JEE Questions

Sequences Series

If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150th term of this AP is

  1. 0
  2. 150
  3. -150
  4. 150 times its 50th term

Sequences Series

Fifth term of a GP is 2, then the product of its 9 terms is

  1. 128
  2. 256
  3. 512
  4. 1024

Sequences Series

Sum of infinite number of terms in GP is 20 and sum of their square is 100. The common ratio of GP is

  1. 1/5
  2. 3/5
  3. 8/5
  4. 5

Matrices Determinants Sequences Series

If the system of linear equations x + 2ay + az = 0, x + 3by + bz = 0, x + 4cy + cz = 0 has a non-­zero solution, then a, b, c

  1. satisfy a + 2b + 3c
  2. are in G.P
  3. are in A.P
  4. are in H.P

Binomial Theorem

The positive integer just greater than (1 + .0001)10000 is

  1. 2
  2. 3
  3. 4
  4. 5

Binomial Theorem Sets

If X = {4n - 3n -1 : n ∈ N} and Y = {9(n - 1) : n ∈ N}, where N is the set of natural numbers, then X ∪ Y is equal to

  1. Y
  2. Y - X
  3. X
  4. N

Binomial Theorem

The coefficient of x7 in the expansion of (1 - x - x2 + x3)6 is

  1. 132
  2. -132
  3. 144
  4. -144

Permutation Combination

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

  1. 6 . 7 . 8C4
  2. 7 . 6C4 . 8C4
  3. 8 . 6C4 . 7C4
  4. 6 . 8 . 7C4

Permutation Combination

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

  1. 600
  2. 601
  3. 602
  4. 603

Permutation Combination

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

  1. 5! x 6!
  2. 5! x 4!
  3. 7! x 5!
  4. 30

Permutation Combination

Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 are

  1. 216
  2. 375
  3. 400
  4. 720

Permutation Combination

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is

  1. at least 750 but less than 1000
  2. at least 500 but less than 750
  3. less than 500
  4. at least 1000

Matrices Determinants

If A and B are square matrices of size n × n such that A2 – B2 = (A – B)(A + B), then which of the following will be always true?

  1. either A or B is an identity matrix
  2. either A or B is a zero matrix
  3. AB = BA
  4. A = B

Matrices Determinants

Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

  1. If det A = ± 1, then A-1 exists and all its entries are integers
  2. If det A = ± 1, then A-1 exists and all its entries are non-integers
  3. If det A = ± 1, then A-1 exists and all its entries are not necessarily integers
  4. If det A = ± 1, then A-1 need not exist

Matrices Determinants

Let P and Q be 3 × 3 matrices with P ≠ Q. If P3 = Q3 and P2Q = Q2P, then determinant of (P2 + Q2) is equal to

  1. 0
  2. 1
  3. -1
  4. -2

Complex Numbers

Let a,b be real and z be a complex number. If z2 + az + b = 0 has two distinct roots on the line Re(z) = 1, then it is necessary that

  1. |b| = 1
  2. b ∈ (0,1)
  3. b ∈ (1,∞)
  4. b ∈ (-1,0)

Complex Numbers

Let z1 and z2 be two roots of the equation z2 + az + b = 0, z being complex further, assume that the origin, z1 and z2 form an equilateral triangle, then

  1. a2 = 4b
  2. a2 = 3b
  3. a2 = 2b
  4. a2 = b

Complex Numbers

If z2 + z + 1 = 0, where z is a complex number, then the value of

(z + 1/z)2 + (z2 + 1/z2)2 + ... + (z6 + 1/z6)2

  1. 6
  2. 12
  3. 18
  4. 54

Complex Numbers Coordinate Geometry

The locus of the centre of a circle which touches the circle |z - z1| = a and |z - z2| = b externaly (z, z1 & z2 are complex numbers) will be

  1. a hyperbola
  2. an ellipse
  3. a circle
  4. a straight line

Vectors

The vectors a and b are not perpendicular and c and d are two vectors satisfying: b x c = b x d and a.d = 0. Then the vector d is equal to

  1. b - (b.c/a.d)c
  2. c + (a.c/a.b)b
  3. c - (a.c/a.b)b
  4. b - (b.c/a.d)c

Vectors

If the vectors a = i - j + 2k, b = 2i + 4j + k and c = ai + j + bk are mutually orthogonal, then (a,b) =

  1. (-2,3)
  2. (3,-2)
  3. (-3,2)
  4. (2,-3)

Quadratic Equations

If p and q are the roots of the equation x2 + px + q = 0, then

  1. p = 1, q = -2
  2. p = -2, q = 1
  3. p = -2, q = 0
  4. p = 0, q = 1

Quadratic Equations

If a and b are the roots of the equation x2 - x + 1 = 0, then a2009 + b2009 is equal to

  1. -2
  2. 2
  3. -1
  4. 1

Quadratic Equations

The equation esinx – e-sinx – 4 = 0 has

  1. Infinite number of real roots
  2. No real roots
  3. Exactly one real root
  4. Exactly four real roots

Relations Functions

The domain of sin-1[log3(x/3)] is

  1. [-9, -1]
  2. [-9, 1]
  3. [-1,9]
  4. [1, 9]

Relations Functions

Let W denote the words in the English dictionary. Define the relation R by:

R = {(x, y) ε W × W | the words x and y have at least one letter in common}. Then R is

  1. reflexive, symmetric and not transitive
  2. reflexive, symmetric and transitive
  3. not reflexive, symmetric and transitive
  4. reflexive, not symmetric and transitive

Relations Functions

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

  1. (-∞,1/3] ; 3x2 - 2x + 1
  2. [2,∞) ; 2x3 - 3x2 -12x + 6
  3. (-∞,∞) ; x3 - 3x2 + 3x + 3
  4. (-∞,-4] ; x3 + 6x2 + 6

Communication Systems

If fm is the modulation frequency in FM, the modulation index is proportional to

  1. fm
  2. 1/fm2
  3. fm2
  4. 1/fm

Communication Systems

What should be the minimum length of the antenna capable of emitting audio signal of wavelength λ?

  1. λ
  2. λ/2
  3. λ/4
  4. λ/8

Communication Systems

If the band width is 1.6 x 1012 Hz, how many communication channels can be obtained with 16 KHz band width radio signal?

  1. 108
  2. 1011
  3. 1010
  4. 1015

Communication Systems

An insulator used in a transmission line has dielectric constant equal to 0.25. What is the velocity factor of the transmission line?

  1. 2
  2. 4
  3. 4/3
  4. 3/4

Communication Systems

A T.V. tower has a height 200 m. By how much the height of tower be increased to triple its coverage range?

  1. 1800 m
  2. 1600 m
  3. 800 m
  4. 600 m

Electronic Devices

The combination of gates shown below yields

  1. NAND gate
  2. NOT gate
  3. XOR gate
  4. OR gate

Electronic Devices

A strip of copper and another germanium are cooled from room temperature to 80 K. The resistance of

  1. each of these decreases
  2. each of these increases
  3. copper strip increases and that of germanium decreases
  4. copper strip decreases and that of germanium increases

Matter & Atoms

If N0 is the original mass of the substance of half-life period t1/2 = 5 years, then the amount of substance left after 15 years is

  1. N0/16
  2. N0/8
  3. N0/4
  4. N0/2

Matter & Atoms

If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is

  1. 0 eV
  2. 3.4 eV
  3. 6.8 eV
  4. 10.2 eV

Matter & Atoms

The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately

  1. 220 nm
  2. 310 nm
  3. 400 nm
  4. 540 nm

Matter & Atoms

The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc = 1240 eV.nm)

  1. 1.41 eV
  2. 1.51 eV
  3. 1.68 eV
  4. 3.09 eV

Matter & Atoms

Energy required for the electron excitation in Li++ from the first to the third Bohr orbit is

  1. 12.1 eV
  2. 12.4 eV
  3. 36.3 eV
  4. 108.8 eV

Matter & Atoms EM Waves

If a source of power 4 kW produces 1020 photons/second, the radiation belongs to a part of the spectrum called

  1. microwaves
  2. X rays
  3. γ rays
  4. ultraviolet rays

Electrostatics

A charged oil drop is suspended in a uniform field of 3×104 v/m so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge = 9.9×10-15 kg and g = 10 m/s2)

  1. 1.6 X 10-18
  2. 3.2 X 10-18
  3. 3.3 X 10-18
  4. 4.8 X 10-18

Optics

Diameter of a plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is 2 × 108 m/s, the focal length of the lens is:

  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 30 cm

Optics

Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of Polaroid through 30° makes the two beams appear equally bright. If the initial intensities of the two beams are IA and IB respectively, then IA/IB equals:

  1. 1
  2. 3
  3. 3/2
  4. 1/3

Optics

A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is

  1. (1/10) m/s
  2. (1/15) m/s
  3. 10 m/s
  4. 15 m/s

Optics

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in young’s double-slit experiment is

  1. infinite
  2. five
  3. three
  4. zero

Optics

If two mirrors are kept at 60° to each other, then the number of images formed by them is

  1. 5
  2. 6
  3. 7
  4. 8

Optics

Let the x - z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has refractive index of √2 and medium 2 with z < 0 has a refractive index of √3. A ray of light in medium 1 given by the vector A = 6√3i + 8√3j - 10k in incident on the plane of separation. The angle of refraction in medium 2 is

  1. 75°
  2. 60°
  3. 45°
  4. 30°

EM Waves

An electromagnetic wave of frequency v = 3.0 MHz passes from vacuum into a dielectric medium with permittivity ∈ = 4.0. Then

  1. wave length is double and frequency becomes half
  2. wave length is double and the frequency remains unchanged
  3. wave length is halved and frequency remains unchanged
  4. wave length and frequency both remain unchanged

EMI AC

A boat is moving due east in a region where the earth's magnetic field is 5.0 × 10-5 NA-1m-1 due north and horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 ms-1, the magnitude of the induced emf is

  1. 0.15 mV
  2. 0.50 mV
  3. 0.75 mV
  4. 1 mV

EMI AC

A resistor 'R' and 2μF capacitor in series is connected through a switch to 20 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5s after the switch has been closed. (log102.5 = 0.4)

  1. 2.7 x 106 Ω
  2. 1.3 x 104 Ω
  3. 1.7 x 105 Ω
  4. 3.3 x 107 Ω