NSEJS 2019 17th Nov Question Paper

Let $$\alpha$$ and $$\beta$$ be the roots of $$x^2 - 5x + 3 = 0$$ with $$\alpha > \beta$$. If $$a_n = \alpha^n - \beta^n$$ for $$n \ge 1$$, then the value of $$\frac{3a_6+a_8}{a_7}$$ is

The number of triples $$(x,y,z)$$ such that any one of these numbers is added to the product of the other two and the result is $$2$$ is

In rectangle ABCD, $$AB=5$$ and $$BC=3$$. Points F and G are on the line segment CD so that $$DF=1$$ and $$GC=2$$. Lines AF and BG intersect at E. What is the area of AEB?

In the given figure, two concentric circles are shown with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of quadrilateral ABCD?

How many positive integers N give a remainder $$8$$ when $$2008$$ is divided by N?

What is the product of all the roots of the equation $$\sqrt{5|x|+8}$$=$$\sqrt{x^2-16}$$?

LCM of two numbers is $$5775$$. Which of the following cannot be their HCF?

If $$a,b,c$$ are distinct real numbers such that $$a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}$$, evaluate $$abc$$.

If the equation $$(\alpha^2-5\alpha+6)x^2+(\alpha^2-3\alpha+2)x+(\alpha^2-4)=0$$ has more than two roots, then the value of $$\alpha$$ is

Mr. X with his eight children of different ages is on a family trip. His oldest child, who is 9 years old saw a license plate with a 4-digit number in which each of two digits appear two times. The number is evenly divisible by the age of each child, and the last two digits happen to be Mr. X's age. Which of the following is not the age of one of Mr. X's children?

How many numbers lie between 11 and 1111 which divided by 9 leave a remainder 6 and when divided by 21 leave a remainder 12?

Two unbiased dice are rolled. What is the probability of getting a sum which is neither 7 nor 11?

The solution of the equation $$1+4+7+\cdots+x=925$$ is

If $$\tan\theta+\sec\theta=1.5$$, then the value of $$\sin\theta$$ is

An observer standing at the top of a tower finds that the angle of elevation of a red bulb on the top of a light house of height $$H$$ is $$\alpha$$. Further, he finds that the angle of depression of the reflection of the bulb in the ocean is $$\beta$$. Therefore, the height of the tower is

The sum of the roots of $$\frac{1}{x+a}+\frac{1}{x+b}=\frac{1}{c}$$ is zero. The product of roots is

In the convex quadrilateral ABCD, the diagonals AC and BD meet at O and the measure of angle AOB is $$30^\circ$$. If the areas of triangles AOB, BOC, COD and AOD are 1, 2, 8 and 4 square units respectively, what is the product of the lengths of diagonals AC and DB in square units?

If $$\sin^2x+\sin^2y+\sin^2z=0$$, then which of the following is NOT a possible value of $$\cos x+\cos y+\cos z$$?

Find the remainder when $$x^{51}$$ is divided by $$x^2-3x+2$$.

In an equilateral triangle, three coins of radii 1 unit each are kept so that they touch each other and also sides of the triangle. The area of triangle ABC in square units is

Gymnosperms are called naked seed bearing plants because they lack

In case of mice coat colour, two genes are responsible for colour of the hair. Gene ‘A’ is responsible for distribution of pigments on shaft of hair. Wild type allele of ‘A’ produces a yellow band on dark hair shaft (agouti), whereas recessive allele produces no yellow band. There is another allele of A, known as $$A^Y$$, which is embryonic lethal in homozygous condition only. In an experiment, two yellow mice were crossed to obtain a progeny of 6 pups. What would be the most probable number of agouti mice among them?

A stain was developed by a group of scientists to stain a particular cell organelle. The stain was tested on various tissues derived from an autopsy sample from a mammal. The organelles were counted. The results showed maximum number of the organelles in cells of brain, lesser in cells of heart, least in mature sperms and absent in erythrocytes. Identify the organelles from following options.

Pinus sylvestris grows at low temperatures in Russia. The plant survives under such freezing conditions due to the presence of

In an experimental setup, certain pathogen caused a disease in primates with nasal congestion, sore throat and fever being the common symptoms. The scientists injected an extract from blue-green mold as the first line of action. However, the symptoms did not subside. The possible causative agents of the disease were listed out as follows.
i. a virus   ii. a fungus    iii. a conjugation deficient bacterium    iv. a tapeworm
Choose the correct option from the following that indicate the pathogen.

An organism has 27 pairs of homologous chromosomes. In each daughter cell after mitosis and in each gamete after after completion meiosis II, ______ and ______ chromosomes would be present respectively?

A group of students was studying development of an organism under controlled laboratory conditions. Following observations were made by them.
i. The larvae had a rod-like supporting structure that separated the nervous system and the gut.
ii. A prominent central cavity was present in the transverse section of the part of the nervous system of the larvae; while the adults had cerebral ganglia as the main component of the nervous system.
iii. The eyes were prominently seen in larvae.
iv. The tails were absent in the adults, which the larvae had.
v. A lot of phagocytic activity was observed before conversion of larvae into adults.
vi. The adults had a cuticular exoskeleton.
The organism under study must be belonging to:

A process is represented in the adjacent figure. The arrows indicate the flow of a biochemical reaction. The arrowhead points to the product and the base of the arrow indicates the template biomolecule. What do P, Q, R and S represent?

The whooping cranes were on the verge of extinction with only 21 individuals in wild in 1941. After conservation measures, the cranes are now included in the endangered category by IUCN. The highlight of the conservation efforts is the reintroduction of the whooping cranes in wild. This was possible due to raising of the young cranes in absence of their parents by biologists dressed in crane costumes. Aircraft Guided bird migration technique was used for teaching the captive-bred cranes to follow the scientists to learn the migratory route. What type of animal behaviour might be responsible for these captive-bred cranes to follow the crane costume dressed scientists?

In the baking industry, when the dough is prepared, various ingredients are mixed together with the flour. At one instance, the dough was fermented, but failed to rise sufficiently during the baking process. Choose the correct cause(s) from following possibilities.
i. The salt was mixed before the fermentation process was completed
ii. The sugar was added in excess
iii. Yeast granules were not activated prior to mixing with the flour.

Given four statements, identify which are false. 

I. Prokaryotic cells are unicellular while eukaryotes are multicellular. 

II. Histones are present in eukaryotes and absent in prokaryotes.

III. The nucleoid contains genetic material in prokaryotes and eukaryotes. 

IV. Prokaryotic flagellum is composed of flagellin while eukaryotic flagellum is composed of tubulin.

The students of a college were working on regeneration using Planaria (Platyhelminthes) and Asterias (Echinodermata). Planaria was cut in three pieces, namely, a piece with head, with tail and the middle piece. Asterias (bearing five arms) was cut in such a way that after separation, six pieces were obtained, namely, an arm with a portion of the central disc, four pieces cut from tips of each of the remaining arms and the remaining body. The animals were allowed to regenerate completely. How many Planaria and Asterias respectively will be obtained after the completion of regeneration in both?

Fecundity in animal world is the maximum possible ability of an individual to produce offsprings during its entire lifetime. Following factors were checked for their effect on fecundity of different animal models.
i. Availability of food during breeding season
ii. Mode of fertilization
iii. Population density
Which of these factor(s) can regulate fecundity?

Rahul sprayed a chemical X on a plant with rosette habit. After a few days, the internodal distances increased suddenly. The chemical X might be

In case of peppered moths, pale and dark moths are observed. Pale variety is known to be the wild type variety. During industrial revolution, industrial melanism led to prevalence of dark variety around the cities and pale variety continued to be in majority in areas away from the industries. After enforcement of regulations for controlling pollution, reappearance of pale moths in majority was observed around cities again. Driving force(s) for these adaptive changes is/are:
i. Increased pollution around industries
ii. A stable transposition of a gene in moths
iii. Limitations of the vision of birds to differentiate dark moths on darkened barks and pale moths in presence of lichens
iv. Ability of lichens to grow on barks in less polluted areas only.

Any damage or injury to a particular area causes nociceptors to release some chemicals, which carry the signal to the higher centres in the nervous system for the processing and a subsequent action. However, there is a difference in the way in which the stimulus is received which is related to the acuity of the detection. Fingertips are more sensitive as compared to the forearm. Following reasons for the observed phenomenon were suggested.
i. The receptive fields in the fingertip are smaller
ii. The number of nociceptors per receptive field in the forearm is lesser
iii. The amount of prostaglandins released by the nociceptors per receptive field is more in fingertips
The most probable reason(s) for this may be:

Plants with leathery leaves with thick cuticle, vivipary, salt glands, apogeotropic roots and stomata limited to the abaxial surface were observed. The plants might be

Rate of photosynthesis in hydrophytes depends on various parameters. The adjacent graph shows the effect of one parameter on the rate of photosynthesis. Identify the parameter plotted along the X axis.

A $$4\,\mu\text{m}$$ long bacterial cell was magnified and drawn to a dimension of $$6\text{ cm}$$. How many times has it been magnified?

Four different human body fluid samples were subjected to quantification of hydrogen ion concentration. mEq/L is the unit of measurement for hydrogen ion concentration. The results of the experiment were as follows:
Sample A is $$1.6\times10^2$$ units, sample B is $$4.5\times10^{-5}$$ units, 

sample C is $$1\times10^{-3}$$ units and sample D is $$3\times10^{-2}$$ units. 

Identify the samples in sequence from A to D.

Four grams of a mixture of calcium carbonate and sand is treated with excess HCl and $$0.880\text{ g}$$ of carbon dioxide is produced. What is the percentage of calcium carbonate in the original mixture?

How many sigma bonds are present between any two carbon atoms in fullerenes?

Gammaxene insecticide powder is prepared by the reaction shown in the adjacent figure. If $$78\text{ g}$$ of benzene reacts with $$106.5\text{ g}$$ of chlorine, how much Gammaxene is formed?

An element Y is a white translucent solid at room temperature and exhibits various allotropic forms. Some compounds of Y find application in agriculture. Y forms two solid oxides which dissolve in water to form comparatively weak acids. The element Y is

A student was studying reactions of metals with dilute NaOH at room temperature. The student took dilute NaOH in four different test tubes and added copper powder to test tube A, zinc dust to test tube B, aluminium powder to test tube C and iron powder to test tube D and observed effervescence in__.

Which of the following polymeric materials will be ideal for remoulding?

A magician dipped a Rs. 50 note in a 50 percent solution of alcohol in water and held it on a burning flame, but the note did not burn. The reason behind this is-

Which of the following is isostructural with $$\mathrm{CO_2}$$?

Substance X is a white crystalline solid which melts after 10 seconds on a burner flame. It is soluble in water and insoluble in $$\mathrm{CCl_4}$$ and is a poor conductor of electricity in molten state as well as in aqueous solution. Substance X is

In a beaker, $$50\text{ ml}$$ of a normal HCl solution was taken and $$\mathrm{NH_3}$$ gas was passed through it. The contents were then titrated and required $$60\text{ ml}$$ of semi-normal NaOH solution. How much ammonia was passed through the beaker?

Which is the correct order of metals with reference to their melting point in increasing order?

Sodium tungstate has formula $$\mathrm{Na_2WO_4}$$ and lead phosphate has formula $$\mathrm{Pb_3(PO_4)_2}$$. The formula for lead tungstate should be

What is the ratio of reducing agent to oxidizing agent if the following reaction is correctly balanced? $$\mathrm{NH_3+O_2\rightarrow NO+H_2O}$$

Arrange the following solutions in increasing hydronium ion concentration. The solutions are (P) $$0.1\,\mathrm{M\ HCl}$$, (Q), $$0.1\,\mathrm{M\ H_2SO_4}$$, (R), $$0.001\,\mathrm{M\ NH_4OH}$$, and (S), $$0.001\,\mathrm{M\ Ca(OH)_2}$$.

The correct order will be

In one litre of pure water, $$44.4\text{ g}$$ of calcium chloride is dissolved. The number of ions in one millilitre of the resultant solution is

A zinc rod was dipped in $$100\text{ cm}^3$$ of $$1\text{ M}$$ copper chloride solution. After some time the molarity of $$\mathrm{Cu^{2+}}$$ ions was found to be $$0.8\text{ M}$$. If the zinc rod weighs $$20\text{ g}$$, the molarity of chloride ions is

When four dilute solutions of (I) vinegar, (II) common salt, (III) caustic soda and (IV) baking soda are tested with universal indicator, which is the correct observation?

Which of the following species is/are isoelectronic with Neon?
i) $$\mathrm{N^{3-}}$$ ii) $$\mathrm{Mg^{2+}}$$
iii) $$\mathrm{K^+}$$ iv) $$\mathrm{Ca^{2+}}$$

Which gases will have equal volume at STP if the weight of each gas is $$14.0\text{ g}$$? 

i) $$\mathrm{N_2O}$$  ii)$$\mathrm{NO_2}$$  iii)$$\mathrm{N_2}$$  iv)$$\mathrm{CO}$$.

Which of the following are not ionic? $$\mathrm{AlCl_3}$$, $$\mathrm{CaCl_2}$$, $$\mathrm{MgCl_2}$$ and $$\mathrm{LiCl}$$.

Apples dropping from apple trees were observed by many people before Newton. Why they fall was explained by Newton's law of universal gravitation. Which statement best describes the situation?

A rectangular metal plate shown in the adjacent figure has a charge of $$420\,\mu\text{C}$$ uniformly distributed over it. How much charge is present over the shaded area? No part of the metal plate is cut. The circles and diagonal are shown for clarity only. Take $$\pi=\frac{22}{7}$$.

In the adjacent circuit, the voltages across AD, BD and CD are $$2\text{ V}$$, $$6\text{ V}$$ and $$8\text{ V}$$ respectively. If resistance $$R_A=1\text{ k}\Omega$$, then the values of resistances $$R_B$$ and $$R_C$$ are

A new linear scale of temperature measurement is to be designed. It is called a ‘Z scale’ on which the freezing and boiling points of water are $$20 Z$$ and $$220 Z$$ respectively. What will be the temperature shown on the ‘Z scale’ corresponding to a temperature of $$20 $$ degree on the Celsius scale?

Consider the motion of a small spherical steel body of mass m, falling freely through a long column of a fluid that opposes its motion with a force proportional to its speed. Initially the body moves down fast, but after some time attains a constant velocity known as terminal velocity. If weight mg, opposing force (Fv) and buoyant force (Fb) act on the body, then the correct equation relating these forces, after the terminal velocity is reached, is:

A piece of wire P and three identical cells are connected in series. An amount of heat is generated in a certain time interval in the wire due to passage of current. Now the circuit is modified by replacing P with another wire Q and N identical cells, all connected in series. Q is four times longer in length than P. The wire P and Q are of same material and have the same diameter. If the heat generated in second situation is also same as before in the same time interval, then find N.

Some waveforms among I, II, III and IV superpose to produce waveforms P, Q, R and S. Match the resultant waveforms with the corresponding superpositions.

At any instant, the total energy of a simple pendulum is the sum of kinetic energy $$\frac12mv^2$$ and potential energy $$\frac12kx^2$$. The amplitude is $$10\text{ cm}$$ and total energy is $$4\text{ mJ}$$. Find k.

At any instant of time, the total energy (E) of a simple pendulum is equal to the sum of its kinetic energy $$(\frac12mv^2)$$ and potential energy ($$\frac12kx^2$$), where, m is the mass, v is the velocity, x is the displacement of the bob and k is a constant for the pendulum. The amplitude of oscillation of the pendulum is 10 cm and its total energy is 4 mJ. Find k.

A rigid body of mass m is suspended from point O using an inextensible string of length L. When it is displaced through an angle $$\theta$$, what is the change in potential energy of the mass?

Refer to the adjacent figure. A variable force F is applied to a body of mass $$6\text{ kg}$$ at rest. The body moves along the x axis as shown. The speed of the body at $$x=5\text{ m}$$ and $$x=6\text{ m}$$ is

When a charged particle with charge $$q$$ and mass $$m$$ enters uniform magnetic field $$B$$ with velocity $$v$$ at right angles to $$B$$, the force on the moving particle is given by $$qvB$$. This force acts as the centripetal force making the charged particle go in a uniform circular motion with radius $$r=\frac{mv}{Bq}$$.Now if a hydrogen ion and a deuterium ion enter the magnetic field with velocities in the ratio 2:1 respectively, then the ratio of their radii will be __________.

A piece of ice is floating in water at $$4^\circ\text{C}$$ in a beaker. When the ice melts completely, the water level in the beaker will

In a screw-nut assembly (shown below) the nut is held fixed in its position and the screw is allowed to rotate inside it. A convex lens (L) of focal length 6.0 cm is fixed on the nut. An object pin (P) is attached to the screw head. The image of the object is observed on a screen Y. When the screw head is rotated through one rotation, the linear distance moved by the screw tip is 1.0 mm. The observations are made only when the image is obtained in the same orientation on the screen. At a certain position of P, the image formed is three times magnified as that of the pin height. Through how many turns should the screw head be rotated so that the image is two times magnified?

A school is located between two cliffs. When the metal bell is struck by school attendant, first echo is heard by him after $$2.4 s$$ and second echo follows after $$2.0 s$$ for him at the same position near the bell. If the velocity of sound in air is $$340 ms-1$$ at the temperature of the surroundings, then the distance between the cliffs is approximately____.

The triangular face of a crown glass prism ABC is isosceles with $$AB=AC$$. The rectangular face with edge AC is silvered. A ray is incident normally on the rectangular face with edge AB, reflects internally at AC and AB, and emerges normally through the rectangular base with edge BC. The angle BAC is

The radius of curvature of a convex mirror is x. The distance of an object from the focus of this mirror is y. What is the distance of the image from the focus?

A physics teacher and his family are travelling in a car on a highway during a severe lightning storm. Choose the correct option.

A conductor in the form of a circular loop is carrying current I. The direction of the current is as shown. Then which figure represents the correct direction of magnetic field lines on the surfaces of the planes XY and XZ. (Consider those surfaces of the XY and XZ planes which are seen in the figure.)

A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance $$S_1$$ in the first 10 seconds and $$S_2$$ in the next 10 seconds, the relation between $$S_1$$ and $$S_2$$ is

sound wave is produced by a vibrating metallic string stretched between its ends.
Four statements are given below. Some of them are correct.
(P) Sound wave is produced inside the string.
(Q) Sound wave in the string is transverse.
(R) Wavelength of the sound wave in surrounding air is equal to the wavelength of the transverse wave on the string.
(S) Loudness of sound is proportional to the square of the amplitude of the vibrating string.
Choose the correct option.