JEE Questions

Consider 5 independent Bernoulli's trials each with probability of success P. If the probability of at least one failure is greater than or equal to 31/32, then P lies in the interval

(3/4,11/2]
(11/2,1]
(1/2,3/4]
[0,1/2]

Three numbers are chosen at random without replacement

Probability

Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is

Assuming the balls to be identical except for difference in colours

Probability

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

One ticket is selected at random from 50 tickets numbered

Probability

One ticket is selected at random from 50 tickets numbered 00, 01, 02, ... , 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals

1/7
1/14
5/14
1/50

Five horses are in a race. Mr.A selects two of the horses

Probability

Five horses are in a race. Mr.A selects two of the horses at random and bets on them. The probability that Mr.A selected the winning horse is

If the mean deviation about the median of the numbers

If the mean deviation about the median of the numbers a, 2a, ..., 50a is 50, then |a| equals

The average marks of boys in class is 52 and that of girls is 42

Statistics

The average marks of boys in class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

If the mean deviation of the numbers 1, 1+d, 1+2d, ... , 1+100d

If the mean deviation of the numbers 1, 1 + d, 1 + 2d, ... , 1 + 100d from their mean is 255, then the d is equal to

10
10.1
20
20.2

In a frequency distribution, the mean and median are 21 and 22

Statistics

In a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

25.5
24.0
22.0
20.5

The angle between the lines whose direction cosines satisfy

3D Geometry

The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l² + m² + n² = 0 is

π/2
π/3
π/4
π/6

If the lines (x-1)/2 = (y+1)/2 = (z-1)/4 and (x-3)/1 = (y-k)/2 = z/1

3D Geometry

If the lines (x - 1)/2 = (y + 1)/2 = (z - 1)/4 and (x - 3)/1 = (y - k)/2 = z/1 intersect, then k is equal to

9/2
2/9
-1
0

If the angle between the line x = (y - 1)/2 = (z - 3)/λ and the plane

3D Geometry

If the angle between the line x = (y - 1)/2 = (z - 3)/λ and the plane x + 2y + 3z = 4 is cos^-1(5/14) then λ is equal to

A line AB in three-dimensional space makes angles 45° and 120°

3D Geometry

A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals

30°
45°
60°
75°

Let the line (x - 2)/3 = (y - 1)/-5 = (z - 2)/2 lie in the plane

3D Geometry

Let the line (x - 2)/3 = (y - 1)/-5 = (z - 2)/2 lie in the plane x + 3y - αz + β = 0. Then (α, β) equals

(-5, 5)
(5, -15)
(-6, 7)
(6, -17)

The distance of the point (1,0,2) from the point of intersection

3D Geometry

The distance of the point (1,0,2) from the point of intersection of the line (x - 2)/3 = (y + 1)/4 = (z - 2)/12 and the plane x - y + z = 16 is

13
8
3√21
2√14

Let P be the point on the parabola, y^2 = 8x

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

The locus of the foot of perpendicular drawn from the center

Coordinate Geometry

The locus of the foot of perpendicular drawn from the center of the ellipse x² + 3y² = 6 on any tangent to it is

(x² - y²)² = 6x² + 2y²
(x² - y²)² = 6x² - 2y²
(x² + y²)² = 6x² - 2y²
(x² + y²)² = 6x² + 2y²

An ellipse is drawn by taking a diameter of the circle (x - 1) + y = 1

Coordinate Geometry

An ellipse is drawn by taking a diameter of the circle (x - 1) + y = 1 as its semi-minor axis and a diameter of the circle x² + (y - 2)² = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

x² + 4y² = 8
4x² + y² = 4
x² + 4y² = 16
4x² + y² = 8

The slope of the line touching both the parabolas

Coordinate Geometry

The slope of the line touching both the parabolas y² = 4x and x² = -32y is

The eccentricity of the hyperbola whose length of the latus rectum

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:

4/√3
√3
4/3
2/√3

Let O be the vertex and Q be any point on the parabola, x^2 = 8y

Coordinate Geometry

Let O be the vertex and Q be any point on the parabola, x² = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is

x² = y
y² = x
x² = 2y
y² = 2x

Let a, b, c and d be non-zero numbers

Coordinate Geometry

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes then

3bc - 2ad = 0
3bc + 2ad = 0
2bc + 3ad = 0
2bc - 3ad = 0

If the pair of straight lines x^2 - 2pxy - y^2 = 0

Coordinate Geometry

If the pair of straight lines x² - 2pxy - y² = 0 and x² - 2qxy - y² = 0 be such that each pair bisects the angle between the other pair, then

pq = -1
p = -q
pq = 1
p = q

The shortest distance between the line y - x = 1 and curve

Coordinate Geometry

The shortest distance between the line y - x = 1 and curve y = x² is

√3/4
4/√3
8/3√2
3√2/8

If the line 2x + y = k passes through the point which divides

Coordinate Geometry

If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3:2, then k equals

5
6
29/5
11/5

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle

Coordinate Geometry

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is

x² + y² + 2x + 2y = 47
x² + y² + 2x - 2y = 47
x² + y² - 2x + 2y = 62
x² + y² - 2x + 2y = 47

The two circles x^2 + y^2 = ax and x^2 + y^2 = c^2

Coordinate Geometry

The two circles x² + y² = ax and x² + y² = c² (c > 0) touch each other if

a = 2c
|a| = 2c
|a| = c
2|a| = c

The differential equation which represents the family of curves

Differential Equation

The differential equation which represents the family of curves y = c₁e^c₂x where c₁ and c₂ are arbitrary constants, is

yy'' = y'
y'' = y'y
y' = y²
yy'' = (y')²

Let y(x) be the solution of the differential equation

Differential Equation

Let y(x) be the solution of the differential equation (x log x)(dy/dx) + y = 2x log(x), (x≥1). Then y(e) is equal to

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

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

Differential Equation

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

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

The integral is equal to: #03

Integration

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

4√3 - 4
4√3 - 4 - π/3
2π/3 - 4 - 4√3
π - 4

The integral is equal to: #02

Integration

The integral ∫(1 + x - 1/x)e^{x + 1/x} dx is equal to

xe^{x + 1/x} + c
(x + 1)e^{x + 1/x} + c
(x - 1)e^{x + 1/x} + c
-xe^{x + 1/x} + c

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
2
-2
1

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

Integration

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

g(x) - g(π)
g(x) / g(π)
g(x) + g(π)
g(x).g(π)

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

Integration

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

-π/2
1
-1
π/2

Let f(x) = 4 and f′(x) = 4

Limits Continuity

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

-4
2
-2
3

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

discontinuous only at x = 0
discontinuous only at non-zero integral values of x
continuous only at x = 0
continuous for every real x

Let y be an implicit function of x defined by

Differentiation

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

-1
1
-log 2
log 2

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)/x^3/2, x > 0

is continuous for all x in R, are:

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

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

G.P.
A.P.
A.P. - G.P.
H.P.

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

31
29.5
28
26.5

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

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