JEE Questions

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations

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

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

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

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

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

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

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

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

Trigonometry

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

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

Coordinate Geometry

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

right angled but not isosceles
neither right angled nor isosceles
isosceles and right angled
isosceles but not right angled

If the two circles (x-1)^2 + (y-3)^2 = r^2 and x^2 + y^2 - 8x + 2y + 8 = 0 intersect in two distinct point

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

2 < r < 8
r = 2
r > 2
r < 2

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

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

2x - y + z = 5
x + 2y - z = 1
x - y + z = 1
x + y + z = 5

The number of ways of selecting 15 teams from 15 men and 15 women

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:

1880
1120
1240
1960

If 2+3i is one of the roots of the equation 2x^3 – 9x^2 + kx – 13 = 0

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:

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

Let the sum of the first three terms of an AP be 39 and the sum of its last four terms be 178

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:

26.5
28
29.5
31

If the coefficients of the three successive terms in the binomial expansion of (1+x)^n are in the ratio 1:7:42

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:

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

Quadratic Equations

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

If the difference between the roots of ax^2 + bx + c = 0 is 1

Quadratic Equations

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

b² = a(a + 4c)
a² = b(b + 4c)
a² = c(a + 4c)
b² = a(b + 4c)

If α and β are the roots of the equation x^2 - q(1+x) - r = 0, then what is (1+α)(1+β)

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 - r
q - r
1 + r
q + r

If A and B given, then what is determinant of AB

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?

A and B are two matrices such that AB = A and BA = B then what is B^2 equal to

Matrices Determinants

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

B
A
I
-I

If the 2nd, 5th and 9th terms of a non-constant AP are in GP

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:

Let P be the point on the parabola, y^2 = 8x which is at a minimum distance

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:

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

The system of linear equations has a non-trivial solution for

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:

exactly one value of λ.
exactly two values of λ.
exactly three values of λ.
infinitely many values of λ.

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8

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: