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

- 0
- 150
- -150
- 150 times its 50
^{th}term

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

- 128
- 256
- 512
- 1024

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

- 1/5
- 3/5
- 8/5
- 5

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

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

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

- 2
- 3
- 4
- 5

If X = {4^{n} - 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

- Y
- Y - X
- X
- N

The coefficient of x^{7} in the expansion of (1 - x - x^{2} + x^{3})^{6} is

- 132
- -132
- 144
- -144

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

- 6 . 7 .
^{8}C_{4} - 7 .
^{6}C_{4}.^{8}C_{4} - 8 .
^{6}C_{4}.^{7}C_{4} - 6 . 8 .
^{7}C_{4}

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

- 600
- 601
- 602
- 603

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

- 5! x 6!
- 5! x 4!
- 7! x 5!
- 30

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

- 216
- 375
- 400
- 720

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

- at least 750 but less than 1000
- at least 500 but less than 750
- less than 500
- at least 1000

If A and B are square matrices of size n × n such that A^{2} – B^{2} = (A – B)(A + B), then which of the following will be always true?

- either A or B is an identity matrix
- either A or B is a zero matrix
- AB = BA
- A = B

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

- If det A = ± 1, then A
^{-1}exists and all its entries are integers - If det A = ± 1, then A
^{-1}exists and all its entries are non-integers - If det A = ± 1, then A
^{-1}exists and all its entries are not necessarily integers - If det A = ± 1, then A
^{-1}need not exist

Let P and Q be 3 × 3 matrices with P ≠ Q. If P^{3} = Q^{3} and P^{2}Q = Q^{2}P, then determinant of (P^{2} + Q^{2}) is equal to

- 0
- 1
- -1
- -2

Let a,b be real and z be a complex number. If z^{2} + az + b = 0 has two distinct roots on the line Re(z) = 1, then it is necessary that

- |b| = 1
- b ∈ (0,1)
- b ∈ (1,∞)
- b ∈ (-1,0)

Let z_{1} and z_{2} be two roots of the equation z^{2} + az + b = 0, z being complex further, assume that the origin, z_{1} and z_{2} form an equilateral triangle, then

- a
^{2}= 4b - a
^{2}= 3b - a
^{2}= 2b - a
^{2}= b

If z^{2} + z + 1 = 0, where z is a complex number, then the value of

(z + 1/z)^{2} + (z^{2} + 1/z^{2})^{2} + ... + (z^{6} + 1/z^{6})^{2}

- 6
- 12
- 18
- 54

The locus of the centre of a circle which touches the circle |z - z_{1}| = a and |z - z_{2}| = b externaly (z, z_{1} & z_{2} are complex numbers) will be

- a hyperbola
- an ellipse
- a circle
- a straight line

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

- b - (b.c/a.d)c
- c + (a.c/a.b)b
- c - (a.c/a.b)b
- b - (b.c/a.d)c

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

- (-2,3)
- (3,-2)
- (-3,2)
- (2,-3)

If p and q are the roots of the equation x^{2} + px + q = 0, then

- p = 1, q = -2
- p = -2, q = 1
- p = -2, q = 0
- p = 0, q = 1

If a and b are the roots of the equation x^{2} - x + 1 = 0, then a^{2009} + b^{2009} is equal to

- -2
- 2
- -1
- 1

The equation e^{sinx} – e^{-sinx} – 4 = 0 has

- Infinite number of real roots
- No real roots
- Exactly one real root
- Exactly four real roots

The domain of sin^{-1}[log_{3}(x/3)] is

- [-9, -1]
- [-9, 1]
- [-1,9]
- [1, 9]

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

- reflexive, symmetric and not transitive
- reflexive, symmetric and transitive
- not reflexive, symmetric and transitive
- reflexive, not symmetric and transitive

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

- (-∞,1/3] ; 3x
^{2}- 2x + 1 - [2,∞) ; 2x
^{3}- 3x^{2}-12x + 6 - (-∞,∞) ; x
^{3}- 3x^{2}+ 3x + 3 - (-∞,-4] ; x
^{3}+ 6x^{2}+ 6

If f_{m} is the modulation frequency in FM, the modulation index is proportional to

- f
_{m} - 1/f
_{m}^{2} - f
_{m}^{2} - 1/f
_{m}

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

- λ
- λ/2
- λ/4
- λ/8

If the band width is 1.6 x 10^{12} Hz, how many communication channels can be obtained with 16 KHz band width radio signal?

- 10
^{8} - 10
^{11} - 10
^{10} - 10
^{15}

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

- 2
- 4
- 4/3
- 3/4

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

- 1800 m
- 1600 m
- 800 m
- 600 m

The combination of gates shown below yields

- NAND gate
- NOT gate
- XOR gate
- OR gate

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

- each of these decreases
- each of these increases
- copper strip increases and that of germanium decreases
- copper strip decreases and that of germanium increases

If N_{0} is the original mass of the substance of half-life period t_{1/2} = 5 years, then the amount of substance left after 15 years is

- N
_{0}/16 - N
_{0}/8 - N
_{0}/4 - N
_{0}/2

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

- 0 eV
- 3.4 eV
- 6.8 eV
- 10.2 eV

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

- 220 nm
- 310 nm
- 400 nm
- 540 nm

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)

- 1.41 eV
- 1.51 eV
- 1.68 eV
- 3.09 eV

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

- 12.1 eV
- 12.4 eV
- 36.3 eV
- 108.8 eV

If a source of power 4 kW produces 10^{20} photons/second, the radiation belongs to a part of the spectrum called

- microwaves
- X rays
- γ rays
- ultraviolet rays

A charged oil drop is suspended in a uniform field of 3×10^{4} 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/s^{2})

- 1.6 X 10
^{-18} - 3.2 X 10
^{-18} - 3.3 X 10
^{-18} - 4.8 X 10
^{-18}

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 × 10^{8} m/s, the focal length of the lens is:

- 10 cm
- 15 cm
- 20 cm
- 30 cm

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 I_{A} and I_{B} respectively, then I_{A}/I_{B} equals:

- 1
- 3
- 3/2
- 1/3

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

- (1/10) m/s
- (1/15) m/s
- 10 m/s
- 15 m/s

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

- infinite
- five
- three
- zero

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

- 5
- 6
- 7
- 8

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

- 75°
- 60°
- 45°
- 30°

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

- wave length is double and frequency becomes half
- wave length is double and the frequency remains unchanged
- wave length is halved and frequency remains unchanged
- wave length and frequency both remain unchanged

A boat is moving due east in a region where the earth's magnetic field is 5.0 × 10^{-5} NA^{-1}m^{-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

- 0.15 mV
- 0.50 mV
- 0.75 mV
- 1 mV

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. (log_{10}2.5 = 0.4)

- 2.7 x 10
^{6}Ω - 1.3 x 10
^{4}Ω - 1.7 x 10
^{5}Ω - 3.3 x 10
^{7}Ω