Maths-
General
Easy

Question

The distance between the line fraction numerator x minus 2 over denominator 1 end fraction equals fraction numerator y plus 2 over denominator negative 1 end fraction equals fraction numerator z minus 3 over denominator 4 end fraction and the plane stack r with ‾ on top times left parenthesis stack i with ‾ on top plus 5 stack j with ‾ on top plus stack k with ‾ on top right parenthesis equals 5 is (units)

  1. fraction numerator 10 over denominator 3 square root of 3 end fraction  
  2. fraction numerator 10 over denominator 3 end fraction  
  3. fraction numerator 10 over denominator 9 end fraction  
  4. fraction numerator 5 over denominator 2 end fraction  

The correct answer is: fraction numerator 10 over denominator 3 square root of 3 end fraction

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Related Questions to study

General
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The number of solutions of the equation Sin space 3 alpha equals 4 Sin space alpha times Sin space left parenthesis x plus alpha right parenthesis times Sin space left parenthesis x minus alpha right parenthesis where 0 less than alpha less than pi for straight x in the interval  left square bracket 0 comma pi right square bracket is

The number of solutions of the equation Sin space 3 alpha equals 4 Sin space alpha times Sin space left parenthesis x plus alpha right parenthesis times Sin space left parenthesis x minus alpha right parenthesis where 0 less than alpha less than pi for straight x in the interval  left square bracket 0 comma pi right square bracket is

maths-General
General
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The displacement-time graph of a moving object is shown in figure. Which of the velocity-time graphs shown in figure could represent the motion of the same body?

Think of the lope of the given displacement-time graph at different points and you would arrive at the correct answer.
Alternatively, look at the self-illustrative figure.

The displacement-time graph of a moving object is shown in figure. Which of the velocity-time graphs shown in figure could represent the motion of the same body?

physics-General
Think of the lope of the given displacement-time graph at different points and you would arrive at the correct answer.
Alternatively, look at the self-illustrative figure.
General
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The value of k for which the lines fraction numerator x plus 1 over denominator negative 3 end fraction equals fraction numerator y plus 5 over denominator 2 k end fraction equals fraction numerator z minus 4 over denominator 2 end fraction and fraction numerator x minus 3 over denominator 3 k end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z plus 1 over denominator 7 end fraction are perpendicular is

The value of k for which the lines fraction numerator x plus 1 over denominator negative 3 end fraction equals fraction numerator y plus 5 over denominator 2 k end fraction equals fraction numerator z minus 4 over denominator 2 end fraction and fraction numerator x minus 3 over denominator 3 k end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z plus 1 over denominator 7 end fraction are perpendicular is

maths-General
General
maths-

If the straight lines x=1+s,y=-3-λs,z=1+λs and x equals fraction numerator t over denominator 2 end fraction comma y equals 1 plus t, z=2-t, with parameters s and t respectively, are co planar, then λ=

If the straight lines x=1+s,y=-3-λs,z=1+λs and x equals fraction numerator t over denominator 2 end fraction comma y equals 1 plus t, z=2-t, with parameters s and t respectively, are co planar, then λ=

maths-General
General
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If 5 cas 2 theta plus 2 Cos squared space left parenthesis theta divided by 2 right parenthesis plus 1 equals 0 comma 0 less than theta less than pi not stretchy rightwards double arrow theta equals

If 5 cas 2 theta plus 2 Cos squared space left parenthesis theta divided by 2 right parenthesis plus 1 equals 0 comma 0 less than theta less than pi not stretchy rightwards double arrow theta equals

maths-General
General
physics-

A boy begins to walk eastward along a street infront of his house and the graph of his displacement from home is shown in the following figure. His average speed for in the whole-time interval is equal to

D i s p l a c e m e n t blank f o r m blank 0 blank t o blank 5 blank s blank equals blank 40 blank m
D i s p l a c e m e n t blank f r o m blank 5 blank t o blank 10 blank s blank equals blank 40 blank m
D i s p l a c e m e n t blank f r o m blank 0 blank t o blank 15 blank s blank equals blank minus blank 20 blank m
A n d blank d i s p l a c e m e n t blank f r o m blank 15 blank t o blank 20 blank s equals 0 blank m
therefore N e t blank d i s p l a c e m e n t equals 40 plus 40 minus 20 plus 0 equals 60 blank m
T o t a l blank t i m e blank t a k e n equals 5 plus 5 plus 15 plus 5 equals 30 blank m i n.
H e n c e comma blank a v e r a g e blank s p e e d equals fraction numerator d i s p l a c e m e n t blank open parentheses m close parentheses over denominator t i m e blank open parentheses m i n close parentheses end fraction equals fraction numerator 60 over denominator 30 end fraction equals 2 m blank m i n to the power of negative 1 end exponent.

A boy begins to walk eastward along a street infront of his house and the graph of his displacement from home is shown in the following figure. His average speed for in the whole-time interval is equal to

physics-General
D i s p l a c e m e n t blank f o r m blank 0 blank t o blank 5 blank s blank equals blank 40 blank m
D i s p l a c e m e n t blank f r o m blank 5 blank t o blank 10 blank s blank equals blank 40 blank m
D i s p l a c e m e n t blank f r o m blank 0 blank t o blank 15 blank s blank equals blank minus blank 20 blank m
A n d blank d i s p l a c e m e n t blank f r o m blank 15 blank t o blank 20 blank s equals 0 blank m
therefore N e t blank d i s p l a c e m e n t equals 40 plus 40 minus 20 plus 0 equals 60 blank m
T o t a l blank t i m e blank t a k e n equals 5 plus 5 plus 15 plus 5 equals 30 blank m i n.
H e n c e comma blank a v e r a g e blank s p e e d equals fraction numerator d i s p l a c e m e n t blank open parentheses m close parentheses over denominator t i m e blank open parentheses m i n close parentheses end fraction equals fraction numerator 60 over denominator 30 end fraction equals 2 m blank m i n to the power of negative 1 end exponent.
General
maths-

The values of theta satisfying Sin space 5 theta equals Sin space 3 theta minus Sin space theta and 0 less than theta less than pi over 2 are

The values of theta satisfying Sin space 5 theta equals Sin space 3 theta minus Sin space theta and 0 less than theta less than pi over 2 are

maths-General
General
physics-

A body of mass m is resting on a wedge of angle theta as shown in figure. The wedge is given at acceleration alpha. What is the value of a son that the mass m just falls freely?

The horizontal acceleration a of the wedge should be such that in time the wedge moves the horizontal distance B C. The body must fall through a vertical distance A B under gravity. Hence,
B C equals fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent and A B equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent
tantheta equals fraction numerator A B over denominator B C end fraction equals fraction numerator g over denominator a end fractionor a equals fraction numerator g over denominator t a n theta end fraction equals g blank c o t theta

A body of mass m is resting on a wedge of angle theta as shown in figure. The wedge is given at acceleration alpha. What is the value of a son that the mass m just falls freely?

physics-General
The horizontal acceleration a of the wedge should be such that in time the wedge moves the horizontal distance B C. The body must fall through a vertical distance A B under gravity. Hence,
B C equals fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent and A B equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent
tantheta equals fraction numerator A B over denominator B C end fraction equals fraction numerator g over denominator a end fractionor a equals fraction numerator g over denominator t a n theta end fraction equals g blank c o t theta
General
physics-

A cyclist starts from the centre O of a circular park of radius one kilometre, reaches the edge P of the park, then cycles along the circumference and returns to the centre along Q O as shown in figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is

Net displacement equals 0 and total distance equals O P plus P Q plus Q O
equals 1 plus fraction numerator 2 pi cross times 1 over denominator 4 end fraction plus 1 equals fraction numerator 14.28 over denominator 4 end fraction blank k m
Average speedblank equals fraction numerator 14.28 over denominator 4 cross times 10 divided by 60 end fraction
equals fraction numerator 6 cross times 14.28 over denominator 4 end fraction equals 21.42 blank k m divided by h

A cyclist starts from the centre O of a circular park of radius one kilometre, reaches the edge P of the park, then cycles along the circumference and returns to the centre along Q O as shown in figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is

physics-General
Net displacement equals 0 and total distance equals O P plus P Q plus Q O
equals 1 plus fraction numerator 2 pi cross times 1 over denominator 4 end fraction plus 1 equals fraction numerator 14.28 over denominator 4 end fraction blank k m
Average speedblank equals fraction numerator 14.28 over denominator 4 cross times 10 divided by 60 end fraction
equals fraction numerator 6 cross times 14.28 over denominator 4 end fraction equals 21.42 blank k m divided by h
General
physics-

A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected)

In the positive region the velocity decreases linearly (during rise) and in the negative region velocity increases linearly (during fall) and the direction is opposite to each other during rise and fall, hence fall is shown in the negative region

A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected)

physics-General
In the positive region the velocity decreases linearly (during rise) and in the negative region velocity increases linearly (during fall) and the direction is opposite to each other during rise and fall, hence fall is shown in the negative region
General
physics-

Which of the following graphs cannot possibly represent one dimensional motion of a particle

I is not possible because total distance covered by a particle increases with time
II is not possible because at a particular time, position cannot have two values
III is not possible because at a particular time, velocity cannot have two values
IV is not possible because speed can never be negative

Which of the following graphs cannot possibly represent one dimensional motion of a particle

physics-General
I is not possible because total distance covered by a particle increases with time
II is not possible because at a particular time, position cannot have two values
III is not possible because at a particular time, velocity cannot have two values
IV is not possible because speed can never be negative
General
physics-

Which of the following graphs cannot possibly represent one dimensional motion of a particle

I is not possible because total distance covered by a particle increases with time
II is not possible because at a particular time, position cannot have two values
III is not possible because at a particular time, velocity cannot have two values
IV is not possible because speed can never be negative

Which of the following graphs cannot possibly represent one dimensional motion of a particle

physics-General
I is not possible because total distance covered by a particle increases with time
II is not possible because at a particular time, position cannot have two values
III is not possible because at a particular time, velocity cannot have two values
IV is not possible because speed can never be negative
General
maths-

The solution of left parenthesis sin space x minus 2 right parenthesis squared plus left parenthesis cos space x minus 3 divided by 2 right parenthesis squared equals 0 is

The solution of left parenthesis sin space x minus 2 right parenthesis squared plus left parenthesis cos space x minus 3 divided by 2 right parenthesis squared equals 0 is

maths-General
General
maths-

If Sin space x plus Cos space x equals square root of 2 cos space alpha not stretchy rightwards double arrow x equals midline horizontal ellipsis

If Sin space x plus Cos space x equals square root of 2 cos space alpha not stretchy rightwards double arrow x equals midline horizontal ellipsis

maths-General
General
physics-

Acceleration velocity graph of a particle moving in a straight line is as shown in figure. The slope of velocity-displacement graph

From acceleration-velocity graph, we have a equals k blank v blankwhere k is a constant which represents the slope of the given line.
As, a equals v fraction numerator d v over denominator d s end fraction comma so v equals fraction numerator d v over denominator d s end fraction equals k v
or fraction numerator d v over denominator d s end fraction equals k equals a constant
Thus, the slope of velocity-displacement graphs is same as that of acceleration velocity. Which is constant.

Acceleration velocity graph of a particle moving in a straight line is as shown in figure. The slope of velocity-displacement graph

physics-General
From acceleration-velocity graph, we have a equals k blank v blankwhere k is a constant which represents the slope of the given line.
As, a equals v fraction numerator d v over denominator d s end fraction comma so v equals fraction numerator d v over denominator d s end fraction equals k v
or fraction numerator d v over denominator d s end fraction equals k equals a constant
Thus, the slope of velocity-displacement graphs is same as that of acceleration velocity. Which is constant.