14949 + Interview Questions in Maths in Class 11 Page 111 InterviewSolution

5501.	Prove that root(3)(x^(3)+7)-root(3)(x^(3)+4) is approximately equal to (1)/(x^(2)) when x is large.
Answer» ANSWER :`=(x+(7)/(3)xx(1)/(x^(2)))-(x+(4)/(3)xx(1)/(x^(2)))=(1)/(x^(2))`.

Discussion

5502.	Change the complex number 4(cos 300^(@) + i sin 300^(@)) to cartesian form
Answer» ANSWER :`2-2 SQRT3I`

Discussion

5503.	There are three straight lines through the origin with direction cosines proportional to (1,2,2), (2,3,6) (3,4,12), Find the direction cosines of a a line equally inclined to the given lines.
Answer» ANSWER :`((1)/(SQRT(3)),(-1)/(sqrt(3)),(-1)/sqrt(3))or((-1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3)))`

Discussion

5504.	If A=[(1/2,alpha),(0,1/2)]prove that sum^(n)_(k=1) =1/3(1-1/4^(n))
Answer» ANSWER : `SUM^(N)_(k=1) =1/3(1-1/4^(n))`

Discussion

5505.	Prove that, cos^(2)x+cos^(2)(x+(pi)/(3))+cos^(2)(x-(pi)/(3))=(3)/(2).
Answer» ANSWER :`3/2=R.H.S.`

Discussion

5506.	Construct the index numbers for 2014 taking 2010 as the base year from the following data by simple average of price relative method:
Answer» ANSWER :122.32

Discussion

5507.	(sin^(2)alpha)/(1+cot^(2) alpha) + (tan^(2)alpha)/((1+tan^(2) alpha)^(2)) + cos^(2) alpha =
Answer» -1 0 1 2 Answer :C

Discussion

5508.	Obtain equation of ellipse satisfying given conditions Coordinates of the foci (pm 3, 0) and passes from points (4,1).
Answer» Answer :`(X^(2))/(18) + (y^(2))/(9) = 1`

Discussion

5509.	If{a_(n)} is a G.P. of positive terms then :(sqrt(a_(1)a_(2))+sqrt(a_(3)a_(4))+cdots+sqrt(a_(2n-1).a_(2n)))/(sqrt(a_(2)a_(3))+sqrt(a_(4)a_(5))+cdots+sqrt(a_(2n.)a_(2n-1)))=
Answer» `a_(1)+a_(3)+cdots+a_(2N-1)` `a_(2)+a_(4)+cdots+a_(2n)` `(a_(2)+a_(4)+cdots+a_(2n))/(a_(1)+a_(3)+cdots+a_(2n-1))` `(a_(1)+a_(3)+cdots+a_(2n-1))/(a_(2)+a_(4)+cdots+a_(2n))` ANSWER :D

Discussion

5510.	If the sum of an infinite geometric series is 15 and the sum of the squares of these terms is 45 , find the G.P.
Answer» Answer :`5,(10)/(3),(20)/(9)`

Discussion

5511.	Find the mean deviation using arithmetic mean of the following data: 16,22,26,14,12,15,13,18,
Answer» SOLUTION : Here `N=8, sum x_(1)=136` `:.` Arthmetic mean `BARX=(sum x_(i))/n=136/8=17` Mean deviatinon `=(sum_(i=1)^(n)\|x_(i)-barx\|)/n` `=30/8=3.75`

Discussion

5512.	Find the equation of the circle passing through the points (2,3) and (-1,1) and whose centre is on the line x-3y-11=0.
Answer» ANSWER :`X^(2)+y^(2)-7x+5y-14=0`

Discussion

5513.	cot 15^@ + cot 75^@ + cot 135^@=
Answer» 0 1 2 3 Answer :D

Discussion

5514.	d/(dx){x^(tanx)} =
Answer» `X^(TANX){(tanx)/x+sec^2x.logx}` `x^(tanx){(tanx)/(x)-sec^2x.logx}` `x^(tanx){x/(tanx)+sec^2x.logx}` `x^(tanx){x/(tanx)-sec^2x.logx}` ANSWER :A

Discussion

5515.	Find the derivativ of the function from first principles : (ax + b )/(cx +d ) (d ne - (d)/(c))
Answer» ANSWER :`X NE - d //C`

Discussion

5516.	The sum of n odd natural numbers is
Answer» `N^(2)` `2N` `(n+1)/(2)` `n^(2)+1` ANSWER :A

Discussion

5517.	(sin ^(2) A - sin ^(2) B)/( sin A cos A - sin B cos B)is equal to
Answer» `TNA (A-B)` `TAN (A+B)` `COT (A-B)` `cot (A+B)` ANSWER :B

Discussion

5518.	A tower stands at the center of a circular park. A and B are two points on the boundary of the park such thatAB(=a) subtends an angle of 60^(@) at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30^(@). The height of the tower is
Answer» `(2A)/(SQRT(3))` `2asqrt(3)` `(a)/(sqrt(3))` `asqrt(3)` ANSWER :C

Discussion

5519.	Evaluate the following limits in Exercises lim_(xto0)(sin(ax))/(sin (bx)) (a,bne0)
Answer» ANSWER :`(a)/(B)`

Discussion

5520.	If bar(e)=lbar(i)+mbar(j)+nbar(k) is a unit vector then maximum value of 'lm+mn+nl' is
Answer» -1/2 2 3 4 Answer :A

Discussion

5521.	Evaluate Lt_(xtooo)(1+1/(ax+b))^(cx+d) where a, b, c, d are positive constants.
Answer» ANSWER :`E^(c//a)`

Discussion

5522.	Fill in the blanks d/(dx) (cos x) =....
Answer» SOLUTION :- SIN X

Discussion

5523.	If sin^(2)x-asinx+b=0 has only one solution in (0,pi) then which of the following statemnets are correct?
Answer» `a in (- infty, 1] cup [2, infty)` `b in (- infty, 0] cup [1, infty)` `a = 1 + b` `a in ( - infty, 0) cup (0, infty)` ANSWER :A::B::C

Discussion

5524.	The range of log_(sqrt(5))[ sqrt(2)(sin x-cosx)+3] is
Answer» [0,2] [1,2] [0,3] [1,3] ANSWER :A

Discussion

5525.	Solve the following systems of homogeneous equations. 2x+5y+6z=0 x-3y-8z=0 3x+y-4z=0
Answer» ANSWER :`x=2k,y=-2k,z=K, k in R`

Discussion

5526.	(i) If A and B are symmetric matrices of same order AB-BA is a skew symmetric matrix.(ii)[(1,-1,2),(5,7,2),(6,6,4)] is a singular matrix(iii)(AB)^(-1)=A^(-1)B^(-1)(iv) If A=((1,3),(0,1)) thus A^(3)=((1,27),(0,1)).State which option is correct.
Answer» (i) and (II) are TRUE (i) and (III) are true (ii) and (iii) are true (iii) and (IV) are true Answer :A

Discussion

5527.	The pilot in the helicopter sees two buildings A and B which are at distances 100m and 50m from the pilot.From the pilot point of view the angle between the buildings is 60^o .How far apart the buildings?
Answer» ANSWER :`50sqrt3 m`

Discussion

5528.	lim_(xto-4^(-))[x]=……….
Answer» 5 -5 -4 4 Answer :B

Discussion

5529.	The slope of a line is double of the slope of another line. If tangent of the angle between them is (1)/(3), find the slopes of the lines.
Answer» ANSWER :If `x=-1` then SLOPES are `=-1 and -2`

Discussion

5530.	Find the approximate value of sin 60^(@)1'(1^(@) = 0.0175 "radian")
Answer» ANSWER :0.86615

Discussion

5531.	If f:RR rarrRR and g:RR rarrRR are defined by f(x)=2x+3 and g(x)=x^(2)+7, then the values of x such that g(f(x))=8 are
Answer» 1, 2 `-1, 2` `-1, -2` `1, -2` ANSWER :C

Discussion

5532.	The wholesale price index of the rice in 2016 compared to 2010 is 148. If the cost of rice was Rs. 46 per kg in 2010, calculate the cost in 2015
Answer» ANSWER :`rs68.08`

Discussion

5533.	Find the modulus of the following complex numbers (1+i)/(1-i) - (1-i)/(1+i)
Answer» ANSWER :2

Discussion

5534.	If sec theta + cos theta = 2 then sin^(2) theta + tan^(2) theta=
Answer» 0 1 2 4 Answer :A

Discussion

5535.	If y = x^2 + 1/(x^2 + 1/(x^2 + 1/(x^2 +....oo))), then (dy)/(dx) is
Answer» `(2XY)/(2Y - x^2)` `(XY)/(y - x^2)` `(xy)/(y - x^2)` `(2xy)/(2 + (x^2)/y)` ANSWER :A

Discussion

5536.	If 4a^2+9b^2_c^2+12ab=0 then the family of straight lines ax+by+c=0 is concurrent at
Answer» (2,3) or (-2,-3) (2,-3) or (-2,6) (-2,-4) or (-2,3) (2,5) or (-1,-5) ANSWER :A

Discussion

5537.	If \|Cosx\|^(sin^(2)x-(3)/(2)sinx+(1)/(2))=1 then x=
Answer» `{npi+(-1)^(n)(pi)/(6)}UU(npi}` `(2n+1)(pi)/(6)` `npi+-(pi)/(4)` `2npi+-(pi)/(8)` Answer :A

Discussion

5538.	Find y if the line passes from points (3,y) and (2,7) is parallel to the line passes from points (-1,4) and (0,6).
Answer» ANSWER :`9`

Discussion

5539.	If the algebraic sum of the perpendicular distances from the points (2,0),(0,2),(4,4) to a variable line is equal to zero. Then the line passes through the point.
Answer» (2,2) (2,1) (1,2) (-1,-1) ANSWER :A

Discussion

5540.	Evaluate the limits : lim_(x to 5) (sqrt(x+4)-3)/(x-5)
Answer» ANSWER :`1/6`

Discussion

5541.	If the line lx + my = 1 is a tangent to the circle x^(2) + y^(2) = a^(2), then the point (l,m) lies on a circle.
Answer» ANSWER :FALSE

Discussion

5542.	If an electricity consumer has the consumer number say 238:110:29, then describe the linking and count of house connections upto the 29th consumer "connection" linked to the larger capacity transformer number 238 subject to the condtition that each smaller capacity transformer can have a maximal consumer link of say 100.
Answer» ANSWER :`10900+29=10929`

Discussion

5543.	Ifm and n ( gt m)are positive integer, the number of solutions of the equation n \| sin x\| = m \| cos x \|in[0, 2 pi]is
Answer» 4 3 2 1 Answer :A

Discussion

5544.	Let vec(a), vec(b), vec(c ) be three vectors satisfying vec(a) xx vec(b) = 2vec(a) xx vec(c ), \|vec(a)\| = \|vec(c )\| =1, \|vec(b)\|=4 and \|vec(b) xx vec(c )\|= sqrt15. If vec(b)- 2vec(c )= lamda vec(a), find the value of lamda.
Answer» ANSWER :`+- 4`

Discussion

5545.	The roots of the equation px^(2)-2(p+1)x+3p=0 are alpha and beta. If alpha-beta=2, calculate the value of alpha,beta and p.
Answer» <P> ANSWER :`alpha=3,BETA1,p=2, or alpha-1,beta=-3,p=(-2)/(3)`.

Discussion

5546.	Write down the converse of following statements: If all three angles of a triangles are equal, then the triangle is equilateral.
Answer» ANSWER :TRIANGLE are EQUAL.

Discussion

5547.	The sum of two angles is 80 grades and their differnceis 18^(@). Find the angles.
Answer» ANSWER :`45^(@) , 27^(@)` .

Discussion

5548.	The solution of (sqrt(5) - 1)/(sin x) + (sqrt(10 + 2 sqrt(5)))/(cos x) = 8, x in (0, (pi)/(2)) is
Answer» `(PI)/(10), (3 pi)/(5)` `(pi)/(5), (3 pi)/(10)` `(pi)/(5), (3 pi)/(5)` `(pi)/(10), (3 pi)/(10)` ANSWER :D

Discussion

5549.	Write the following interval in set builder form. (-7, 1)
Answer» Answer :`{X : x in R, -7 LT x lt 1}`

Discussion

5550.	If f(x) = a log \|x\| + bx^(2) + x has extreme values at x = -1 and x = 2 , then the ordered pair (a,b) =
Answer» a=2, B =-1 `a=2,b=-(1)/(2)` `a=-2,b=(1)/(2)` `a=2,b=1//2` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Prove that root(3)(x^(3)+7)-root(3)(x^(3)+4) is approximately equal to (1)/(x^(2)) when x is large.

Change the complex number 4(cos 300^(@) + i sin 300^(@)) to cartesian form

There are three straight lines through the origin with direction cosines proportional to (1,2,2), (2,3,6) (3,4,12), Find the direction cosines of a a line equally inclined to the given lines.

If A=[(1/2,alpha),(0,1/2)]prove that sum^(n)_(k=1) =1/3(1-1/4^(n))

Prove that, cos^(2)x+cos^(2)(x+(pi)/(3))+cos^(2)(x-(pi)/(3))=(3)/(2).

Construct the index numbers for 2014 taking 2010 as the base year from the following data by simple average of price relative method:

(sin^(2)alpha)/(1+cot^(2) alpha) + (tan^(2)alpha)/((1+tan^(2) alpha)^(2)) + cos^(2) alpha =

Obtain equation of ellipse satisfying given conditions Coordinates of the foci (pm 3, 0) and passes from points (4,1).

If{a_(n)} is a G.P. of positive terms then :(sqrt(a_(1)a_(2))+sqrt(a_(3)a_(4))+cdots+sqrt(a_(2n-1).a_(2n)))/(sqrt(a_(2)a_(3))+sqrt(a_(4)a_(5))+cdots+sqrt(a_(2n.)a_(2n-1)))=

If the sum of an infinite geometric series is 15 and the sum of the squares of these terms is 45 , find the G.P.

Find the mean deviation using arithmetic mean of the following data: 16,22,26,14,12,15,13,18,

Find the equation of the circle passing through the points (2,3) and (-1,1) and whose centre is on the line x-3y-11=0.

cot 15^@ + cot 75^@ + cot 135^@=

d/(dx){x^(tanx)} =

Find the derivativ of the function from first principles : (ax + b )/(cx +d ) (d ne - (d)/(c))

The sum of n odd natural numbers is

(sin ^(2) A - sin ^(2) B)/( sin A cos A - sin B cos B)is equal to

A tower stands at the center of a circular park. A and B are two points on the boundary of the park such thatAB(=a) subtends an angle of 60^(@) at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30^(@). The height of the tower is

Evaluate the following limits in Exercises lim_(xto0)(sin(ax))/(sin (bx)) (a,bne0)

If bar(e)=lbar(i)+mbar(j)+nbar(k) is a unit vector then maximum value of 'lm+mn+nl' is

Evaluate Lt_(xtooo)(1+1/(ax+b))^(cx+d) where a, b, c, d are positive constants.

Fill in the blanks d/(dx) (cos x) =....

If sin^(2)x-asinx+b=0 has only one solution in (0,pi) then which of the following statemnets are correct?

The range of log_(sqrt(5))[ sqrt(2)(sin x-cosx)+3] is

Solve the following systems of homogeneous equations. 2x+5y+6z=0 x-3y-8z=0 3x+y-4z=0

(i) If A and B are symmetric matrices of same order AB-BA is a skew symmetric matrix.(ii)[(1,-1,2),(5,7,2),(6,6,4)] is a singular matrix(iii)(AB)^(-1)=A^(-1)B^(-1)(iv) If A=((1,3),(0,1)) thus A^(3)=((1,27),(0,1)).State which option is correct.

The pilot in the helicopter sees two buildings A and B which are at distances 100m and 50m from the pilot.From the pilot point of view the angle between the buildings is 60^o .How far apart the buildings?

lim_(xto-4^(-))[x]=……….

The slope of a line is double of the slope of another line. If tangent of the angle between them is (1)/(3), find the slopes of the lines.

Find the approximate value of sin 60^(@)1'(1^(@) = 0.0175 "radian")

If f:RR rarrRR and g:RR rarrRR are defined by f(x)=2x+3 and g(x)=x^(2)+7, then the values of x such that g(f(x))=8 are

The wholesale price index of the rice in 2016 compared to 2010 is 148. If the cost of rice was Rs. 46 per kg in 2010, calculate the cost in 2015

Find the modulus of the following complex numbers (1+i)/(1-i) - (1-i)/(1+i)

If sec theta + cos theta = 2 then sin^(2) theta + tan^(2) theta=

If y = x^2 + 1/(x^2 + 1/(x^2 + 1/(x^2 +....oo))), then (dy)/(dx) is

If 4a^2+9b^2_c^2+12ab=0 then the family of straight lines ax+by+c=0 is concurrent at

If |Cosx|^(sin^(2)x-(3)/(2)sinx+(1)/(2))=1 then x=

Find y if the line passes from points (3,y) and (2,7) is parallel to the line passes from points (-1,4) and (0,6).

If the algebraic sum of the perpendicular distances from the points (2,0),(0,2),(4,4) to a variable line is equal to zero. Then the line passes through the point.

Evaluate the limits : lim_(x to 5) (sqrt(x+4)-3)/(x-5)

If the line lx + my = 1 is a tangent to the circle x^(2) + y^(2) = a^(2), then the point (l,m) lies on a circle.

Ifm and n ( gt m)are positive integer, the number of solutions of the equation n | sin x| = m | cos x |in[0, 2 pi]is

Let vec(a), vec(b), vec(c ) be three vectors satisfying vec(a) xx vec(b) = 2vec(a) xx vec(c ), |vec(a)| = |vec(c )| =1, |vec(b)|=4 and |vec(b) xx vec(c )|= sqrt15. If vec(b)- 2vec(c )= lamda vec(a), find the value of lamda.

The roots of the equation px^(2)-2(p+1)x+3p=0 are alpha and beta. If alpha-beta=2, calculate the value of alpha,beta and p.

Write down the converse of following statements: If all three angles of a triangles are equal, then the triangle is equilateral.

The sum of two angles is 80 grades and their differnceis 18^(@). Find the angles.

The solution of (sqrt(5) - 1)/(sin x) + (sqrt(10 + 2 sqrt(5)))/(cos x) = 8, x in (0, (pi)/(2)) is

Write the following interval in set builder form. (-7, 1)

If f(x) = a log |x| + bx^(2) + x has extreme values at x = -1 and x = 2 , then the ordered pair (a,b) =