14949 + Interview Questions in Maths in Class 11 Page 133 InterviewSolution

6601.	Find the term independent of x in the expansion of ((3)/(2) x^(2) - (1)/(3x) )^(9).
Answer» ANSWER :`=(7)/(18)`.

Discussion

6602.	Find the derivative of y = cos(logx + e^x)
Answer» ANSWER :`-((1)/(x) + E ^(x)) sin (log x + e ^(x))`

Discussion

6603.	There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pair is ""^12C_2-""^5C_2+1,
Answer» ANSWER :`=""^12C_2-""^5C_2+1,`

Discussion

6604.	Find the sum of the series 0.3+ 0.33 + 0.333+ ……to n terms
Answer» ANSWER :`(1)/(3) N- (1)/(27) (1- 10^(-n))`

Discussion

6605.	A line passes through a fixed point A(a, b). The locus of the foot of the perpendicular on it from origin is
Answer» `X^(2)+y^(2)+ax+by=0` `x^(2)+y^(2)-ax-by=0` `x^(2)+y^(2)-ax+by=0` `x^(2)+y^(2)+ax-by=0` ANSWER :2

Discussion

6606.	Obtain equation of ellipse satisfying given conditions Foci (pm 2,0) and eccentricity (1)/(2)
Answer» Answer :`(x^(2))/(16) + (y^(2))/(12) = 1`

Discussion

6607.	If non-zero number a,b,c are H.P. , then the straight line x/a+y/b+1/c=0 always passes through a fixed point. That points is
Answer» (-1,2) (-1,-2) (1,-2) `(1,-1/2)` ANSWER :C

Discussion

6608.	Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is a student of Class XI of your school}. . .{x : x student of yourschool}
Answer» ANSWER :`⊂`

Discussion

6609.	f(x) = (1 + x)^(5//x) , x in 0, f (0) = e^(5), at x =0 f is
Answer» CONTINUOUS DISCONTINUOUS not DETERMINED NONE ANSWER :A

Discussion

6610.	S_(n) denots the sum of first n terms of an A.P. Its first term is a and common difference is d. If d= S_(n)-k S_(n-1) + S_(n-2) then k= ……….
Answer» 1 2 3 None of these Answer :B

Discussion

6611.	If cos alpha+ cos beta= a, sin alpha+ sin beta= b and alpha- beta= 2 theta. Then (cos 3 theta)/(cos theta)=
Answer» `a^2+B^2-2` `a^2+b^2-3` `3-a^2-b^2` `(a^2+b^2)//4` ANSWER :B

Discussion

6612.	If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets : B = {d, e, f, g}
Answer» ANSWER :`{ a, B, C, H }`

Discussion

6613.	If 2 Costheta=x+1/x then 2 cos 3theta=
Answer» `X^(3)-1/x^(3)` `x^(3)+1/x^(3)` `x^(4)-1/x^(4)` `x-1/x` ANSWER :B

Discussion

6614.	If y=f(x) = (5x+3)/(4x-5), then f(y)=
Answer» `-X` x `(5x+3)/(4x-5)` `2X` ANSWER :B

Discussion

6615.	Find the direction cosines of the line joining the points (-4,1,7),(2,-3,2)
Answer» ANSWER :`((6)/(77),(-4)/(77),(5)/(77))`

Discussion

6616.	Find the mean deviation about the mean for the following data: 6, 7, 10, 12, 13, 4, 8, 12
Answer» ANSWER :2.75

Discussion

6617.	Find the mean deviation about the mean for the data in 4, 7, 8, 9, 10, 12, 13, 17
Answer» ANSWER :3

Discussion

6618.	Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?
Answer» ANSWER :`1/2 , 104.5` CRORES

Discussion

6619.	Write an explanation on Newton's laws.
Answer» Solution :(i) Newton's laws are vector laws. The equation `vecF=mveca` is a vector equation and essentially it is equal to three scalar equations. (ii) The acceleration ALONG the x direction depends only on the component of force acting along the X-direction. (iii) `F_y =ma_z =` The acceleration along the z direction depends only on the component of force acting along the z-direction. (iv) The force acting along y direction cannot ALTER the acceleration along x direction. In the same way, `F_z` cannot affect `a_y`and `a_x` .(v) The acceleration experienced by the body at time t depends on the force which ACTS on the body at that instant of time. It does not depend on the force which acted on the body before the time t. This can be expressed as ` vecF(t) = mveca(t)` (vi) Acceleration of the object does not depend on the previous history of the force. For example, when a spin bowler or a fast bowler THROWS the ball to the batsman, once the ball leaves the hand of the bowler, it experiences only gravitational force and air frictional force. (vii) The acceleration of the ball is independent of how the ball was bowled (with a lower or a higher speed). (viii)In GENERAL, the direction of a force may be different from the direction of motion. . (ix) Though in some cases, the object may move in the same direction as the direction of the force, it is not always true.

Discussion

6620.	If \|bar(a)\| = 13, \|bar(b)\| = 5, and bar(a).bar(b) = 60, then find \|bar(a) xx bar(b)\|.
Answer» ANSWER :25

Discussion

6621.	If f(4)=16 ,f'(4)=2 and f is differentiable of x=4 then lim_(xto4)(sqrt(f(x))-4)/(x-4)=…...
Answer» 2 1 `(1)/(4)` `(1)/(16)` ANSWER :C

Discussion

6622.	Find the standard deviation by using 20 as assumed mean.
Answer» SOLUTION : Here `a=20` STANDARD DEVIATION `sigma=SQRT((sumf_(i)d_(i)^(2))/(sumf_(i))-((sumf_(i)d_(i))/(sumf_(i)))^(2))` `=sqrt(6525/37-(265/37)^(2))` `=sqrt(176.35-51.30)` `=sqrt(125.05)=11.18`

Discussion

6623.	Write downthe slopes of the lines parallel to the line joining A(-1, 5) and B(-6, -7)
Answer» ANSWER : `12/(5)`

Discussion

6624.	If y=f(x) =(x+2)/(x-1)(x ne 1,-2) then show that x=f(y)
Answer» `x=f(y)` `f(1)=3` y increases with x for `x lt 1` f is rational function of x Answer :A

Discussion

6625.	A stationary point of f(x)=sqrt(16-x^(2)) is
Answer» `(4,0)` `(-4,0)` `(0,4)` `(-4,4)` ANSWER :C

Discussion

6626.	Find x if the distance between (5,-1,7) and (x,5,1) is 9 units.
Answer» ANSWER :8, 2

Discussion

6627.	Evaluate Lt_(x to 3) (x^3 - 3x^2)/(x^2 - 5x + 6)
Answer» ANSWER :9

Discussion

6628.	Sum up 1 + (1+2)+(1+ 2+3) +...+(1+2+3+...+ n ).
Answer» ANSWER :`(1)/(6) N (n+1) (n-: 2)`

Discussion

6629.	Find the quation of the parabolas with vertices at the origin and satisfying the following conditions. Focus at (0,a)
Answer» ANSWER :`X^(2)= 4AY`

Discussion

6630.	Find the quation of the parabolas with vertices at the origin and satisfying the following conditions. Focus at (a,0)
Answer» ANSWER :`y^(2)= 4AX`

Discussion

6631.	Find the quation of the parabolas with vertices at the origin and satisfying the following conditions. Focus at (0,-a)
Answer» ANSWER :`X^(2)= -4AY`

Discussion

6632.	Observe the following statements The correct matching is
Answer» `{:(I,II,III,IV),(C,E,D,A):}` `{:(I,II,III,IV),(C,E,B,D):}` `{:(I,II,III,IV),(C,D,E,B):}` `{:(I,II,III,IV),(C,B,D,A):}` ANSWER :B

Discussion

6633.	Evaluate the following limits : Lim_(xto 1) (x^(m)-1)/(x^(n)-1)
Answer» ANSWER :`m/n`

Discussion

6634.	Which of the following sentences are statements? Justify Where is your bag?
Answer» ANSWER :It is not STATEMENT.

Discussion

6635.	In Delta ABC, if a=13 ,b=14 , c=15, then r_1=
Answer» ANSWER :` 21//2`

Discussion

6636.	Solve the system of inequalities: 3x-7 lt 5+x""…(1) 11-5 x le 1""…(2)
Answer» ANSWER :`2 LE X lt6`

Discussion

6637.	If 2(sinh2+sinh3+sinh5) (e^(5))/(e^(5)-1)=a+be^(2)+ce^(3)+de^(5) then match the following and choose correct answer {:("List-I","List-II"),((I)a+b,(a)2),((II)a+c+b,(b)1),((III)b-d,(c )3),((IV)d,(d)0),(,(e )5):}
Answer» a, C,b, d a, c, d, b b, c, a, d b, c,d, a Answer :B

Discussion

6638.	State whether each of the following set is finite or infinite: The set of circles passing through the origin (0,0)
Answer» ANSWER :it is an INFINITE SET

Discussion

6639.	If P (1,-3,4) and Q (-4,1,2) are given then d(PQ) = unit.
Answer» ANSWER :`3SQRT5`

Discussion

6640.	If cosxcos((pi)/(3)+x).cos((pi)/(3)-x)=(1)/(4),x in[0,6pi], then find the sum of all the solutions of the equations.
Answer» ANSWER :`30PI`

Discussion

6641.	The solution set of sin(x+(pi)/4)=sin 2x
Answer» `(n PI - ((pi)/(4)))/(1 + (-1)^(n)(2))` `(n pi + ((pi)/(4)))/(1 + (-1)^(n)(2))` `(n pi + ((pi)/(4)))/(1 - (-1)^(n)(2))` `(n pi - ((pi)/(4)))/(1 - (-1)^(n)(2))` ANSWER :D

Discussion

6642.	Find three numbers in G.P. whose sum is 19 and product is 216.
Answer» ANSWER :4,6,9, or , 9,6,4

Discussion

6643.	A rod AB os length 10 cms slides between two perpendicular lines OX ,OY . The maximum area of the DeltaOAB
Answer» 50 20 25 60 Answer :C

Discussion

6644.	Find the mean deviation using arithmetic mean from the folloiwng observations:
Answer» Solution : ARITHMETIC MEAN `BARX=(sumf_(i).x_(i))/(sumf_(i))=1320/48=27.5` Mean deviation `=(sumf_(i)\|x_(i)-barx\|)/(sumf_(i))=450/48=9.375`

Discussion

6645.	construct truthtable for(~p ^^ ~q) v(p ^^ ~q)
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E04_026_A01##)`

Discussion

6646.	Find the distancce of the point P(-2, 3) from the line AB which is x-y=5.
Answer» ANSWER : `5sqrt(2)`

Discussion

6647.	Find the equation of the line intersecting the x-axis at a distance of 3 units to the left of origin with slope -2.
Answer» ANSWER :`2X + y + 6 = 0 `

Discussion

6648.	If A+B=45^(@), then (1+tanA)(1+tanB)=?
Answer» 2 `-2` 1 0 Solution :N//A

Discussion

6649.	Use the expansion of tan (A-B)to find tan 15 ^(@)without the use of tables, leaving your answer in surd form with an integral denominator.
Answer» ANSWER :`2 - SQRT3`

Discussion

6650.	If sin A=(12)/(13), cos B= (3)/(5) and neither A nor B is in the first quadrant, then find the quadrant in which A+B lies.
Answer» ANSWER :`I^(ST)` QUADRANT

Discussion

Explore topic-wise InterviewSolutions in .

Find the term independent of x in the expansion of ((3)/(2) x^(2) - (1)/(3x) )^(9).

Find the derivative of y = cos(logx + e^x)

There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pair is ""^12C_2-""^5C_2+1,

Find the sum of the series 0.3+ 0.33 + 0.333+ ……to n terms

A line passes through a fixed point A(a, b). The locus of the foot of the perpendicular on it from origin is

Obtain equation of ellipse satisfying given conditions Foci (pm 2,0) and eccentricity (1)/(2)

If non-zero number a,b,c are H.P. , then the straight line x/a+y/b+1/c=0 always passes through a fixed point. That points is

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is a student of Class XI of your school}. . .{x : x student of yourschool}

f(x) = (1 + x)^(5//x) , x in 0, f (0) = e^(5), at x =0 f is

S_(n) denots the sum of first n terms of an A.P. Its first term is a and common difference is d. If d= S_(n)-k S_(n-1) + S_(n-2) then k= ……….

If cos alpha+ cos beta= a, sin alpha+ sin beta= b and alpha- beta= 2 theta. Then (cos 3 theta)/(cos theta)=

If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets : B = {d, e, f, g}

If 2 Costheta=x+1/x then 2 cos 3theta=

If y=f(x) = (5x+3)/(4x-5), then f(y)=

Find the direction cosines of the line joining the points (-4,1,7),(2,-3,2)

Find the mean deviation about the mean for the following data: 6, 7, 10, 12, 13, 4, 8, 12

Find the mean deviation about the mean for the data in 4, 7, 8, 9, 10, 12, 13, 17

Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?

Write an explanation on Newton's laws.

If |bar(a)| = 13, |bar(b)| = 5, and bar(a).bar(b) = 60, then find |bar(a) xx bar(b)|.

If f(4)=16 ,f'(4)=2 and f is differentiable of x=4 then lim_(xto4)(sqrt(f(x))-4)/(x-4)=…...

Find the standard deviation by using 20 as assumed mean.

Write downthe slopes of the lines parallel to the line joining A(-1, 5) and B(-6, -7)

If y=f(x) =(x+2)/(x-1)(x ne 1,-2) then show that x=f(y)

A stationary point of f(x)=sqrt(16-x^(2)) is

Find x if the distance between (5,-1,7) and (x,5,1) is 9 units.

Evaluate Lt_(x to 3) (x^3 - 3x^2)/(x^2 - 5x + 6)

Sum up 1 + (1+2)+(1+ 2+3) +...+(1+2+3+...+ n ).

Find the quation of the parabolas with vertices at the origin and satisfying the following conditions. Focus at (0,a)

Find the quation of the parabolas with vertices at the origin and satisfying the following conditions. Focus at (a,0)

Find the quation of the parabolas with vertices at the origin and satisfying the following conditions. Focus at (0,-a)

Observe the following statements The correct matching is

Evaluate the following limits : Lim_(xto 1) (x^(m)-1)/(x^(n)-1)

Which of the following sentences are statements? Justify Where is your bag?

In Delta ABC, if a=13 ,b=14 , c=15, then r_1=

Solve the system of inequalities: 3x-7 lt 5+x""…(1) 11-5 x le 1""…(2)

If 2(sinh2+sinh3+sinh5) (e^(5))/(e^(5)-1)=a+be^(2)+ce^(3)+de^(5) then match the following and choose correct answer {:("List-I","List-II"),((I)a+b,(a)2),((II)a+c+b,(b)1),((III)b-d,(c )3),((IV)d,(d)0),(,(e )5):}

State whether each of the following set is finite or infinite: The set of circles passing through the origin (0,0)

If P (1,-3,4) and Q (-4,1,2) are given then d(PQ) = unit.

If cosxcos((pi)/(3)+x).cos((pi)/(3)-x)=(1)/(4),x in[0,6pi], then find the sum of all the solutions of the equations.

The solution set of sin(x+(pi)/4)=sin 2x

Find three numbers in G.P. whose sum is 19 and product is 216.

A rod AB os length 10 cms slides between two perpendicular lines OX ,OY . The maximum area of the DeltaOAB

Find the mean deviation using arithmetic mean from the folloiwng observations:

construct truthtable for(~p ^^ ~q) v(p ^^ ~q)

Find the distancce of the point P(-2, 3) from the line AB which is x-y=5.

Find the equation of the line intersecting the x-axis at a distance of 3 units to the left of origin with slope -2.

If A+B=45^(@), then (1+tanA)(1+tanB)=?

Use the expansion of tan (A-B)to find tan 15 ^(@)without the use of tables, leaving your answer in surd form with an integral denominator.

If sin A=(12)/(13), cos B= (3)/(5) and neither A nor B is in the first quadrant, then find the quadrant in which A+B lies.