JEE Maths Questions

Quadratic Equations

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

  1. 18 months
  2. 19 months
  3. 20 months
  4. 21 months

Quadratic Equations

If α ≠ β but α2 = 5α - 3 and β2 = 5β - 3, then the equation having α/β and β/α as its roots is

  1. 3x2 - 19x - 3 = 0
  2. 3x2 - 19x + 3 = 0
  3. x2 - 5x + 3 = 0
  4. 3x2 + 19x - 3 = 0

Quadratic Equations Sequences Series

Let a and b be roots of the equation px2 + qx + r, p ≠ 0. If p, q, r are in A.P. and 1/a + 1/b = 4, then the value of |a - b| is

  1. 2√17 / 9
  2. √61 / 9
  3. √34 / 9
  4. 2√13 / 9

Relations Functions

The domain of the function f(x) = 1/√(|x| - x) is

  1. (0,∞)
  2. (-∞,0)
  3. (-∞,∞)
  4. (-∞,∞) - {0}

Relations Functions

The function f(x) = log (x + √(x2 +1)) is

  1. an even function
  2. an odd function
  3. neither an even nor an odd function
  4. a periodic function

Relations Functions

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

  1. not symmetric
  2. transitive
  3. reflexive
  4. a function

Relations Functions

If a ϵ R and the equation -3(x - [x])2 + 2(x - [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval

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

Sets

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is

  1. 510
  2. 256
  3. 275
  4. 219

Sets

If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then

  1. B = C
  2. A = C
  3. A ∩ B = φ
  4. A = B

Relations Functions

A function f from the set of natural numbers to integers defined by

f(n) = (n-1)/2, when n is odd

f(n) = -n/2, when n is even

  1. one-­one and onto both
  2. one-­one and but not onto
  3. neither one-­one nor onto
  4. onto but not one-­one

Relations Functions

For real x, let f(x) = x3 + 5x + 1, then

  1. f is one-one and onto R
  2. f is onto R but not one-one
  3. f is neither one-one nor onto R
  4. f is one-one but not onto R

Complex Numbers

If ((1 + i)/(1 - i))x = 1, then

  1. x = 4n, where n is any positive integer.
  2. x = 2n, where n is any positive integer.
  3. x = 4n + 1, where n is any positive integer.
  4. x = 2n + 1, where n is any positive integer.

Complex Numbers

If |z - 4| < |z - 2|, its solution is given by

  1. Re(z) > 3
  2. Re(z) > 0
  3. Re(z) < 0
  4. Re(z) > 2

Quadratic Equations

If (1 – p) is a root of quadratic equation x2 + px + (1 – p) = 0, then its roots are

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

Quadratic Equations

If a, b, c are distinct +ve real numbers and a2 + b2 + c2 = 1, then ab + bc + ca is

  1. greater than 1
  2. equal to 1
  3. less than 1
  4. any real number

Matrices Determinants

If  A2 – A + I = 0, then the inverse of A is

  1. A - I
  2. A
  3. I + A
  4. I - A

Permutation Combination

Number greater than 1000 but less than 4000 is formed using the digits 0, 2, 3, 4 when repetition allowed is

  1. 105
  2. 125
  3. 128
  4. 625

Mathematical Induction

Let S(k) = 1 + 3 + 5 + .. + (2k – 1) = 3 + k2 . Then which of the following is true?

  1. principle of mathematical induction can be used to prove the formula
  2. S(k) implies S(k + 1)
  3. S(k) implies S(k - 1)
  4. S(1) is correct

Limits Continuity

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

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

Differentiation

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uniform acceleration f. Let α be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time

  1. t = (u sin α)/f
  2. t = (f cos α)/u
  3. t = (u sin α)
  4. t = (u cos α)/f

Integration

010π |sin x| dx is

  1. 8
  2. 10
  3. 18
  4. 20

Integration

The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x-axis is

  1. 3
  2. 6
  3. 9
  4. 12

Differential Equation

The order and degree of the differential equation (1 + 3dy/dx)2/3 = 4d3y/dx3 are

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

Statistics

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

  1. 74
  2. 65
  3. 68
  4. 73

Statistics

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then median of the new set

  1. is two times the original median
  2. is increased by 2
  3. remains the same as that of the original set
  4. is decreased by 2

Probability

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is

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

Probability

Events A, B, C are mutually exclusive events such that P(A) = (3x + 1)/3, P(B) = (x - 1)/4, P(C) = (1 - 2x)/4. The set of possible values of x are in the interval

  1. [1/3, 1/2]
  2. [1/3, 13/3]
  3. [0, 1]
  4. [1/3, 2/3]

Trigonometry

The number of solution of tan x + sec x = 2 cos x in [0, 2π) is

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

Mathematical Reasoning

The negation of the statement "If I become a teacher, then I will open a school" is

  1. I will not become a teacher or I will open a school
  2. Either I will not become a teacher or I will not open a school
  3. Neither I will become a teacher nor I will open a school
  4. I will become a teacher and I will not open a school

Coordinate Geometry

A triangle with vertices (4, 0), (-1, -1), (3, 5) is

  1. right angled but not isosceles
  2. neither right angled nor isosceles
  3. isosceles and right angled
  4. isosceles but not right angled

Coordinate Geometry

If the two circles (x-1)2 + (y-3)2 = r2 and x2 + y2 - 8x + 2y + 8 = 0 intersect in two distinct point, then

  1. 2 < r < 8
  2. r = 2
  3. r > 2
  4. r < 2

3D Geometry

A plane which passes through the point (3, 2, 0) and the line (x-4)/1 = (y-7)/5 = (z-4)/4 is

  1. 2x - y + z = 5
  2. x + 2y - z = 1
  3. x - y + z = 1
  4. x + y + z = 5

Permutation Combination

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is:

  1. 1880
  2. 1120
  3. 1240
  4. 1960

Complex Numbers

If 2+3i is one of the roots of the equation 2x3 – 9x2 + kx – 13 = 0, k ∈ R, then the real root of this equation:

  1. does not exist
  2. exists and is equal to 1/2
  3. exists and is equal to -1/2
  4. exists and is equal to 1

Progressions

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. 26.5
  2. 28
  3. 29.5
  4. 31

Binomial Theorem

If the coefficients of the three successive terms in the binomial expansion of (1+x)n are in the ratio 1:7:42, then the first of these terms in the expansion is:

  1. 6th
  2. 7th
  3. 8th
  4. 9th

Quadratic Equations

What is the sum of the squares of the roots of the equation x2 + 2x - 143 = 0?

  1. 170
  2. 180
  3. 190
  4. 290

Quadratic Equations

If the difference between the roots of ax2 + bx + c = 0 is 1, then which one of the following is correct?

  1. b2 = a(a + 4c)
  2. a2 = b(b + 4c)
  3. a2 = c(a + 4c)
  4. b2 = a(b + 4c)

Quadratic Equations

If α and β are the roots of the equation x2 - q(1+x) - r = 0, then what is (1+α)(1+β) equal to?

  1. 1 - r
  2. q - r
  3. 1 + r
  4. q + r

Matrices Determinants

If \( A = \begin{bmatrix}1 & 2 \\2 & 3 \end{bmatrix} \) and \( B = \begin{bmatrix}1 & 0 \\1 & 0 \end{bmatrix} \) then what is determinant of AB?

  1. 0
  2. 1
  3. 10
  4. 20

Matrices Determinants

A and B are two matrices such that AB = A and BA = B then what is B2 equal to?

  1. B
  2. A
  3. I
  4. -I

Progressions

If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

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

Coordinate Geometry

Let P be the point on the parabola, y2 = 8x which is at a minimum distance from the centre C of the circle, x2 + (y + 6)2 = 1. Then the equation of the circle, passing through C and having its centre at P is:

  1. x2 + y2 – x + 4y – 12 = 0
  2. x2 + y2 – x/4 + 2y – 24 = 0
  3. x2 + y2 – 4x + 9y + 18 = 0
  4. x2 + y2 – 4x + 8y + 12 = 0

Matrices Determinants

The system of linear equations
x + λy – z = 0
λx – y – z = 0
x + y – λz = 0
has a non-trivial solution for:

  1. exactly one value of λ.
  2. exactly two values of λ.
  3. exactly three values of λ.
  4. infinitely many values of λ.

Coordinate Geometry

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal half of the distance between its foci, is:

  1. 4/√3
  2. 2/√3
  3. √3
  4. 4/3

Statistics

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

  1. 3a2 – 32a + 84 = 0
  2. 3a2 – 34a + 91 = 0
  3. 3a2 – 23a + 44 = 0
  4. 3a2 – 26a + 55 = 0

Integration

The integral \( \int \dfrac{2x^{12}+5x^9}{(x^5+x^3+1)^3} dx \) is equal to:

  1. \( \dfrac{-x^5}{(x^5+x^3+1)^2} + C \)
  2. \( \dfrac{x^{10}}{2(x^5+x^3+1)^2} + C \)
  3. \( \dfrac{x^5}{2(x^5+x^3+1)^2} + C \)
  4. \( \dfrac{-x^{10}}{2(x^5+x^3+1)^2} + C \)

3D Geometry

If the line, (x-3)/2 = (y+2)/-1 = (z+4)/3, lies in the plane, lx + my – z = 9, then l2 + m2 is equal to:

  1. 18
  2. 5
  3. 2
  4. 26

Trigonometry

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation
cosx + cos2x + cos3x + cos4x = 0 is:

  1. 5
  2. 7
  3. 9
  4. 3