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November 21st, 2017, 04:15 PM
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Re: Sample Papers of Karunya Entrance Exam

Here I am providing syllabus and question paper of Karunya Entrance Exam (KEE) for your reference:

Karunya Entrance Exam (KEE) Syllabus:

MATHEMATICS:
Applications of Matrices and Determinants:
Adjoint, inverse – properties, computation of inverses, solution of system of linear equations
bymatrix inversion method. Rank of a matrix – elementary transformation on a matrix, Cramer’srule, non-homogeneous equations, homogeneous linear system and rank method.

Complex Numbers:
Complex number system - conjugate, properties, ordered pair representation. Modulus –
Properties, geometrical representation, polar form, principal value, conjugate, sum, difference,product, quotient, vector interpretation, solutions of polynomial equations, De Moivre’s theoremand its applications.Roots of a complex number – nth roots, cube roots, fourth roots.

Analytical Geometry of two dimensions:
Definition of a conic – general equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity. Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms- Directrix, Focusand Latus rectum - parametric form of conics and chords. – Tangents and normals – Cartesian form and parametric form- equation of chord of contact of tangents from a point (x1 ,y1 ) to allthe above said curves. Asymptotes, Rectangular hyperbola – Standard equation of a rectangularhyperbola.

Vector Algebra:
Scalar Product – angle between two vectors, properties of scalar product and applications of dotproducts. Vector product right handed and left handed systems, properties of vector product andapplications of cross product - Product of three vectors – Scalar triple product, properties ofscalar triple product, vector triple Product.

Differential Calculus:
Derivative as a rate measurer - rate of change, velocity, acceleration, related rates, derivative as ameasure of slope, tangent, normal and angle between curves, maxima and minima. Mean valuetheorem - Rolle’s Theorem, Lagrange Mean Value Theorem, Taylor’s and Maclaurin’s series, L’Hospital’s Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexityand points of inflexion.

Integral Calculus and its Applications:
Simple definite integrals – fundamental theorems of calculus, properties of definite integrals.
Reduction formulae – reduction formulae for ∫ sinnx dx and ∫ cosnx dx , Bernoulli’s formula.
Area of bounded regions, length of the curve.

Differential Equations:
Differential equations - formation of differential equations, order and degree, solving differentialequations (1st order), variables separable, homogeneous and linear equations. Second order lineardifferential equations - second order linear differential equations with constant co-efficients,finding the particular integral if f (x) = emx, sinmx, cosmx, x, x2

Probability Distributions:
Probability – Axioms – Addition law - Conditional probability – Multiplicative law - Baye’s
Theorem - Random variable - probability density function, distribution function, mathematicalexpectation, variance Theoretical distributions - discrete distributions, Binomial, Poissondistributions- Continuous distributions, Normal distribution.

Discrete Mathematics:
Mathematical logic – logical statements, connectives, truth tables, logical equivalence, tautology.

Groups:
Binary operations, semigroups, monoids, groups, order of a group, order of an element, properties of groups.


Karunya Entrance Exam (KEE)Sample Question Paper

PHYSICS:

2. A dipole is placed in a uniform electric field with its axis parallel to the field. It experiences
(a) Only a net force
(b) Only a torque
(c) Both a net force and torque
(d) Neither a net force nor a torque
3. A charge of 60 C passes through an electric lamp in 2 minutes. Then the current in lamp is
(a) 30 A
(b) 1 A
(c) 0.5 A
(d) 5 A
4. Peltier coefficient at a junction of a thermocouple depends on
(a) The current in the thermocouple
(b) The time for which current flows
(c) The temperature of the junction
(d) The charge that passes through the thermocouple
5. A coil of area of cross section 0.5 m2 with 10 turns is in a plane which is perpendicular to an uniform magnetic field of 0.2 Wb m-2. The flux through the coil is
(a) 100 Wb
(b) 10 Wb
(c) 1 Wb
(d) Zero
6. The self inductance of a straight conductor is
(a) Zero
(b) Infinity
(c) Very large
(d) Very small
7. If the wavelength of the light is reduced to one fourth, then the amount of scattering is
(a) Increased by 16 times
(b) Decreased by 16 times
(c) Increased by 256 times
(d) Decreased by 256 times
8. The first excitation potential energy or the minimum energy required to excite the atom from ground state of hydrogen atom is
(a) 13.6 eV
(b) 10.2 eV
(c) 3.4 eV
(d) 1.89 eV
9. X-ray is
(a) Phenomenon of conversion of kinetic energy into radiation
(b) Conversion of momentum
(c) Conversion of energy into mass
(d) Principle of conversation of charge
10. Calculate the de Broglie wave length of an electron of kinetic energy 120 eV.
(a) 11.21 Å
(b) 1.121 Å
(c) 112.1 Å
(d) 1121 Å
11. The nuclear radius of 4Be8 nucleus is
(a) 1.3 fm
(b) 2.6 fm
(c) 13 pm
(d) 26 pm
12. The explosion of atom bomb is based on the principle of
(a) Uncontrolled fission reaction
(b) Controlled fission reaction
(c) Fusion reaction
(d) Thermonuclear reaction
13. Avalanche breakdown is primarily dependent on the phenomenon of
(a) Collision
(b) Ionization
(c) Doping
(d) Recombination
14. According to the laws of Boolean algebra, the expression (A+AB) is equal to
(a) A
(b) B
(c) AB
(d) BA
15. In amplitude modulation, the band width is
(a) Equal to the signal frequency
(b) Twice the signal frequency
(c) Thrice the signal frequency
(d) Four times the signal frequency

CHEMISTRY
1. Sommerfield’s theory suggests _____ orbits for atomic structure.
(a) Spherical (b) circular (c) elliptical (d) dumb-bell
2. In filling u of electrons in orbitals, electrons will pair up only when all the available
orbitals have at least one electron each. This is called _____.
(a) Afbau’s principle (b) Pauli’s exclusion principle (c) Hund’s rule (d) Sommerfield’s theory
3. Octet rule is deviated in _____.
4. The imperfect crystallization with a few atoms missed in the crystal lattice is called _____.
(a) Sckottky defect (b) Frenkel defect (c) Screw dislocation (d) Fresnel defect
5. A sample of Strontium–90 is found to have decayed to one – eighth of its original amount
after 87.3 years. What is the half life of Strontium–90?
(a) 40 years (b) 35.6 years (c) 29.1 years (d) 43.6 years
6. The Arrhenius equation is ____.
(a) k = A. eRT/tQ (b) k = A. eRT/Ea (c) k = A. eEa/RT (d) k = A. e-Ea/RT
8. The IUPAC name of the following compound is ____.
(a) 4,5-Dimethylhexan-2-one (b) 1,2-Dimethylhexan-4-one (c) 4,5-Dimethylpentan-2- one (d) 1,2-Dimethylpentan-3-one
9. One of the following compound forms a Schiff’s base. Indentify the compound.
(a) Alcohol (b) ether (c) aldehyde (d) ester
10. In Rosenmund reduction, the catalyst used is _____.
(a) Pd/Ba(NO3)2 (b) Pd/CuSO4 (c) Ni/Pt (d) Pd/BaSO4
11. The carbonyl group can be converted into a –CH2– group by ______ reduction.
(a) Catalytic (b) Clemmenson (c) Wolf-Kishner (d) Rosenmund
12. Carbylamine reaction is associated with ____.
(a) Urea (b) aniline (c) benzophenone (d) benzaldehyde
13. Aromatic nitrocompounds are ___.
(a) Yellow in color (b) blue in color (c) pleasant in smell (d) highly volatile
14. Addition of Conc. Sulphuric acid to glucose leads to ____.
(a) gluconic acid (b) glutaric acid (c) charring of glucose (d) explosion
15. All the amino acids in the human body are ___ .
(a) D-amino acids (b) L-amino acids (c) DL-amino acids (d) deoxy amino acids

GENERAL APTITUDE
1. Find the missing number in the series 54, 49, ___, 39, 34
a. 47 b. 44 c. 45 d. 46
2. SCD, TEF, UGH, ____, WKL
a. CMN b. UJI c. VIJ d. IJT
3. Here are some words translated from an artificial language
moolokarn means blue sky
wilkospadi means bicycle race
moolowilko means blue bicycle
Which word could mean “racecar”
a. wilkozwet b. spadiwilko c. haploch d. spadivolo
Find the necessary part of the underlined word.
4. HARVEST
a. autumn b. stockpile c. tractor d. crop
Find out the correct words for the following
5. ORDAIN
a. arrange b. command c. contribute d. establish
6. ADAGE
a. advice b. proverb c. enlargement d. advantage
7. BEHEST
a. behaviour b. hold down c. hold up d. relieve
8. Two bus tickets from city A to B and three tickets from city A to C cost `. 77. But three tickets from city A to B and tow tickets from city A to C cost `. 73. What are the fares for cities B and C from A?
a. Rs. 4, & Rs. 23 b. Rs. 13, & Rs. 17 c. Rs.15, & Rs. 14 d. Rs. 17, & Rs. 13
9. What least value must be assigned to * so that the number 197*5462 is divisible by 9?
a. 2 b. 4 c. 6 d. 8
10. As ‘wheel’ is related to ‘Vehicle’ similarly ‘clock’ is related to what?
a. Needle b. Nail c. Stick d. None of these
11. Blueberries cost more than strawberries
Blueberries cost less than raspberries
Raspberries cost more than both strawberries and blueberries
If the first tow statements are true, the third statement is
a. True b. False c. Uncertain d. None
12. A, B, C, D, and E play a game of cards. A says to B, “If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has. “A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have?
a. 22 b. 23 c. 25 d. 35
13. King : Throne, Rider: ?
a. Seat b. Horse c. Saddle d. Chair
14. Find the next letter of the following series J, F, M, A, M, J, J _______
a. J b. A c. S d. O
15. Find the first number in the series : ……….19, 23, 29, 31
a. 12 b. 15 c. 16 d. 17
Attached Files
File Type: pdf Karunya Entrance Exam (KEE) Syllabus.pdf (146.4 KB, 70 views)


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