and the other end to a heavy object of negligible size. Within $$60$$ oscillations of this pendulum, she finds that the pulse of a wounded soldier beats $$110$$ times. A symptom of bradycardia is pulse less than $$60$$ per minute and that of tachycardia is greater than $$100$$ per minute. Then the length of the string is nearly and soldier has symptoms of

Each resistance in the adjacent circuit is $$R\ \Omega$$. In order to have an integral value for equivalent resistance between $$A$$ and $$B$$, the minimum value of $$R$$ must be

A block of wood floats on water with $$\frac{3}{8}$$ of its volume above water. It is now made to float on a salt solution of relative density $$1.12$$. The fraction of its volume that remains above the salt solution now, is nearly

Suppose our scientific community had chosen force, speed and time as the fundamental mechanical quantities instead of length, mass and time respectively and they chose the respective units of magnitudes $$10\ \text{N}$$, $$100\ \text{m/s}$$ and $$\frac{1}{100}\ \text{s}$$. Then the unit of mass in their system is equivalent to in our system.

Two equally charged identical pith balls are suspended by identical massless strings as shown in the adjacent figure. If this set up is on Mercury with $$g=3.7\ \text{m/s}^2$$, Earth with $$g=9.8\ \text{m/s}^2$$ and Jupiter with $$g=24.5\ \text{m/s}^2$$, then angle $$2\theta$$ will be

Three objects of the same material coloured white, blue and black can withstand temperatures up to $$2000^\circ\text{C}$$. All these are heated to $$1500^\circ\text{C}$$ and viewed in dark. Which option is correct?

A car running with a velocity of $$30\ \text{m/s}$$ reaches midway between two vertical parallel walls separated by $$360\ \text{m}$$, when the driver sounds the horn for a moment. Speed of sound in air is $$330\ \text{m/s}$$. After blowing horn, the first three echoes will be heard by the driver respectively at

Choose correct option from the following statements from electrostatics:
(I) If two copper spheres of same radii, one hollow and the other solid are charged to
the same electrical potential, the solid sphere will have more charge.
(II) A charged body can attract another uncharged body.
(III) Electrical lines of force originating from like charges will exert a lateral force on
each other, while those originating from opposite charges can intersect each other.

Refer the adjacent circuit. The voltmeter reads $$117\ \text{V}$$ and ammeter reads $$0.13\ \text{A}$$. If the resistance of voltmeter and ammeter are $$9\ \text{k}\Omega$$ and $$0.015\ \Omega$$ respectively, the value of $$R$$ is

A bar magnet is allowed to fall freely from the same height towards a current carrying loop along its axis, as shown in the four situations I to IV. Arrows show direction of conventional current. Choose the situations in which the potential energy of the magnet coil interaction is maximum

A beaker is completely filled with water at $$4^\circ\text{C}$$. Consider statements:

I) that water will overflow if the beaker is cooled for some time  

II) that water will overflow if the beaker is heated for some time. 

Select correct option regarding I and II.

$$P^{3-}$$ has a larger radius than atom of $$P$$ because

A substance is dissolved in water, forming a $$0.5\ \text{molar}$$ solution. If $$4.0\ \text{L}$$ of solution contains $$240\ \text{g}$$ of the substance, what is the molecular mass of the substance?

A car battery was kept for charging and after getting fully charged density of the battery acid $$H_2SO_4$$ was measured and found to be $$1.28\ \text{g cm}^{-3}$$. If initial molarity of battery acid was $$4.2\ \text{M}$$ then mass percentage will be around

Element $$X$$ with atomic mass $$10$$ was allowed to react completely with element $$Y$$ of atomic mass $$20$$ to form a compound. When this compound was analysed it was found that it contains $$60\%$$ of $$X$$ and $$40\%$$ of $$Y$$ by weight. The simplest formula of this compound will be

$$4.095\times10^{24}$$ nitrogen atoms are filled in an enclosed gas cylinder of capacity two litre. The number of moles of nitrogen gas in the cylinder is

When a surface tension experiment with capillary tube is performed, water rises up to $$0.1\ \text{m}$$. If the experiment is carried out in space, water will rise in capillary tube

Deepa was studying properties of gases. She took a flask and filled it with sulphur dioxide gas, and weighed it at temperature $$T$$ and pressure $$P$$. The weight of the flask containing the gas was found to be $$W_1$$. She then flushed the flask, cleaned and filled it with methane at the same temperature and pressure. The weight of the flask containing methane was found to be $$W_2$$. She repeated the process with oxygen under the same conditions and found the weight to be $$W_3$$. The ratio of the gas masses corresponding to $$W_1$$, $$W_2$$ and $$W_3$$ is

Four gas jars filled with sulphur dioxide gas were inverted into troughs of water by
four students P, Q, R, S. The following observations and inference were reported by them.
P: Water did not enter the gas jar and sulphur dioxide is soluble in water.
Q: Water rushed into the gas jar and sulphur dioxide is soluble in water.
R: Water did not enter in the gas jar and sulphur dioxide is insoluble in water.
S: A small amount of water entered the gas jar slowly and sulphur dioxide is sparingly
soluble in water.
Then the correct set of observations and inference is reported by,

A solution of pure aluminium sulphate containing $$0.170\ \text{g}$$ of aluminium ions is treated with excess of barium hydroxide solution. Total weight of the precipitate will be

A region of one square meter area was given to each Suhas, Bobby, Sandy and Kimi in a garden. The daffodil plants grow best in the soil having a pH range of $$6.0$$ to $$6.5$$. If the soil has a pH $$4.5$$, to grow daffodils, Suhas added common salt, Bobby added sodium phosphate, Sandy added aluminium sulphate and Kimi added ammonium chloride in their allotted area. Who was successful in growing daffodil?

Electrons in the last shell of $$X$$, $$Y$$, $$W$$ and $$Z$$ are $$2$$, $$6$$, $$4$$ and $$1$$ respectively. Which of the following statement is correct?

$$W$$ g of pure coal was combusted in pure dry oxygen. The carbon dioxide gas obtained was absorbed in $$0.1\ \text{M}$$ KOH solution. The complete absorption of $$CO_2$$ required $$5\ \text{cm}^3$$ of $$0.1\ \text{M}$$ KOH. The amount of coal combusted is

Sulphur dioxide gas and ammonia gas were mixed in different proportions. The pair of gases containing same number of molecules at NTP is

A strip of iron with mass $$15.5\ \text{g}$$ is placed in a solution containing $$21.0\ \text{g}$$ copper sulphate. After some time the reaction stops. Iron strip was found to have mass $$8.5\ \text{g}$$. The mass of copper formed was found to be $$8.60\ \text{g}$$. Find the mass of ferrous sulphate formed in this reaction.

Sonu has $$N/2$$ HCl solution and Monu has $$N/10$$ HCl solution. They are asked to prepare $$2\ \text{litres}$$ of $$N/5$$ HCl solution. What volume of two solutions be mixed?

A solution P was prepared by dissolving $$6.3\ \text{g}$$ of oxalic acid in $$100\ \text{mL}$$ water. $$25\ \text{mL}$$ of this solution was taken and was further diluted to $$250\ \text{mL}$$ to prepare solution Q. What weight of NaOH in ppm will be required to neutralize $$10\ \text{mL}$$ of solution Q?

Which of the following can improve the quality of petrol?

Consider the reaction $$2KBrO_3+12H^++10e^-\rightarrow Br_2+6H_2O+2K^+$$. From above reaction the equivalent weight of $$KBrO_3$$ can be calculated as, where $$M$$ is molecular weight of $$KBrO_3$$

Shaila took about $$10\ \text{cm}^3$$ of a diluted potassium hydrogen carbonate solution in a test tube. To this solution she added few drops of universal indicator. The colour of the solution turned

Which of the following is incorrect?

Let $$AB$$ be a diameter of a circle $$C_1$$ of radius $$30\ \text{cm}$$ and with center $$O$$. Two circles $$C_2$$ and $$C_3$$ of radii $$15\ \text{cm}$$ and $$10\ \text{cm}$$ touch $$C_1$$ internally at $$A$$ and $$B$$ respectively. A fourth circle $$C_4$$ touches $$C_1$$, $$C_2$$ and $$C_3$$. What is the largest possible radius of $$C_4$$?

A $$5\times5\times5$$ cube is built using unit cubes. How many different cuboids that differ in at least one unit cube can be formed using the same number of unit cubes?

What is the largest value of the positive integer $$k$$ such that $$k$$ divides $$n^2(n^2-1)(n^2-n-2)$$ for every natural number $$n$$?

A person kept rolling a regular six faced die until one of the numbers appeared third time on the top. This happened in $$12$$th throw and the sum of all the numbers in $$12$$ throws was $$46$$. Which number appeared least number of times?

In a square $$ABCD$$, a point $$P$$ is inside the square such that $$ABP$$ is an equilateral triangle. The segment $$AP$$ cuts the diagonal $$BD$$ in $$E$$. Suppose $$AE=2$$. The area of $$ABCD$$ is

Let $$n$$ be a positive integer not divisible by $$6$$. Suppose $$n$$ has $$6$$ positive divisors. The number of positive divisors of $$9n$$ is

The value of $$\frac{\sqrt{a+x}-\sqrt{a-x}}{\sqrt{a+x}+\sqrt{a-x}}$$, when $$x=\frac{2ab}{b^2+1}$$ is

Two regular polygons of different number of sides are taken. In one of them, its sides are coloured red and diagonals are coloured green; in the other, sides are coloured green and diagonals are coloured red. Suppose there are $$103$$ red lines and $$80$$ green lines. The total number of sides the two polygons together have is

A box contains some red and some yellow balls. If one red ball is removed, one seventh of the remaining balls would be red; if one yellow ball is removed, one-sixth of the remaining balls would be red. If $$n$$ denotes the total number of balls in the box, then the sum of the digits of $$n$$ is

Let $$ABCD$$ be a rectangle. Let $$X$$ and $$Y$$ be points respectively on $$AB$$ and $$CD$$ such that $$AX\colon XB=1\colon2=CY\colon YD$$. Join $$AY$$ and $$CX$$; let $$BY$$ intersect $$CX$$ in $$K$$; let $$DX$$ intersect $$AY$$ in $$L$$. If $$\frac{m}{n}$$ denotes the ratio of the area of $$XKYL$$ to that of $$ABCD$$, then $$m+n$$ equals

Let $$ABC$$ be an equilateral triangle. The bisector of $$\angle BAC$$ meets the circumcircle of $$ABC$$ in $$D$$. Suppose $$DB+DC=4$$. The diameter of the circumcircle of $$ABC$$ is

Let $$T_k$$ denote the $$k$$th term of an arithmetic progression. Suppose there are positive integers $$m\ne n$$ such that $$T_m=\frac{1}{n}$$ and $$T_n=\frac{1}{m}$$. Then $$T_{mn}$$ equals

In a triangle $$ABC$$, let $$AD$$ be the median from $$A$$; let $$E$$ be a point on $$AD$$ such that $$AE\colon ED=1\colon2$$; and let $$BE$$ extended meet $$AC$$ in $$F$$. The ratio of $$AF/FC$$ is

If $$\sin\theta$$ and $$\cos\theta$$ are roots of the equation $$px^2+qx+r=0$$, then

For a regular $$k$$-sided polygon, let $$\alpha(k)$$ denote its interior angle. Suppose $$n>4$$ is such that $$\alpha(n-2)$$, $$\alpha(n)$$, $$\alpha(n+3)$$ form an arithmetic progression. The sum of digits of $$n$$ is

The sum of $$5$$ numbers in geometric progression is $$24$$. The sum of their reciprocals is $$6$$. The product of the terms of the geometric progression is

Digits $$a$$ and $$b$$ are such that the product of the three-digit numbers $$\overline{4a1}$$ and $$\overline{25b}$$ is divisible by $$36$$ in base ten. The number of ordered pairs $$(a,b)$$ is

The integer closest to $$\sqrt{111\ldots1-222\ldots2}$$, where there are $$2018$$ ones and $$1009$$ twos, is

In a triangle $$ABC$$, a point $$D$$ on $$AB$$ is such that $$AD\colon AB=1\colon4$$ and $$DE$$ is parallel to $$BC$$ with $$E$$ on $$AC$$. Let $$M$$ and $$N$$ be the mid points of $$DE$$ and $$BC$$ respectively. What is the ratio of the area of the quadrilateral $$BNMD$$ to that of triangle $$ABC$$?

The number of distinct integers in the collection $$\left\lfloor\frac{10^2}{1}\right\rfloor,\left\lfloor\frac{10^2}{2}\right\rfloor,\left\lfloor\frac{10^2}{3}\right\rfloor,\ldots,\left\lfloor\frac{10^2}{20}\right\rfloor$$, where $$\lfloor x\rfloor$$ denotes the largest integer not exceeding $$x$$, is

True coelom is not present in animals of

The intracellular organelle that is responsible for formation of acrosomal vesicle is

The genetically modified GM brinjal in India has been developed for

A scientist observed few cells under a microscope with following characters. 

i) Cells divided by binary fission or fragmentation, or budding. 

ii)Cells moved with the help of flagella. 

iii)Ether lipids were observed in cell membranes. 

iv) Peptidoglycans were noted in the cell walls. 

Which of the following category do the cells belong to?

Characters of acquired immunity are

Instead of using chemical fertilizers in a paddy field, a farmer thought of employing nitrogen fixation technique. Amongst the following which would be beneficial for his cause?

An action potential in the nerve fibre is produced when positive and negative charges on outside and inside of the axon membrane are reversed because

A geneticist was studying the pathway of synthesis of an amino acid X in an organism. The presence of X is a must for survival. She isolated several mutants that require X to grow and tested whether each mutant would grow when different additives P, Q, R, S and T were used. A plus sign indicates growth and a minus sign indicates inability to grow. Find out the correct sequence of additives in the biosynthetic pathway of X.

In a case of mammalian coat color, the principal gene identified is C which codes for a tyrosinase enzyme. In rabbits four different phenotypes are observed in the order Full Color > Chinchilla > Himalayan > Albino (in order of the expression of gene ‘C’ and its
alleles). In a progeny obtained after crossing two rabbits, the percentages of Chinchilla, Himalayan and Albino rabbits were $$50\%$$, $$25\%$$ and $$25\%$$ respectively. What must have been the genotypes of the parent rabbits?

It was observed in a group of tadpoles of a mutant frog reared in a laboratory that their development was arrested at a particular stage. The exact tissue that was affected by the mutation is unknown. The development was then resumed and accelerated by injecting the tadpoles with extracts prepared from various tissues of the wild type frogs.The
observations of the experiment are given below.

From the above observations, find out the tissue that is affected by the mutation.

Identify the odd ones from each group A and B based on same criterion.

A patient was administered a chemical agent called Guanfacine hydrochloride after the patient showed the symptoms like shortness of breath and headache. Guanfacine hydrochloride is a known stimulant of central $$\alpha_2$$-adrenergic receptors of the medulla regulating the sympathetic nervous system. The patient in this case must be suffering from

A bacterial double-stranded DNA molecule, $$2988\ \text{bp}$$ in length, was found to have the composition shown below. The respective values of $$X$$ and $$Y$$ are

What would be the length of a polypeptide translated from mRNA which is encoded by $$2988\ \text{bp}$$ of a bacterial gene?

A student recorded the data for five types of cells as given below.

The five cell types P, Q, R, S and T are

An environment conservation group performed a survey of some diverse locations in the country and represented it as under. Which amongst these sites should be included as a biodiversity hotspot?

A bacterium has a generation time of $$50\ \text{minutes}$$. A culture containing $$10^8$$ cells per $$\text{mL}$$ is incubated for $$300\ \text{minutes}$$. What will be the number of cells after $$300\ \text{minutes}$$?

The blood grouping system is an example of ‘multiple allelism’. In order to find out
the gene products of various gene variants, different enzymes (codes used for the purpose
of experimentation are X and Y) from four blood samples were assayed. The enzymes were
quantified and the information obtained from these experiments is given in percentages in
the following table. ‘+’ indicates presence of an enzyme and ‘-’ indicates the absence of
that enzyme from the blood sample. The standard codes for dominant and recessive alleles
are considered. Identify the blood groups of subjects and choose the correct option of their
genotypes from given options. (In table: P means present, A means absent)

In an experiment, a scientist discovered a darkly stained chromatin body on the periphery of nucleus of epithelial cells obtained from an eight year old boy. This is indicative of a particular syndrome. Find out the best possible chromosome combination of their parents from the options given below which have the highest probability of producing the child under investigation. A indicates autosome. X and Y represent the sex chromosomes.

A millionaire Mr. Jim died recently. Two women, Mary and Lou, claiming to have a child by Jim approached the police demanding a share in his wealth. Fortunately Jim's semen sample was cryopreserved. The scientists used DNA fingerprinting technique to study three highly variable chromosome regions. The results obtained are shown in the adjoining figure. After studying the DNA profile, which of the alleged heirs are children of Jim?