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JEE Advanced > Vectors

Explore popular questions from Vectors for JEE Advanced. This collection covers Vectors previous year JEE Advanced questions hand picked by experienced teachers.

Q 1.

Correct4

Incorrect-1

A particle starts from rest at the origin with a constant acceleration {tex} \vec { a } = 2 \hat { i } + 8 \hat { j } - 6 \hat { k } \ \mathrm { ms } ^ { - 2 } {/tex}. Its position at {tex} t = 5 \mathrm { s } {/tex} is

{tex} ( 25 \hat { i } + 100 \hat { j } - 75 \hat { k } ) \mathrm { m } {/tex}

B

{tex} ( 25 \hat { i } - 100 \hat { j } - 75 \hat { k } ) \mathrm { m } {/tex}

C

{tex} ( 100 \hat { i } - 25 \hat { j } + 75 \hat { k } ) \mathrm { m } {/tex}

D

{tex} ( 25 \hat { i } - 100 \hat { j } + 75 \hat { k } ) \mathrm { m } {/tex}

Explanation


Q 2.

Correct4

Incorrect-1

The sum, difference and cross product of two vectors {tex} \vec { A } {/tex} and {tex} \vec { B } {/tex} are mutually perpendicular if

A

{tex} \vec { A } {/tex} and {tex} \vec { B } {/tex} are perpendicular to each other

B

{tex} \vec { A } {/tex} and {tex} \vec { B } {/tex} are perpendicular but their magnitudes are arbitrary

{tex} | \vec { A } | = | \vec { B } | {/tex} and their directions are arbitrary

D

{tex} \vec { A } \perp \vec { B } {/tex} and {tex} | \vec { A } | = | \vec { B } | {/tex}

Explanation

Q 3.

Correct4

Incorrect-1

The value of {tex} p {/tex} so that the vectors {tex} 2 \hat { i } - \hat { j } + \hat { k } , \quad \hat { i } + 2 \hat { j } - 3 \hat { k } {/tex} and {tex} 3 \hat { i } + p \hat { j } + 5 \hat { k } {/tex} are coplanar should be

A

{tex}16{/tex}

B

{tex} - 4 {/tex}

{tex}4{/tex}

D

{tex} - 8 {/tex}

Explanation

Q 4.

Correct4

Incorrect-1

Which of the following group of forces will not accelerate a body?

{tex} 5 \mathrm { N } , 10 \mathrm { N } , 12 \mathrm { N } {/tex}

B

{tex} 5 \mathrm { N } , 10 \mathrm { N } , 16 \mathrm { N } {/tex}

C

{tex} 8 \mathrm { N } , 10 \mathrm { N } , 20 \mathrm { N } {/tex}

D

{tex} 7 \mathrm { N } , 5 \mathrm { N } , 15 \mathrm { N } {/tex}

Explanation

Q 5.

Correct4

Incorrect-1

A particle moves from point {tex} ( 1,0,2.5 ) {/tex} to the point {tex} ( - 2,3,4 ) \mathrm { m } {/tex} when a force {tex} \vec { F } = ( \hat { i } + 4 \hat { k } ) \mathrm { N } {/tex} acts on it. The work done on it is

A

{tex} 6 \mathrm{ J} {/tex}

B

{tex} 30 \mathrm { J } {/tex}

{tex} 3 \mathrm{ J} {/tex}

D

{tex} 9 \mathrm{ J} {/tex}

Explanation

Q 6.

Correct4

Incorrect-1

The area of a triangle bounded by vectors {tex} \vec { a } , \vec { b } {/tex} and {tex} \vec { c } {/tex} is

A

{tex} \frac { 1 } { 2 } | \vec { a } + \vec { b } + \vec { c } | {/tex}

B

{tex} \frac { 1 } { 2 } | \vec { a } \cdot \vec { b } + \vec { b } \cdot \vec { c } + \vec { c } \cdot \vec { a } | {/tex}

{tex} \frac { 1 } { 6 } | [ ( \vec { b } \times \vec { c } ) + ( \vec { c } \times \vec { a } ) + ( \vec { a } \times \vec { b } ) ] | {/tex}

D

{tex} \frac { 1 } { 2 } | ( \vec { a } \cdot \vec { b } ) + ( \vec { b } \cdot \vec { c } ) + ( \vec { c } \cdot \vec { a } ) | {/tex}

Explanation

Q 7.

Correct4

Incorrect-1

Following set of forces act on a body. In which case the resultant cannot be zero?

A

{tex} 10 \mathrm { N } , 10 \mathrm { N } , 20 \mathrm { N } {/tex}

B

{tex} 10 \mathrm { N } , 10 \mathrm { N } , 10 \mathrm { N } {/tex}

C

{tex} 10 \mathrm { N } , 20 \mathrm { N } , 20 \mathrm { N } {/tex}

{tex} 10 \mathrm { N } , 20 \mathrm { N } , 40 \mathrm { N } {/tex}

Explanation

Q 8.

Correct4

Incorrect-1

{tex} \frac { d } { d t } ( \vec { A } \times \vec { B } ) {/tex}

A

{tex} \vec { A } \times \frac { d \vec { B } } { d t } + \vec { B } \times \frac { d \vec { A } } { d t } {/tex}

{tex} \frac { d \vec { A } } { d t } \times \vec { B } + \vec { A } \times \frac { d \vec { B } } { d t } {/tex}

C

{tex} - \vec { A } \times \frac { d \vec { B } } { d t } - \frac { d \vec { A } } { d t } \times \vec { B } {/tex}

D

{tex} \vec { 0 } {/tex}

Explanation