JEE Maths Questions

If dy/dx = y + 3 > 0 and y(0) = 2

Differentiation

If dy/dx = y + 3 > 0 and y(0) = 2, then y(ln2) is equal to

  1. -13
  2. 5
  3. 7
  4. 2

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The solution of the equation d^2y/dx^2 = e^-2x is

Differential Equation

The solution of the equation d2y/dx2 = e-2x is

  1. e-2x/4
  2. 1/4 * e-2x + cx2 + d
  3. e-2x/4 + cx + d
  4. 1/4 * e-4x + cx + d

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The integral is equal to: #03

Integration

The integral 0π √(1 + 4 sin2x/2 - 4 sinx/2) dx equals

  1. 4√3 - 4
  2. 4√3 - 4 - π/3
  3. 2π/3 - 4 - 4√3
  4. π - 4

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The integral is equal to: #02

Integration

The integral ∫(1 + x - 1/x)ex + 1/x dx  is equal to

  1. xex + 1/x + c
  2. (x + 1)ex + 1/x + c
  3. (x - 1)ex + 1/x + c
  4. -xex + 1/x + c

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If the integral ∫ (5 tan x / tan x − 2)dx = x + a ln |sin x - 2 cos x| + k

Integration

If the integral ∫ (5 tan x / tan x − 2)dx = x + a ln |sin x - 2 cos x| + k, then a is equal to

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

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If g(x) = 0∫x cos4t dt, then g(x + π) equals

Integration

If g(x) = 0x cos4t dt, then g(x + π) equals

  1. g(x) - g(π)
  2. g(x) / g(π)
  3. g(x) + g(π)
  4. g(x).g(π)

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0∫π [cot x] dx, where [.] denotes the greatest integer function

Integration

0π [cot x] dx, where [.] denotes the greatest integer function, is equal to

  1. -π/2
  2. 1
  3. -1
  4. π/2

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Let f(x) = 4 and f′(x) = 4

Limits Continuity

Let f(x) = 4 and f′(x) = 4. Then Limx→2 (xf(2) - 2f(x))/(x-2) is given by

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

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If f: R → R is a function defined by f(x) = [x] cos((2x - 1)/2)π

Limits Continuity

If f: R → R is a function defined by f(x) = [x] cos((2x - 1)/2)π, where [x] denotes the greatest integer function, then f is

  1. discontinuous only at x = 0
  2. discontinuous only at non-zero integral values of x
  3. continuous only at x = 0
  4. continuous for every real x

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Let y be an implicit function of x defined by

Differentiation

Let y be an implicit function of x defined by x2x - 2xcot y - 1 = 0. Then y′(1) equals

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

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The value of p and q for which the function

Limits Continuity

The value of p and q for which the function

f(x) = (sin(p + 1)x + sinx)/x, x < 0
f(x) = q, x = 0
f(x) = (√(x + x2) - √x)/x3/2, x > 0

is continuous for all x in R, are:

  1. p = 1/2 , q = 3/2
  2. p = -3/2 , q = 1/2
  3. p = 1/2 , q = -3/2
  4. p = 5/2 , q = 1/2

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Let f(x) be a polynomial function of second degree

Sequences Series

Let f(x) be a polynomial function of second degree. If f(1) = f(–1) and a, b, c are in A.P., then f'(a), f'(b) and f'(c) are in

  1. G.P.
  2. A.P.
  3. A.P. - G.P.
  4. H.P.

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Let the sum of the first three terms of an A.P. be 39

Sequences Series

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is

  1. 31
  2. 29.5
  3. 28
  4. 26.5

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The sum to infinity of the series 1 + 2/3 + 6/3^2 + 10/3^3

Sequences Series

The sum to infinity of the series 1 + 2/3 + 6/32 + 10/33 + ... is

  1. 2
  2. 3
  3. 4
  4. 6

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Three positive numbers form an increasing GP

Sequences Series

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is

  1. √2 + √3
  2. 2 + √3
  3. 2 - √3
  4. 3 + √2

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If 100 times the 100th term of an AP

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

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

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

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Sum of infinite number of terms in GP is 20 and sum of their square is 100

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

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If the system of linear equations x+2ay+az=0

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

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

Binomial Theorem

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

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

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If X = {4^n - 3n -1 : n ∈ N} and Y = {9(n - 1) : n ∈ N}

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

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

Binomial Theorem

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

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

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How many different words can be formed by jumbling the letters

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

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If the letters of the word SACHIN are arranged in all possible ways

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

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The number of ways in which 6 men and 5 women can dine

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

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Total number of four digit odd numbers that can be formed

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

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From 6 different novels and 3 different dictionaries

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

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If A and B are square matrices of size n × n such that

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

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Let A be a square matrix all of whose entries are integers

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

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Let P and Q be 3 × 3 matrices with P ≠ Q

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

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Let a,b be real and z be a complex number

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)

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Let z1 and z2 be two roots of the equation z^2 + az + b = 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

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If z^2 + z + 1 = 0, where z is a complex number

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

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The locus of the centre of a circle which touches the circle

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

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The vectors a and b are not perpendicular

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

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If the vectors a = i-j+2k, b = 2i+4j+k and c = ai+j+bk

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)

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

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

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If a and b are the roots of the equation x^2 - x + 1 = 0

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

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

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

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

Relations Functions

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

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

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Let W denote the words in the English dictionary

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

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A function is matched below against an interval

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

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If |z - 4/z| = 2, then the maximum value of |Z| is equal to

Complex Numbers

If |z - 4/z| = 2, then the maximum value of |Z| is equal to

  1. √3 + 1
  2. √5 + 1
  3. 2 + √2
  4. 2

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If w (≠1) is a cube root of unity and (1 + w)^7 = A + Bw

Complex Numbers

If w (≠1) is a cube root of unity and (1 + w)7 = A + Bw. Then (A, B) equals to

  1. (1, 1)
  2. (1, 0)
  3. (0, 1)
  4. (-1, 1)

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The Number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals

Complex Numbers

The Number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals

  1. 0
  2. 1
  3. 2
  4. infinity

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Let a = j - k and c = i - j - k. Then the vector b satisfying a x b + c = 0 and a.b = 3 is

Vectors

Let  a = j - k  and c = i - j - k. Then the vector b satisfying a x b + c = 0 and a.b = 3 is

  1. i - j - 2k
  2. i + j - 2k
  3. 2i - j + 2k
  4. -i + j - 2k

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If |a| = 4, |b| = 2 and the angle between a and b is π/6

Vectors

If |a| = 4, |b| = 2 and the angle between a and b is π/6, then (a × b)2 is equal to

  1. 14
  2. 16
  3. 36
  4. 48

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a, b and c are 3 vectors, such that a + b + c = 0, |a| = 1, |b| = 2|c|

Vectors

a, b and c are 3 vectors, such that a + b + c = 0, |a| = 1, |b| = 2|c|, then a.b + b.c + c.a is equal to

  1. 1
  2. 0
  3. -7
  4. 7

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Let a and b be two unit vectors. If the vectors c = a + 2b and d = 5a - 4b

Vectors

Let a and b be two unit vectors. If the vectors c = a + 2b and d = 5a - 4b are perpendicular to each other, then the angle between a and b is

  1. π/4
  2. π/6
  3. π/2
  4. π/3

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Let two numbers have arithmetic mean 9 and geometric mean 4

Quadratic Equations Sequences Series

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

  1. x2 + 18x + 16 = 0
  2. x2 - 18x - 16 = 0
  3. x2 - 18x + 16 = 0
  4. x2 + 18x - 16 = 0

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