JEE Main > Statistics and Probability

Explore popular questions from Statistics and Probability for JEE Main. This collection covers Statistics and Probability previous year JEE Main questions hand picked by popular teachers.


Q 1.    

Correct4

Incorrect-1

The angle between straight lines whose direction cosines are {tex} \left( \frac { 1 } { 2 } , - \frac { 1 } { 2 } , \frac { 1 } { \sqrt { 2 } } \right) {/tex} and {tex} \left( \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , - \frac { 1 } { \sqrt { 3 } } \right) {/tex} is

A

{tex} \cos ^ { - 1 } \left( \frac { 2 } { \sqrt { 3 } } \right) {/tex}

B

{tex} \cos ^ { - 1 } \left( \frac { 1 } { \sqrt { 6 } } \right) {/tex}

{tex} \cos ^ { - 1 } \left( - \frac { 1 } { \sqrt { 6 } } \right) {/tex}

D

None of these

Explanation


Q 2.    

Correct4

Incorrect-1

Which one of the following is best condition for the plane {tex} a x + b y + c z + d = 0 {/tex} to intersect the {tex} x {/tex} -and {tex} y {/tex} -axis at equal angle?

{tex} | a | = | b | {/tex}

B

{tex} a = - b {/tex}

C

{tex} a = b {/tex}

D

{tex} a ^ { 2 } + b ^ { 2 } = 1 {/tex}

Explanation


Q 3.    

Correct4

Incorrect-1

The equation of a straight line parallel to the {tex} x {/tex} -axis is given by

A

{tex} \frac { x - a } { 1 } = \frac { y - b } { 1 } = \frac { z - c } { 1 } {/tex}

B

{tex} \frac { x - a } { 0 } = \frac { y - b } { 1 } = \frac { z - c } { 1 } {/tex}

C

{tex} \frac { x - a } { 0 } = \frac { y - b } { 0 } = \frac { z - c } { 1 } {/tex}

{tex} \frac { x - a } { 1 } = \frac { y - b } { 0 } = \frac { z - c } { 0 } {/tex}

Explanation


Q 4.    

Correct4

Incorrect-1

If {tex} P ( 2,3 , - 6 ) {/tex} and {tex} Q ( 3 , - 4,5 ) {/tex} are two points, the direction cosines of the line {tex} P Q {/tex} are

A

{tex} - \frac { 1 } { \sqrt { 171 } } , - \frac { 7 } { \sqrt { 177 } } , - \frac { 11 } { \sqrt { 171 } } {/tex}

{tex} \frac { 1 } { \sqrt { 171 } } , - \frac { 7 } { \sqrt { 171 } } , \frac { 11 } { \sqrt { 171 } } {/tex}

C

{tex} \frac { 1 } { \sqrt { 171 } } , \frac { 7 } { \sqrt { 171 } } , - \frac { 11 } { \sqrt { 171 } } {/tex}

D

{tex} - \frac { 7 } { \sqrt { 171 } } , - \frac { 1 } { \sqrt { 171 } } , \frac { 11 } { \sqrt { 171 } } {/tex}

Explanation


Q 5.    

Correct4

Incorrect-1

The ratio in which yz-plane divides the line joining the points {tex} A ( 3,1 , - 5 ) {/tex} and {tex} B ( 1,4 , - 6 ) {/tex} is

{tex} - 3 : 1 {/tex}

B

{tex} 3 : 1 {/tex}

C

{tex} - 1 : 3 {/tex}

D

{tex} 1 : 3 {/tex}

Explanation


Q 6.    

Correct4

Incorrect-1

A straight line is inclined to the axes of {tex} x {/tex} and {tex} z {/tex} at angles {tex} 45 ^ { \circ } {/tex} and {tex} 60 ^ { \circ } , {/tex} respectively, then the inclination of the line to the {tex} y {/tex} -axis is

A

{tex} 30 ^ { \circ } {/tex}

B

{tex} 45 ^ { \circ } {/tex}

{tex} 60 ^ { \circ } {/tex}

D

{tex} 90 ^ { \circ } {/tex}

Explanation


Q 7.    

Correct4

Incorrect-1

The angle between two diagonals of a cube is

A

{tex} \cos \theta = \sqrt { 3 } / 2 {/tex}

B

{tex} \cos \theta = 1 / \sqrt { 2 } {/tex}

{tex} \cos \theta = 1 / 3 {/tex}

D

None of these

Explanation


Q 8.    

Correct4

Incorrect-1

Given that {tex} A ( 3,2 , - 4 ) , B ( 5,4 , - 6 ) {/tex} and {tex} C ( 9,8 , - 10 ) {/tex} are collinear. The ratio in which {tex} B {/tex} divides {tex} A C {/tex} is

{tex} 1 : 2 {/tex}

B

{tex} 2 : 1 {/tex}

C

{tex} - 1 : 2 {/tex}

D

{tex} - 2:1 {/tex}

Explanation


Q 9.    

Correct4

Incorrect-1

If {tex} P _ { 1 } P _ { 2 } {/tex} is perpendicular to {tex} P _ { 2 } P _ { 3 } , {/tex} then the value of {tex} k , {/tex} where {tex} P _ { 1 } ( k , 1 , - 1 ) , P _ { 2 } ( 2 k , 0,2 ) {/tex} and {tex} P _ { 3 } ( 2 + 2 k , k , 1 ) , {/tex} is

3

B

-3

C

2

D

-2

Explanation


Q 10.    

Correct4

Incorrect-1

{tex} A {/tex} is the point {tex} ( 3,7,5 ) {/tex} and {tex} B {/tex} is the point {tex} ( - 3,2,6 ) {/tex} . The projection of {tex} A B {/tex} on the line that joins the points {tex} ( 7,9,4 ) {/tex} and {tex} ( 4,5 , - 8 ) {/tex} is

A

26

2

C

13

D

4

Explanation


Q 11.    

Correct4

Incorrect-1

The shortest distance of the point from {tex} P \left( x _ { 1 } , y _ { 1 } , z _ { 1 } \right) {/tex} on the {tex} x {/tex} -axis is equal to

A

{tex} \sqrt { x _ { 1 } ^ { 2 } + y _ { 1 } ^ { 2 } } {/tex}

B

{tex} \sqrt { x _ { 1 } ^ { 2 } + z _ { 1 } ^ { 2 } } {/tex}

{tex} \sqrt { y _ { 1 } ^ { 2 } + z _ { 1 } ^ { 2 } } {/tex}

D

None of these

Explanation


Q 12.    

Correct4

Incorrect-1

The point of intersection of the {tex} x y {/tex} -plane and the line passing through the points {tex} A = ( 3,4,1 ) {/tex} and {tex} B = ( 5,1,6 ) {/tex} are

A

{tex} \left( - \frac { 13 } { 5 } , \frac { 23 } { 5 } , 0 \right) {/tex}

{tex} \left( \frac { 13 } { 5 } , \frac { 23 } { 5 } , 0 \right) {/tex}

C

{tex} \left( \frac { 13 } { 5 } , - \frac { 23 } { 5 } , 0 \right) {/tex}

D

{tex} \left( - \frac { 13 } { 5 } , - \frac { 23 } { 5 } , 0 \right) {/tex}

Explanation



Q 13.    

Correct4

Incorrect-1

The equation of the plane containing the line {tex} \frac { x - \alpha } { l } = \frac { y - \beta } { m } = \frac { z - \gamma } { n } {/tex} is {tex} a ( x - \alpha ) + b ( y - \beta ) + c ( z - \gamma ) = 0 , {/tex} where {tex} a l + b m + c n {/tex} is equal to

A

1

B

-1

C

2

0

Explanation


Q 14.    

Correct4

Incorrect-1

The shortest distance between the two straight lines {tex} \frac { x - 4 / 3 } { 2 } = \frac { y + 6 / 5 } { 3 } = \frac { z - 3 / 2 } { 4 } {/tex} and {tex} \frac { 5 y + 6 } { 8 } = \frac { 2 z - 3 } { 9 } = \frac { 3 x - 4 } { 5 } {/tex} is

A

{tex} \sqrt { 29 } {/tex}

B

3

0

D

6{tex} \sqrt { 10 } {/tex}

Explanation


Q 15.    

Correct4

Incorrect-1

A straight line passes through the point {tex} ( 2 , - 1 , - 1 ) {/tex} . It is parallel to the plane {tex} 4 x + y + z + 2 = 0 {/tex} and is perpendicular to the line {tex} \frac { x } { 1 } = \frac { y } { - 2 } = \frac { z - 5 } { 1 } {/tex} . The equation of the straight line is

A

{tex} \frac { x - 2 } { 4 } = \frac { y + 1 } { 1 } = \frac { z + 1 } { 1 } {/tex}

B

{tex} \frac { x + 2 } { 4 } = \frac { y - 1 } { 1 } = \frac { z - 1 } { 1 } {/tex}

{tex} \frac { x - 2 } { - 1 } = \frac { y + 1 } { 1 } = \frac { z + 1 } { 3 } {/tex}

D

{tex} \frac { x + 2 } { - 1 } = \frac { y - 1 } { 1 } = \frac { z - 1 } { 3 } {/tex}

Explanation


Q 16.    

Correct4

Incorrect-1

If centre of a sphere is {tex} ( 1,4 , - 3 ) {/tex} and the radius is 3 units, then the equation of the sphere is

{tex} x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 2 x - 8 y + 6 z + 17 = 0 {/tex}

B

{tex} 2 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) - 2 x - 8 y + 6 z + 17 = 0 {/tex}

C

{tex} x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 16 y + 12 z + 17 = 0 {/tex}

D

{tex} x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 2 x + 8 y - 6 z - 17 = 0 {/tex}

Explanation


Q 17.    

Correct4

Incorrect-1

If equation of a sphere is {tex} 2 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) - 4 x - 8 y + 12 z - 7 = 0 {/tex} and one extremity of its diameter is {tex} ( 2 , - 1,1 ) , {/tex} then the other extremity of diameter of the sphere will be

A

{tex} ( 2,9 , - 13 ) {/tex}

B

{tex} ( 0,9,7 ) {/tex}

{tex} ( 0,5,7 ) {/tex}

D

{tex} ( 2,5 , - 13 ) {/tex}

Explanation


Q 18.    

Correct4

Incorrect-1

The direction cosines of the line that is perpendicular to the lines with direction cosines proportional to {tex} ( 1 , - 2 , - 2 ) , ( 0,2,1 ) {/tex} are

{tex} \left( \frac { 2 } { 3 } , - \frac { 1 } { 3 } , \frac { 2 } { 3 } \right) {/tex}

B

{tex} \left( \frac { 2 } { 3 } , \frac { - 1 } { 3 } , \frac { - 2 } { 3 } \right) {/tex}

C

{tex} \left( \frac { 2 } { 3 } , \frac { 1 } { 3 } , \frac { - 2 } { 3 } \right) {/tex}

D

{tex} \left( \frac { - 2 } { 3 } , \frac { - 1 } { 3 } , \frac { - 2 } { 3 } \right) {/tex}

Explanation


Q 19.    

Correct4

Incorrect-1

The points {tex} ( 4,7,8 ) , ( 2,3,4 ) , ( - 1 , - 2,1 ) {/tex} and {tex} ( 1,2,5 ) {/tex} are

The vertices of a parallelogram

B

Collinear

C

The vertices of a trapezium

D

Concyclic

Explanation


Q 20.    

Correct4

Incorrect-1

The equation of the plane parallel to the plane {tex} 4 x - 3 y + 2 z + 1 {/tex} {tex} = 0 {/tex} and passing through the point {tex} ( 5,1 , - 6 ) {/tex} is

{tex} 4 x - 3 y + 2 z - 5 = 0 {/tex}

B

{tex} 3 x - 4 y + 2 z - 5 = 0 {/tex}

C

{tex} 4 x - 3 y + 2 z + 5 = 0 {/tex}

D

{tex} 3 x - 4 y + 2 z + 5 = 0 {/tex}

Explanation


Q 21.    

Correct4

Incorrect-1

A plane is passed through the middle point of the segment {tex} A ( - 2,5,1 ) {/tex} and {tex} B ( 6,1,5 ) {/tex} and is perpendicular to this line. Its equation is

{tex} 2 x - y + z = 4 {/tex}

B

{tex} 2 x + y + z = 4 {/tex}

C

{tex} x - 3 y + z = 5 {/tex}

D

{tex} x - 4 y + 2 z = 5 {/tex}

Explanation


Q 22.    

Correct4

Incorrect-1

A plane meets the coordinates axes in {tex} A , B {/tex} and {tex} C {/tex} such that the centroid of the triangle {tex} A B C {/tex} is {tex} ( a , b , c ) . {/tex} The equation of the plane is

{tex} \frac { x } { a } + \frac { y } { b } + \frac { z } { c } = 3 {/tex}

B

{tex} \frac { x } { a } + \frac { y } { b } + \frac { z } { c } = 1 {/tex}

C

{tex} \frac { x } { a } + \frac { y } { b } + \frac { z } { c } = 2 {/tex}

D

None of these

Explanation


Q 23.    

Correct4

Incorrect-1

The radius of the sphere {tex} ( x + 1 ) ( x + 3 ) + ( y - 2 ) ( y - 4 ) + ( z + 1 ) {/tex} {tex} ( z + 3 ) = 0 {/tex} is

A

{tex} \sqrt { 2 } {/tex}

B

2

{tex} \sqrt { 3 } {/tex}

D

3

Explanation


Q 24.    

Correct4

Incorrect-1

The sum of the direction cosines of a straight line is

A

Zero

B

One

Constant

D

None of these

Explanation


Q 25.    

Correct4

Incorrect-1

The angle between two lines whose direction cosines are given by the equation {tex} l + m + n = 0 , P + m ^ { 2 } + n ^ { 2 } = 0 {/tex} is

{tex} \frac { \pi } { 3 } {/tex}

B

{tex} \frac { 7 \pi } { 3 } {/tex}

C

{tex} \frac { \pi } { 4 } {/tex}

D

None of these

Explanation