JEE Questions

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