14949 + Interview Questions in Maths in Class 11 Page 4 InterviewSolution

151.	If p-q is small compared to either p or q, then show that root(n)((p)/(q))~= ((n+1)p+(n-1)q)/((n-1)p+(n+1)q). Hence find root(8)((15)/(16)).
Answer» ANSWER :`=0.99196`

Discussion

152.	Find the coefficient of (iv) x^4 in the expansion of ((x)/(2) - (3)/(x^2) )^(10).
Answer» ANSWER :`(405)/(256)`

Discussion

153.	Let f be a continuity function on [1,3] . If 'f' takes only reational value of 'x' and f(2)=10 then f(1.5)=
Answer» 8 `(F(1)+(3))/(2)` 20 10 Answer :C

Discussion

154.	Write two examplesfor inertia of motion
Answer» SOLUTION :(i) PASSENGERS experience a forward push during a sudden brake in bus. (II) Ripe FRUITS fall from the trees in the direction of WIND.

Discussion

155.	Value of tan 75^(@) + cot 75^(@) = ?
Answer» `(1)/(4)` `SQRT(3)` 4 `-4` Answer :C

Discussion

156.	Find the derivative of w.r.to x log (tan 5x)
Answer» ANSWER :`10 COSEC 10 X`

Discussion

157.	If the middle term in (a+b)^(10) " is " T_(r-1) then r = ……
Answer» 6 5 7 8 Answer :C

Discussion

158.	How many terms of the A.P., -6,(-11)/(2),-5 ... are needed to give the sum-25 ?
Answer» ANSWER :5 or 20

Discussion

159.	Find the equation of parabolas whose : (i) Focus is (0,0) and directrix is x+5=0 (ii) Focus is (1,2) and directrix is 2x-y-1=0. (iii) Focus is (-2,3) and directrix is 2x-y+3=0. (iv) Focus is (5,3) and directrix is 3x-4y+1=0. (v) Focus is (0,4) and directrix is y+4=0. (i) Focus is (-2,0) and directrix is x-2=0.
Answer» Answer :(i) `y^(2)=10x+25` , (II) `x^(2)+y^(2)-2xy-2x-6y+9=0` (iii) `x^(2)+4y^(2)+4xy+8x-24y+56=0` , (IV) `16x^(2)+9Y^(2)+24xy-256x-142y+849=0` (v) `x^(2)=16y` (vi) `y^(2)=-8x`

Discussion

160.	Given that bar(x) is the mean and sigma^(2) is the variance of n observation x_(1), x_(2), …x_(n). Prove that the mean and sigma^(2) is the variance of n observations ax_(1),ax_(2), ax_(3),….ax_(n) are abar(x) and a^(2)sigma^(2), respectively, (ane0).
Answer» ANSWER :`a^2 sigma^2`

Discussion

161.	Differentiate the following w.r.t. x or t or u as the case may be: 5. y= (2x +5)/( 3x -2)
Answer» ANSWER :`(DY)/( DX ) = (-19)/( (3x-2)^2)`

Discussion

162.	The sum of the first three terms of a G.P. is 21 and the sum of the next three terms is 168. Find the sum of first five terms.
Answer» ANSWER :93

Discussion

163.	Assertion (A) : P(3,5,4), Q(6,5,7) are the vertice of a triangle whose orthocentre is (5,7,5) Reason ( R ) : In a right angled triangle right vertex is orthocentre
Answer» Both A and R are true and R is the corect EXPLANATION of A Both A and R are TRU and R is not the correct explanation of A a is true but Ris FALSE A is false but R is true Answer :A

Discussion

164.	If sin^(-1)((x^2-y^2)/(x^2+y^2)) = loga ,then (dy)/(dx) is equal to
Answer» `x/y` `y/x^2` `(x^2-y^2)/(x^2+y^2)` `y/x` ANSWER :D

Discussion

165.	The vectors barx and bary " satisfy " 2barx +bary =barp and barx+2bary =barq " where " barp=bari+barj and barq=bari-barj. " If " 'theta' " is the angle between " barx and bary, then
Answer» `COS THETA=4/5` `cos theta=1/sqrt2` `cos theta= -4/5` `cos theta=-3/5` ANSWER :C

Discussion

166.	Express (1)/(1-2i)+(3)/(1+i) in the form x + iy
Answer» ANSWER :`17/10-11/10i`

Discussion

167.	Prove the following cos^(2)2x-cos^(2)6x="sin"4x"sin"8x
Answer» ANSWER :RHS

Discussion

168.	let S ={1,2,3,…,24}. Define a relation '~' on S as x ~y is the product of the digits in x is same as that of the digits of y. (Note that is x is a single digit number then the product of the digits in x will be considered to be x.) Then the number of equivalence classes for this equivlence relation is
Answer» 9 10 20 24 Answer :B

Discussion

169.	The sides of a triangle are x+y=1, 7y=x, sqrt3y+x=0. Then which of the following is an interior point of triangle
Answer» Circumcentre Centroid Incentre Orthocentre Answer :A::B

Discussion

170.	Find the term independent of x in the expansion of (3/2x^(2)-1/(3x)).
Answer» ANSWER :`5/12`

Discussion

171.	Z is the set of integers. Describe the following relation in set builder form, given its domain and range. {(0,-7),(2,-5),(4,-3),(-13,-20),.......}
Answer» Answer :`{(x,y)}x in Z , x - y =7}"Domain " = {0,2,4,-13,....}, " Range " = {-7,-5,-3,-20,...}`

Discussion

172.	If bara and barb are non-zero vectors such that abs(bara+barb)^(2) = absbara^(2) +absbarb^(2), then find the angle between bara and barb
Answer» ANSWER :`90^(@)`

Discussion

173.	(i) Find the equation a circle passing through the point (2+3costheta,1+3sintheta) where 'theta' is a parameter. (ii) Prove that the equations x=atheta+bsintheta and y=asintheta-bcostheta represents a circle.
Answer» ANSWER :`(x-2)^(2)+(y-1)^(2)=3^(2)`

Discussion

174.	Find the domain and range of the following function f(x)= (x-2)/(3-x)
Answer» ANSWER :DOMAIN `R- {3}` Range `-(-1}`

Discussion

175.	Seven cards each bearing a letter , can be arranged to spell the word 'DOUBLES' .How many three - letter code- words can be formed from these cards ?
Answer» ANSWER :` 210` (II) ` 90 `

Discussion

176.	Seven cards each bearing a letter , can be arranged to spell the word 'DOUBLES' .How many three - letter code- words can be formed from these cards ? How manyof these wordsconsist of a vowels between two consonants?
Answer» ANSWER :` 120 (II) 36`

Discussion

177.	d/(dx){cos^(-1)x+Sin^(-1)sqrt(1-x^2)}
Answer» 0 1 `2/(SQRT(1-x^2))` `(-2)/(sqrt(1-x^2))` ANSWER :D

Discussion

178.	Given that C_r/(C_(r-1))=(n-r+1)/r Evaluate C_1/C_0,C_2/C_1 and C_3/C_2
Answer» SOLUTION :`N,(n-1)/2,(n-2)/3]`

Discussion

179.	The set of all x in the interval [0,pi] for which 2sin^(2)x-3sinx+1ge0
Answer» `[0,(PI)/6]uu{(pi)/2}uu[(5pi)/6,pi]` `[0,(pi)/6]uu[(5pi)/6,pi]` `[0,(pi)/2]uu[(5pi)/6,pi]` `(0,(pi)/2)uu((5pi)/6,pi)` ANSWER :A

Discussion

180.	If the distance between the points (a, 0, 1) and (0, 1, 2) is sqrt27, then the value of a is ______ .
Answer» 5 `PM5` `PM3` None of these Answer :B

Discussion

181.	If R rarr R b e defined f(x)={{:(a^(2)cos^(2) x+b^(2) sin^(2)x,if xle0),(e^(ax+b),if xgt0):}is a continuous function show that
Answer» ANSWER :2 LOG \|a\|

Discussion

182.	How many automobile licencse plates can be made, if each plate contains two different letters followed by three different digits ?
Answer» ANSWER :`= 4,68,000`

Discussion

183.	Find the modulus of the following complex numbers ((3+2i)^(2))/((4-3i))
Answer» ANSWER :`(13)/(5)`

Discussion

184.	The point (1,2) lies inside the circle x^(2) + y^(2) - 2x + 6y + 1 = 0.
Answer» ANSWER :FALSE

Discussion

185.	A(1, 1), B(2, 3), C(-1, 1) are the points. If P is a point such that the area of the quadrilateral PABC is 3 sq. units, then the locus of P is
Answer» `y^(2)+6y=0` `y^(2)-6y=0` `X^(2)+6x=0` `x^(2)-6x=x` ANSWER :2

Discussion

186.	All the lines whose sum of reciprocals of intercepts is k will be concurrent at the point
Answer» (K,k) `(1/k,1/k)` `(-k,-k)` `(-1/k,-1/k)` ANSWER :B

Discussion

187.	If the circumcentre of the triangle whose verticesare (3, 2, -5), (-3, 8, -5) and (-3, 2, 1) is (-1,lambda, -3) the integer lambda must be equal to .
Answer» ANSWER :4

Discussion

188.	A quadratic equation whose roots are tan15^(@) and cot15^(@) is
Answer» `X^(2)-4x+1=0` `x^(2)+4x-1=0` `x^(2)+4x+1=0` `x^(2)-4x-1=0` ANSWER :A

Discussion

189.	Write Negation of the following statements: Cube is a plane figure.
Answer» ANSWER :CUBE is not a PLANE FIGURE.

Discussion

190.	Write contrapositive and converse of the following statements: If Sanjay does not give examination he will fail.
Answer» ANSWER :Contrapositive: If Sanjay will to fail, he TAKE the examination CONVERSE: If Sanjay WIL fail he does not take the examination.

Discussion

191.	Centriod of triangle whose sides are (x^2+7xy+2y^2)(y-1)=0 is
Answer» `(2/3,0)` `(7/3,2/3)` `((-7)/3,2/3)` `(2,3/2)` ANSWER :C

Discussion

192.	\|{:(x^(2)+x,x+1,x-2),(2x^(2)+3x-1,3x,3x-3),(x^(2)+2x+3,2x-1,2x-1):}\|=ax-12 then a =
Answer» 24 `-12` `-24` 12 Answer :A

Discussion

193.	Solve the system of equations x+y+z=3,2x+2y-z=3,x+y-z=1 by Gauss Jordan method.
Answer» ANSWER :`K in R`

Discussion

194.	The maximum error in T due to possible errors upto 1% in l and 2.5% in g where period T of a simple pendulum is T=2pisqrt(l//g)
Answer» 0.0175 0.0157 0.0168 0.0173 Answer :A

Discussion

195.	If bara, barb, barc are any three vectors such that baraxxbarb=barc, barbxxbarc=bara,barcxxbara=barb then [barabarbbarc]=
Answer» 0 1 2 3 Answer :B

Discussion

196.	The shortest distance betweeen the lines x/2 = y/2 = z/1 and (x+2)/(-1) = (y-4)/(8) = (z-5)/(4) lies in the interval
Answer» `[0,1)` `[1,2)` `(2,3]` `(3,4]` ANSWER :C

Discussion

197.	If p is the length of perpendicular from the origin on the line (x)/(a) + (y)/( b) =1 and a^(2), p^(2) and b^(2) are in A.P., then show that a^(4) + b^(4) =0.
Answer» ANSWER :`a^(4) + B^(4) = 0`, which is required results.

Discussion

198.	If C_(0),C_(1),C_(2),...C_(n) are the binomial coefficients in the expansion of (1+x)^(n) then prove that:C_(0)+(C_(1))/(2)+(C_(2))/(3)+……+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1)
Answer» Solution :`L.H.S. =C_(0) +(C_(1))/(2)+(C_(2))/(3)+….+(C_(N))/(n+1)` `=1+(n)/(2)+(n(n-1))/(\|ul2.3)+....+(1)/(n+1)` ` =(1)/(n+1)[(n+1)+((n+2)n)/(\|ul2)` `+((n+1)n(n-1))/(\|ul3)+.....+1]` `=(1)/(n+1)[{1+(n+1)+((n+1)n)/(\|ul2)` `+((n+1)n(n-1))/(\|ul3)+......+1}-]` `=(1)/(n+1)[{.^(n+1)C_(0)+^(n+1)C_(1)+^(n+1)C_(2)` `+^(n+1)C_(3)+......+^(n+1)C_(n+1)}-1]` `=(1)/(n+1)[2^(n+1)-1]` `=(2^(n+1)-1)/(n+1)=R.H.S.` Hence PROVED

Discussion

199.	{:("Column I "," Column II "),("A) The number of solution of " (x)/(2) + (sin x)/( cos x) = (pi)/(4) i n ( - pi, pi),"p) 0 "),("B) The number of solutions of "x^(4) - 2 x^(2) sin^(2)""(pi x)/(x) + 1 = 0is ,"q 1 "),("C) The number of solutions of " x^(2) + x + 2 sec^(2) pi x + tan^(2) pi x = 0,"r) 2 "),("D) The number of solutions of " 16 (x^(2) + 1) + pi^(2) = \|tan x\| + 8 pi x in (-(pi)/(2), (3 pi)/(2)) x ne (pi)/(2) is ,"s) 3 "),("E) The number of solutions of "2^(\|cos x\|)= 4 ^(\|cos x\|) i n [ - pi, pi] is x ne (pi)/(2),"t) 4 "):}
Answer» <P> Answer :A- s; B - r; C - r; D - p; E - t

Discussion

200.	cosh 2 x + sin h 2x =
Answer» `(1+ TAN H(X))/(1-tan h(x))` `(1-tan h x)/(1+tan h x)` `(tan h x -1)/(tan h x + 1)` `(1-tan h x)/(tan h x - 1)` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

If p-q is small compared to either p or q, then show that root(n)((p)/(q))~= ((n+1)p+(n-1)q)/((n-1)p+(n+1)q). Hence find root(8)((15)/(16)).

Find the coefficient of (iv) x^4 in the expansion of ((x)/(2) - (3)/(x^2) )^(10).

Let f be a continuity function on [1,3] . If 'f' takes only reational value of 'x' and f(2)=10 then f(1.5)=

Write two examplesfor inertia of motion

Value of tan 75^(@) + cot 75^(@) = ?

Find the derivative of w.r.to x log (tan 5x)

If the middle term in (a+b)^(10) " is " T_(r-1) then r = ……

How many terms of the A.P., -6,(-11)/(2),-5 ... are needed to give the sum-25 ?

Given that bar(x) is the mean and sigma^(2) is the variance of n observation x_(1), x_(2), …x_(n). Prove that the mean and sigma^(2) is the variance of n observations ax_(1),ax_(2), ax_(3),….ax_(n) are abar(x) and a^(2)sigma^(2), respectively, (ane0).

Differentiate the following w.r.t. x or t or u as the case may be: 5. y= (2x +5)/( 3x -2)

The sum of the first three terms of a G.P. is 21 and the sum of the next three terms is 168. Find the sum of first five terms.

Assertion (A) : P(3,5,4), Q(6,5,7) are the vertice of a triangle whose orthocentre is (5,7,5) Reason ( R ) : In a right angled triangle right vertex is orthocentre

If sin^(-1)((x^2-y^2)/(x^2+y^2)) = loga ,then (dy)/(dx) is equal to

The vectors barx and bary " satisfy " 2barx +bary =barp and barx+2bary =barq " where " barp=bari+barj and barq=bari-barj. " If " 'theta' " is the angle between " barx and bary, then

Express (1)/(1-2i)+(3)/(1+i) in the form x + iy

Prove the following cos^(2)2x-cos^(2)6x="sin"4x"sin"8x

The sides of a triangle are x+y=1, 7y=x, sqrt3y+x=0. Then which of the following is an interior point of triangle

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

Z is the set of integers. Describe the following relation in set builder form, given its domain and range. {(0,-7),(2,-5),(4,-3),(-13,-20),.......}

If bara and barb are non-zero vectors such that abs(bara+barb)^(2) = absbara^(2) +absbarb^(2), then find the angle between bara and barb

(i) Find the equation a circle passing through the point (2+3costheta,1+3sintheta) where 'theta' is a parameter. (ii) Prove that the equations x=atheta+bsintheta and y=asintheta-bcostheta represents a circle.

Find the domain and range of the following function f(x)= (x-2)/(3-x)

Seven cards each bearing a letter , can be arranged to spell the word 'DOUBLES' .How many three - letter code- words can be formed from these cards ?

Seven cards each bearing a letter , can be arranged to spell the word 'DOUBLES' .How many three - letter code- words can be formed from these cards ? How manyof these wordsconsist of a vowels between two consonants?

d/(dx){cos^(-1)x+Sin^(-1)sqrt(1-x^2)}

Given that C_r/(C_(r-1))=(n-r+1)/r Evaluate C_1/C_0,C_2/C_1 and C_3/C_2

The set of all x in the interval [0,pi] for which 2sin^(2)x-3sinx+1ge0

If the distance between the points (a, 0, 1) and (0, 1, 2) is sqrt27, then the value of a is ______ .

If R rarr R b e defined f(x)={{:(a^(2)cos^(2) x+b^(2) sin^(2)x,if xle0),(e^(ax+b),if xgt0):}is a continuous function show that

How many automobile licencse plates can be made, if each plate contains two different letters followed by three different digits ?

Find the modulus of the following complex numbers ((3+2i)^(2))/((4-3i))

The point (1,2) lies inside the circle x^(2) + y^(2) - 2x + 6y + 1 = 0.

A(1, 1), B(2, 3), C(-1, 1) are the points. If P is a point such that the area of the quadrilateral PABC is 3 sq. units, then the locus of P is

All the lines whose sum of reciprocals of intercepts is k will be concurrent at the point

If the circumcentre of the triangle whose verticesare (3, 2, -5), (-3, 8, -5) and (-3, 2, 1) is (-1,lambda, -3) the integer lambda must be equal to .

A quadratic equation whose roots are tan15^(@) and cot15^(@) is

Write Negation of the following statements: Cube is a plane figure.

Write contrapositive and converse of the following statements: If Sanjay does not give examination he will fail.

Centriod of triangle whose sides are (x^2+7xy+2y^2)(y-1)=0 is

|{:(x^(2)+x,x+1,x-2),(2x^(2)+3x-1,3x,3x-3),(x^(2)+2x+3,2x-1,2x-1):}|=ax-12 then a =

Solve the system of equations x+y+z=3,2x+2y-z=3,x+y-z=1 by Gauss Jordan method.

The maximum error in T due to possible errors upto 1% in l and 2.5% in g where period T of a simple pendulum is T=2pisqrt(l//g)

If bara, barb, barc are any three vectors such that baraxxbarb=barc, barbxxbarc=bara,barcxxbara=barb then [barabarbbarc]=

The shortest distance betweeen the lines x/2 = y/2 = z/1 and (x+2)/(-1) = (y-4)/(8) = (z-5)/(4) lies in the interval

If p is the length of perpendicular from the origin on the line (x)/(a) + (y)/( b) =1 and a^(2), p^(2) and b^(2) are in A.P., then show that a^(4) + b^(4) =0.

If C_(0),C_(1),C_(2),...C_(n) are the binomial coefficients in the expansion of (1+x)^(n) then prove that:C_(0)+(C_(1))/(2)+(C_(2))/(3)+……+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1)

cosh 2 x + sin h 2x =