14949 + Interview Questions in Maths in Class 11 Page 120 InterviewSolution

5951.	........... is the equation of line which makes an angle pi/3 with X - axis having y- intersept 3.
Answer» ANSWER :`sqrt3x-y+3=0`

Discussion

5952.	Find the cartesian equation of the plane through the point A (2,-1,-4) and parallel to the plane 4x-12y-3z-7=0.
Answer» ANSWER :4x-12y-3z=32

Discussion

5953.	Consider the points A (2,4) and B (3,-1) By two point form find the equation of the line AB. Hence find the x - intercept and y-intercept of the line AB.
Answer» SOLUTION :`5X + y - 14 = 0, 14/5, 14, 14/sqrt 26`

Discussion

5954.	If 10^(th) and 4^(th) terms of a G.P are 9 and 4 respectively, then its 7^(th) term is…….
Answer» 6 36 `(4)/(9)` `(9)/(4)` ANSWER :A

Discussion

5955.	The ratio in which (5, 4,-6 ) divides the line segment joining (3,2,-4 ) ,(9,8,-10 ) is
Answer» " 2:1 " " 1 :2 " " 2: 3 " " 3 : 2 " ANSWER :B

Discussion

5956.	Solve the following equations : x^(2)+x+1=0
Answer» ANSWER :`-(1)/(2)+-(SQRT(3))/(2)i`

Discussion

5957.	In the following, state whether A = B or not: A = { 4, 8, 12, 16 } B={ 8, 4, 16, 18}
Answer» ANSWER :`A NE B`

Discussion

5958.	2 sin ^(2) beta + 4 cos (alpha + beta) sin alpha sin beta + cos 2 (alpha + beta )=
Answer» ` SIN 2 ALPHA ` `cos 2 beta ` `cos 2 alpha ` `sin 2 beta ` Answer :C

Discussion

5959.	Given that lim_(x rarr 0) (a^x - 1)/x = log a and lim_(x rarr 0) (tan x)/x = 1 Evaluate lim_(x rarr 0) (5^x - 1)/x
Answer» SOLUTION :`log_e 5`

Discussion

5960.	Find Lt_(xto-oo)(5x^(3)+4)/(sqrt(2x^(4)-1)).
Answer» ANSWER :`-OO`

Discussion

5961.	Express each of the following in the form b or bi, where b is a real number sqrt((-1)/(3))
Answer» ANSWER :`(1)/(3) SQRT3I`

Discussion

5962.	The maximum value of ( cos alpha_1) ( cos alpha_2) … ( cos alpha_n) under the restrictions 0 le alpha_1, alpha_2 ....... alpha_n le (pi)/(2) and cot alpha_1. cot alpha_2 ……cot alpha_n = 1 is
Answer» `(1)/(2^(N//2))` `(1)/(2^(n))` `(1)/(2N)` 1 Answer :A

Discussion

5963.	If A lies in the second quadrant and 3tanA+4=0, then the value of 2cotA-5cosA+sinA is
Answer» `(-53)/(10)` `(23)/(10)` `(37)/(10)` `(7)/(10)` Answer :B

Discussion

5964.	The vector [(bari-barj)xx(barj-bark)]xx(bari+5bark) is
Answer» `5bari-bar4j-bark` `3bari-2barj+5bark` `4bari-5barj-bark` `5bari+4barj-bark` ANSWER :A

Discussion

5965.	If the distance travelled by a particleis x = sqrt(pt^(2)+ 2qt + r) then the acceleration is proportional to
Answer» `(1)/(x)1` `(1)/(x^(2))` `(1)/(SQRT(x))` `(1)/(x^(3))` Answer :D

Discussion

5966.	How many terms are free from radical signs in the expansion of (x^(1/5)+y^(1/10))^(55) .
Answer» ANSWER :6

Discussion

5967.	Find the mean and standard deviation using short-cut method.
Answer» ANSWER :64, 1.69

Discussion

5968.	Find the square roots of the following : 5+12i
Answer» ANSWER :`+-(3+2i)`

Discussion

5969.	If the base angles of a triangle are22 (1^(0) )/(2) , 112 (1^(0))/(2) ,then base and height are in the ratio
Answer» ` 1: 2` ` 1: 3` ` 3: 1 ` ` 2: 1 ` ANSWER :D

Discussion

5970.	Let f(x)={{:(x+2",",xlt-1),(x^(2)",",-1lexlt1),((x-2)^(2)",",xge1):}Then number of times f(x) changes its sign in (-oo,oo) is
Answer» ANSWER :4

Discussion

5971.	Three coins are tossed once. Find the probability of getting (i) 3 heads (ii) 2 heads (iii) at least 2 heads (iv) at most 2 heads (v) no head (vi) 3 tails (vii) exactly two tails (viii) no tail (ix) at most two tails
Answer» Answer :(i) `(1)/(8)` (ii) `(3)/(8)` (III) `(1)/(2)` (iv) `(7)/(8)`(V) `(1)/(8)`(vi) `(1)/(8)` (vii) `(3)/(8)`(viii) `(1)/(8)`(IX) `(7)/(8)`

Discussion

5972.	How many terms of AP - 6-11//2,-5 . . .areneeded to givethe sum - 25 ?
Answer» ANSWER :4

Discussion

5973.	Find Lt_(xto0)(a-x)tan((pix)/(2a))
Answer» ANSWER :`(2A)/PI`

Discussion

5974.	Find the period of the following(i) cos^(4) x (ii) sin ^(2) x
Answer» ANSWER :B

Discussion

5975.	Two cyclists move on two separate roads angle at 60^(@) to each other at the rate of 5m/s and 10m/s respectively. The rate which they are separating from each other is
Answer» `5sqrt(3)` m/s 5m/s 10m/s 20m/s Answer :B

Discussion

5976.	Find theperiodofe^(logsinx)+ tan^(3) x - cosec(3 x-5)
Answer» ANSWER :`PI`

Discussion

5977.	From a committee of 10 persons, in how many ways can we choose a chairman, vice-chairman and president assuming one peron can not hold more than one position ?
Answer» ANSWER :720

Discussion

5978.	If H,G,S, I are respectively othercentre centroid , circumcentre and incentre of a triangle formed by the points (1,2,3), (2,3,1) and (3,1,2) . Then H + G + S + I =
Answer» (2,2,2) (4,4,4) (6,6,6) (8,8,8) ANSWER :D

Discussion

5979.	If A=[a_(ij)]_(mxxn) is a matrix and B is a non-singular square submatrix of order r, then
Answer» rank of A is r rank of A is GREATER than r rank OFA is less than r none of these Answer :B

Discussion

5980.	Statement 1: If I inentire of DeltaABC andl_(1) excenter opposite to A and P is intersection of H_(1) and Bc, then IP, I_(1)P=BP. PC Statement-2: In DeltaABC, 1 is incentre and I_(1)is excenter opposite to a, then IBl_(1) C must be square.
Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement-1 Statement-1 is True, Statement-2 is True, Statement-2 NOT a correct explanation for Statement-1 Statement-1 is True, Statement-2 is False Statement -1 is False, Statement-2 is True Answer :c

Discussion

5981.	Find the locus of the point which is equidistant from the coordinate axes.
Answer» ANSWER :`X^(2)-y^(2)=0`

Discussion

5982.	Find which two are correct from the following. (i)(x^(3) + sin x) is an odd function. (ii) If A is a set having 4 elements then the power set will have 64 elements. (iii) If a relations is reflexive, antisymmetric and transitive it is called equivalence relation. (iv) The product of two odd functions are even.
Answer» (i) and (II) are correct (i) and (iv) are correct (ii) and (III) are correct (iii) and (iv) are correct Answer :B

Discussion

5983.	Find the odd man from the given answers:
Answer» a `a^(a)` `E^(a)` `ALOG(AE)` ANSWER :D

Discussion

5984.	Show that the points A(0, 6), B(2, 1) and C(7, 3) are three corners of a square ABCD. Find (i) the slope of the diagonal BD and (i) the coordinates of the fourth vertex D.
Answer» SOLUTION :`BD PERPENDICULAR AC`

Discussion

5985.	Let f(x) = x^5+ 2x^3 + 3x + 4 then the value of 28 d/(dx) (f^(-1)(x)) at x = -2 is
Answer» `1` `2` `1//14` `-2` ANSWER :B

Discussion

5986.	Find the transformed equation of 3x^(2)+10xy +3y^(2) = 9 when the axes are rotated through an angle pi/4
Answer» ANSWER :`8X^(2)-2Y^(2) = 9`

Discussion

5987.	Find the mean deviation about the median of the following distribution:
Answer» ANSWER :1.25

Discussion

5988.	Which of the following sets can be the subset of the general solution of 1+cos3x=2cos2x, (n in Z) is
Answer» `NPI+(PI)/3` `npi+(pi)/6` `npi-(pi)/6` `2NPI` Answer :B::C::D

Discussion

5989.	Evaluate the following limits : Lim_(x to 0) (tan ax )/(tan bx )
Answer» ANSWER :`a/b`

Discussion

5990.	If a = sqrt3 + 1 cms . , \|__B = 30 ^(@) , \|__C= 45^(@),find C
Answer» ANSWER :` 2 CMS `

Discussion

5991.	What is the resulting sample space if three coins are tossed simultaneously ,
Answer» Answer :S={HHH,HHT,HTH,THH,THT,TTH,TTT}

Discussion

5992.	Find equation of the circle passes through points (2,3) and (4,5) whose centre lies on the line y - 4x + 3 = 0.
Answer» Answer :`X^(2) + y^(2) - 4X - 10Y + 25 = 0`

Discussion

5993.	Evaluate the following limits in lim_(xrarr-1)(x^(10)+x^(5)+1)/(x-1)
Answer» ANSWER :`-(1)/(2)`

Discussion

5994.	The vertex of the parabola y^(2)-2x+8x-23=0 is
Answer» (3,1) (-3,) (1,3) (-3,-1) ANSWER :A

Discussion

5995.	The range of the function f(x)=.^(7-s)P_(x-3) is
Answer» `{1,2,3}` `{1,2,3,4,5}` `{1,2,3,4}` `{1,2,3,4,5,6}` ANSWER :A

Discussion

5996.	Prove that the points (0, -1, -7), (2, 1, -9) and (6, 5, -13) are collinear. Find the ratio in which the first point divides the join of the other two.
Answer» ANSWER :`lamda=-1:3`

Discussion

5997.	Choose the correctstatement
Answer» Derivative of oddfunctionis odd Derivativeof EVENFUNCTION is even Inverseof oddfunction is even Inverse FUNCTION of SIN x is ` sin^(-1) x ` Answer :B

Discussion

5998.	Find the variance and standard deviation for the following distribution.
Answer» ANSWER :13.26

Discussion

5999.	If the p th and qth terms of a GP are q and p respectively, then show that its (p+ q) th term is ((q^(p))/(p^(q)))^((1)/(p-q))
Answer» <P> ANSWER :`((q_(p))/(p^(Q)))^((1)/(p-q))`

Discussion

6000.	Determine the conjugate and the reciprocal of each complex number given below: sqrt(-1)-3
Answer» ANSWER :`-i-3, (-3)/(10)- (1)/(10)i`

Discussion

Explore topic-wise InterviewSolutions in .

........... is the equation of line which makes an angle pi/3 with X - axis having y- intersept 3.

Find the cartesian equation of the plane through the point A (2,-1,-4) and parallel to the plane 4x-12y-3z-7=0.

Consider the points A (2,4) and B (3,-1) By two point form find the equation of the line AB. Hence find the x - intercept and y-intercept of the line AB.

If 10^(th) and 4^(th) terms of a G.P are 9 and 4 respectively, then its 7^(th) term is…….

The ratio in which (5, 4,-6 ) divides the line segment joining (3,2,-4 ) ,(9,8,-10 ) is

Solve the following equations : x^(2)+x+1=0

In the following, state whether A = B or not: A = { 4, 8, 12, 16 } B={ 8, 4, 16, 18}

2 sin ^(2) beta + 4 cos (alpha + beta) sin alpha sin beta + cos 2 (alpha + beta )=

Given that lim_(x rarr 0) (a^x - 1)/x = log a and lim_(x rarr 0) (tan x)/x = 1 Evaluate lim_(x rarr 0) (5^x - 1)/x

Find Lt_(xto-oo)(5x^(3)+4)/(sqrt(2x^(4)-1)).

Express each of the following in the form b or bi, where b is a real number sqrt((-1)/(3))

The maximum value of ( cos alpha_1) ( cos alpha_2) … ( cos alpha_n) under the restrictions 0 le alpha_1, alpha_2 ....... alpha_n le (pi)/(2) and cot alpha_1. cot alpha_2 ……cot alpha_n = 1 is

If A lies in the second quadrant and 3tanA+4=0, then the value of 2cotA-5cosA+sinA is

The vector [(bari-barj)xx(barj-bark)]xx(bari+5bark) is

If the distance travelled by a particleis x = sqrt(pt^(2)+ 2qt + r) then the acceleration is proportional to

How many terms are free from radical signs in the expansion of (x^(1/5)+y^(1/10))^(55) .

Find the mean and standard deviation using short-cut method.

Find the square roots of the following : 5+12i

If the base angles of a triangle are22 (1^(0) )/(2) , 112 (1^(0))/(2) ,then base and height are in the ratio

Let f(x)={{:(x+2",",xlt-1),(x^(2)",",-1lexlt1),((x-2)^(2)",",xge1):}Then number of times f(x) changes its sign in (-oo,oo) is

Three coins are tossed once. Find the probability of getting (i) 3 heads (ii) 2 heads (iii) at least 2 heads (iv) at most 2 heads (v) no head (vi) 3 tails (vii) exactly two tails (viii) no tail (ix) at most two tails

How many terms of AP - 6-11//2,-5 . . .areneeded to givethe sum - 25 ?

Find Lt_(xto0)(a-x)tan((pix)/(2a))

Find the period of the following(i) cos^(4) x (ii) sin ^(2) x

Two cyclists move on two separate roads angle at 60^(@) to each other at the rate of 5m/s and 10m/s respectively. The rate which they are separating from each other is

Find theperiodofe^(logsinx)+ tan^(3) x - cosec(3 x-5)

From a committee of 10 persons, in how many ways can we choose a chairman, vice-chairman and president assuming one peron can not hold more than one position ?

If H,G,S, I are respectively othercentre centroid , circumcentre and incentre of a triangle formed by the points (1,2,3), (2,3,1) and (3,1,2) . Then H + G + S + I =

If A=[a_(ij)]_(mxxn) is a matrix and B is a non-singular square submatrix of order r, then

Statement 1: If I inentire of DeltaABC andl_(1) excenter opposite to A and P is intersection of H_(1) and Bc, then IP, I_(1)P=BP. PC Statement-2: In DeltaABC, 1 is incentre and I_(1)is excenter opposite to a, then IBl_(1) C must be square.

Find the locus of the point which is equidistant from the coordinate axes.

Find the odd man from the given answers:

Show that the points A(0, 6), B(2, 1) and C(7, 3) are three corners of a square ABCD. Find (i) the slope of the diagonal BD and (i) the coordinates of the fourth vertex D.

Let f(x) = x^5+ 2x^3 + 3x + 4 then the value of 28 d/(dx) (f^(-1)(x)) at x = -2 is

Find the transformed equation of 3x^(2)+10xy +3y^(2) = 9 when the axes are rotated through an angle pi/4

Find the mean deviation about the median of the following distribution:

Which of the following sets can be the subset of the general solution of 1+cos3x=2cos2x, (n in Z) is

Evaluate the following limits : Lim_(x to 0) (tan ax )/(tan bx )

If a = sqrt3 + 1 cms . , |__B = 30 ^(@) , |__C= 45^(@),find C

What is the resulting sample space if three coins are tossed simultaneously ,

Find equation of the circle passes through points (2,3) and (4,5) whose centre lies on the line y - 4x + 3 = 0.

Evaluate the following limits in lim_(xrarr-1)(x^(10)+x^(5)+1)/(x-1)

The vertex of the parabola y^(2)-2x+8x-23=0 is

The range of the function f(x)=.^(7-s)P_(x-3) is

Prove that the points (0, -1, -7), (2, 1, -9) and (6, 5, -13) are collinear. Find the ratio in which the first point divides the join of the other two.

Choose the correctstatement

Find the variance and standard deviation for the following distribution.

If the p th and qth terms of a GP are q and p respectively, then show that its (p+ q) th term is ((q^(p))/(p^(q)))^((1)/(p-q))

Determine the conjugate and the reciprocal of each complex number given below: sqrt(-1)-3

If a = sqrt3 + 1 cms . , |B = 30 ^(@) , |C= 45^(@),find C