14949 + Interview Questions in Maths in Class 11 Page 135 InterviewSolution

6701.	If vec(p), vec(q) are two non collinear and non zero vectors such that (b-c) (vec(p) xx vec(q)) + (c-a) vec(p) + (a-b) vec(q)= vec(0) where a,b,c are the length of the sides of a triangle, then the triangle is
Answer» Rt-angled obtuse angled equilateral Isosceles Answer :C

Discussion

6702.	The circle x^2+y^2-6x-10 y+k=0does not touch or intersect the coordinate axes, and the point (1, 4) isinside the circle. Find the range of value of kdot
Answer» <P> ANSWER :`25 LT p lt 29`

Discussion

6703.	If A+B=60^(@) then Sin^(2)A+sin^(2)B-sinA SinB=
Answer» `1/2` `3/4` 1 `3/2` ANSWER :B

Discussion

6704.	(d)/(dx) {cos x ^(0)}=
Answer» ` - sinx^(10)` `-PI/(180) sinx^(0)` `pi/(180) sinx^(0)` `(2pi)/180 sinx^0` Answer :B

Discussion

6705.	Statement-I : Two non zero, non collinear vectors are linearly independent. Statement-II : Any three coplanar vectors are linearly dependent. Which of the above statement is true?
Answer» Only I only II both I and II Neither I nor II Answer :C

Discussion

6706.	Radius of circle with centre C(3,4) and passes from O(0,0) is r = .......... .
Answer» ANSWER :5

Discussion

6707.	The point to which the axes should be translated to eliminate first degree termsin the equation2x^(2)-2y^(2)+z^(2)-4x+8y+2z-5=0 is
Answer» (1,2,-1) (2,4,-2) (3,2,1) (2,6,3) ANSWER :a

Discussion

6708.	The value of cos12^(@)+cos84^(@)+cos156^(@)+cos132^(@) is
Answer» `(1)/(2)` 1 `-(1)/(2)` `(1)/(8)` ANSWER :C

Discussion

6709.	The sides of a triangle are in AP and its area is (3)/(5) th of area of equilateral triangle of same perimeter then ratio of sides
Answer» `3:4:5` `SQRT(7)-1:sqrt(7):sqrt(7)+1` `3:5:7` `sqrt(3):sqrt(2):(sqrt(6)+sqrt(2))/(2)` ANSWER :C

Discussion

6710.	Consider the system of equations x cos ^(3) y + 3 x cosy sin^(2) y = 14 t o (1) and x sin^(3) y + 3 x cos^(2) y sin y = 13 to (2) The value of sin^(2) y + 2 cos^(2) yis
Answer» `(4)/(5)` `(9)/(5)` 2 3 Answer :B

Discussion

6711.	Consider the system of equations x cos ^(3) y + 3 x cosy sin^(2) y = 14 t o (1) and x sin^(3) y + 3 x cos^(2) y sin y = 13 to (2) The value of x is / are
Answer» `PM 5 SQRT(5)` `pm sqrt(5)` `pm (1)/(sqrt(5))` `pm (1)/(sqrt(5))` ANSWER :A

Discussion

6712.	Lines 3x+4y+5=0 and 4x-3y-10=0 intersects at point A. B is the point on line 3x+4y+5=0 and point C lies on line 4x-3y- 10=0. such that AB= AC. Find equation of overset(harr)(BC) passes from point (1,2).
Answer» Answer :`7X + y - 9 = 0, X - 7y + 13 = 0`

Discussion

6713.	The values of parameter a for which the point of minimum of the function f(x)=1+a^(2)x-x^(3)satisfies the inequality (x^(2)+x+2)/(x^(2)+5x+6)lt0 are
Answer» `(2sqrt(3),3sqrt(3))` `(-3sqrt(3),-2sqrt(3))` `(-2sqrt(3),3sqrt(3))` `(-3sqrt(2),2sqrt(3))` ANSWER :A::B

Discussion

6714.	Ifcos theta - sin theta= sqrt(2) sin theta " then " cos theta + sin theta =
Answer» `SQRT(2) COS THETA` `-sqrt(2) cos theta` `sqrt(2) sin theta` `-sqrt(2) sin theta` Answer :A

Discussion

6715.	Obtain equation of circle in Centre (sqrt(-4)cos alpha, 4 sin alpha) and radius 5.
Answer» ANSWER :`X^(2)+y^(2)+8x COS alpha-8y SIN alpha-9=0`

Discussion

6716.	If alpha + beta + lambda= (pi)/(2) and cot alpha, cot beta, cot lambda are in A.P then cot alpha. Cot lambda
Answer» 1 2 3 4 Answer :C

Discussion

6717.	If x^(2)+4xy+4y^(2)+4x+cy+3 can be written as the product of two linear factors then c=
Answer» 2 3 8 4 Answer :C

Discussion

6718.	If (sin^(3)"" (x)/(2)-cos^(3)""(x)/(2))/(2 + sin x) = (cos x)/( 3)then x =
Answer» `n pi +(pi)/2, n in Z` `2 n pi+(pi)/2, n in Z` `n pi-(pi)/2, n in Z` `2 n pi-(pi)/2, n in Z` ANSWER :B

Discussion

6719.	The locus of the point represented by x=cos^(2)t,y=2sint is
Answer» `y^(2)=4X` `y^(2)=4x+1` `y^(2)+4x=1` `y^(2)+4x=4` ANSWER :4

Discussion

6720.	What is the number of terms in the expansion of the following? (a+bx)^(17) - (a-bx)^(17)
Answer» ANSWER :9

Discussion

6721.	Solution set of the equation 3 tan^(2) theta + 4 tan theta + 2 =0 is ...............
Answer» ANSWER :`-8`

Discussion

6722.	If A is in the fourth quadrant and cos A=(5)/(13), find the value of (13 sin A+5 secA)/(5tanA+6" cosec"A).
Answer» ANSWER :`-(2)/(37)`

Discussion

6723.	Find the condition that the slope of one of the lines represented by ax^2 + 2xy +by^2 = 0 is square of slope the other
Answer» ANSWER :`AB(a+b-6h)+8h^3=0`

Discussion

6724.	The reflection of the plane 2x - 3y + 4z - 3=0 in the plane x - y + z -3 =0 is the plane
Answer» `4x - 3Y + 2z- 15 =0` `X - 3y + 2z - 15=0` `4x + 3y - 2z + 15=0` `4x + 3y + 2z + 15 =0` Answer :A

Discussion

6725.	Which of the following statements is true for the funiction f(x)={{:(sqrt(x)",",xge1),(x^(3)",",olexle1),((x^(3))/(3)-4x",",xle0):}
Answer» It is monotonic increasing `Aax inR`. f(x) fails to existfor three distinct REAL values of x. f(x) changes its sign twice as x varies from `-ootooo`. The function ATTAINS its EXTREME values at `x_(1)andx_(2)` , such that `x_(1)x_(2)GT0` Answer :C

Discussion

6726.	(""^(8) C_(0) )/(6) - ""^(8) C_1 + ""^(8) C_(2) . 6-""^(8) C_3 . 6^2 + ... + ""^(8) C_(8) .6^(7) is equal to(i) 0(ii) 6^7(iii) 6^5(iv) (5^8)/(6)
Answer» `0` `6^7` `6^5` `(5^8)/(6)` ANSWER :D

Discussion

6727.	Consider the following population and year graph, find the slope of the line AB and using it, find what will be the population in the year 2010?
Answer» ANSWER :POPULATION in YEAR 2010 is 104.5 CRORES.

Discussion

6728.	If the equation a_(n)x^(n) + a_(n-1) x^(n-1)+"......" + a_(1) x= 0(a_(1) cancel(=)0,nge 2)has a positive root x = alpha then the equation na_(n) x^(n-1)+(n-1)a_(n-1)x^(n-2)+"......"+a_(1) =0 has a positive root, which is
Answer» equal to `ALPHA` `ge alpha` `lt alpha` `GT alpha` Answer :C

Discussion

6729.	The value of (sqrt(5)+1)^(5)-(sqrt(5)-1)^(5) is ………
Answer» 252 352 452 532 Answer :B

Discussion

6730.	If 4 sin 27^@ = sqrt(alpha) + sqrt(beta) then the sum of the digits in (alpha + beta + alpha beta + 2)^4
Answer» ANSWER :4

Discussion

6731.	If barx.bara=barx.barb=barx.barc=0 for some non-zero vector barx and abs(bara)=abs(barb)=abs(barc)=1 then the volume of parallelopiped with bara,barb,barc is
Answer» 1 2 3 0 Answer :D

Discussion

6732.	Let A = (2,5) and B = (4, -1) are two vertices of a AABC. Third vertex C moves along L=9x+7y+4=0. The locus of the centroid of triangle ABC is the line
Answer» 9x-7y-22=0 9x+7y+22=0 27x+21y-77=0 27x+21y-78=0 ANSWER :4

Discussion

6733.	Write the negation of the following simple statements. sqrt(5) is a rational number.
Answer» ANSWER :RATIONALNUMBER.

Discussion

6734.	The y intercept of the line through the point (1,-2) making an angle of 135^(@) with the x - axis is
Answer» 1 `-1` 2 0 Answer :B

Discussion

6735.	25x^(2)-9y^(2)=225
Answer» ANSWER :(i) 6 UNITS, 10units (II) `A(-3,0),B(3,0) ` (III) `F_(1)(-7,0),F_(2)(sqrt(34),0)` (iv) `e=(sqrt(34))/(3)` (v) `16(2)/(3)` units

Discussion

6736.	Show that, (1 xx 2^(2) + 2 xx 3^(2) + ….+ n xx (n+1)^(2))/(1^(2) xx 2 + 2^(2) xx 3 + ….+ n^(2) xx (n+1))= (3n+ 5)/(3n+ 1)
Answer» ANSWER :`(3n+5)/(3n+1)`

Discussion

6737.	Write the first five terms of each of the sequences whose n^(th) terms are: a_(n)= 2^(n)
Answer» ANSWER :2,4, 8,16 and 32

Discussion

6738.	Show that Lim_(x to 2) log_(10){x^(6) +sqrt((x^(2)+1292))}=2
Answer» ANSWER :GIVEN limit` = log_(10)[ Lim_( XTO 2) X^(6) + sqrt(Lim_(x to 2) (x^(2) + 1292))] = log_(10)[ 2^(6) +sqrt(1296) ] = log_(10) 100 = 2 `

Discussion

6739.	Find out which of the following sentences are statements and which are not ?JustifyStand up
Answer» SOLUTION :Not STATEMENT

Discussion

6740.	A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn baJI is white, is
Answer» `(4)/(49)` `(1)/(7)` `(4)/(7)` `(12)/(49)` ANSWER :C

Discussion

6741.	A(1, - 1, 2) B(1, 0, 2) C(2, -2, 3) and D(4, 2, 1) are the vertices of a tetrahedron then find the distance of the plane ABC from the vertex D.
Answer» ANSWER :`2SQRT2`

Discussion

6742.	If bar(a) = bar(i) + 2bar(j) + 3bar(k), bar(b) = 3bar(i) +5bar(j) -bar(k) are 2 sides of a triangle, find its area.
Answer» ANSWER :`(SQRT(390))/(2)` sq.units

Discussion

6743.	Find sum: (1)/(2) + (1)/(3^(2)) + (1)/(2^(3)) + (1)/(3^(4)) + (1)/(2^(5)) + (1)/(3^(6))+ …..oo
Answer» ANSWER :`(19)/(24)`

Discussion

6744.	If tan.(C-A)/(2)=k cot.(B)/(2) then find k .
Answer» ` ( C-a)/(c+ a) ` ` ( c+a)/(c- a) ` ` ( c+a)/(4(c- a)) ` ` ( c+a)/(3(c- a)) ` ANSWER :A

Discussion

6745.	Find the number of terms of the series 21, 18, 15, 12...which must be taken to give a sum of zero.
Answer» ANSWER :15

Discussion

6746.	Match the following from List - I to List - II {:(,"List - I",,"List - II"),(I.,[(1,1),(1,0)],(a),0),(II.,[(1,1),(1,1)],(b),1),(III.,[(0,0),(0,0)],(c),2),(IV.,[(1,0,0),(0,1,0),(0,0,1)],(d),3):}
Answer» a,B,C,d b,c,a,d d,a,b,c c,b,a,d Answer :D

Discussion

6747.	Identify the Quantifiers in the following statements: There exists a statemen in above statements which is not true.
Answer» ANSWER :EXISTENTIAL quanifier is USED

Discussion

6748.	Find the value of sum_(n=1)^(oo)(1)/(2n-1)((1)/(9^(n-1))+(1)/(9^(2n-1))).
Answer» ANSWER :`=(1)/(2)log E^(10)`

Discussion

6749.	Find the derivative of w.r.to x sin (log x)
Answer» ANSWER :`(COS (LOG X))/(x)`

Discussion

6750.	Orthocentre of the triangle formed by line 3x^(2)-xy-2y^(2)=0 and 2x+3y-5=0 is
Answer» `((2)/(5),(3)/(5))` `((3)/(5),(2)/(5))` `((-2)/(5),(-3)/(5))` `((-3)/(5),(-2)/(5))` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

If vec(p), vec(q) are two non collinear and non zero vectors such that (b-c) (vec(p) xx vec(q)) + (c-a) vec(p) + (a-b) vec(q)= vec(0) where a,b,c are the length of the sides of a triangle, then the triangle is

The circle x^2+y^2-6x-10 y+k=0does not touch or intersect the coordinate axes, and the point (1, 4) isinside the circle. Find the range of value of kdot

If A+B=60^(@) then Sin^(2)A+sin^(2)B-sinA SinB=

(d)/(dx) {cos x ^(0)}=

Statement-I : Two non zero, non collinear vectors are linearly independent. Statement-II : Any three coplanar vectors are linearly dependent. Which of the above statement is true?

Radius of circle with centre C(3,4) and passes from O(0,0) is r = .......... .

The point to which the axes should be translated to eliminate first degree termsin the equation2x^(2)-2y^(2)+z^(2)-4x+8y+2z-5=0 is

The value of cos12^(@)+cos84^(@)+cos156^(@)+cos132^(@) is

The sides of a triangle are in AP and its area is (3)/(5) th of area of equilateral triangle of same perimeter then ratio of sides

Consider the system of equations x cos ^(3) y + 3 x cosy sin^(2) y = 14 t o (1) and x sin^(3) y + 3 x cos^(2) y sin y = 13 to (2) The value of sin^(2) y + 2 cos^(2) yis

Consider the system of equations x cos ^(3) y + 3 x cosy sin^(2) y = 14 t o (1) and x sin^(3) y + 3 x cos^(2) y sin y = 13 to (2) The value of x is / are

Lines 3x+4y+5=0 and 4x-3y-10=0 intersects at point A. B is the point on line 3x+4y+5=0 and point C lies on line 4x-3y- 10=0. such that AB= AC. Find equation of overset(harr)(BC) passes from point (1,2).

The values of parameter a for which the point of minimum of the function f(x)=1+a^(2)x-x^(3)satisfies the inequality (x^(2)+x+2)/(x^(2)+5x+6)lt0 are

Ifcos theta - sin theta= sqrt(2) sin theta " then " cos theta + sin theta =

Obtain equation of circle in Centre (sqrt(-4)cos alpha, 4 sin alpha) and radius 5.

If alpha + beta + lambda= (pi)/(2) and cot alpha, cot beta, cot lambda are in A.P then cot alpha. Cot lambda

If x^(2)+4xy+4y^(2)+4x+cy+3 can be written as the product of two linear factors then c=

If (sin^(3)"" (x)/(2)-cos^(3)""(x)/(2))/(2 + sin x) = (cos x)/( 3)then x =

The locus of the point represented by x=cos^(2)t,y=2sint is

What is the number of terms in the expansion of the following? (a+bx)^(17) - (a-bx)^(17)

Solution set of the equation 3 tan^(2) theta + 4 tan theta + 2 =0 is ...............

If A is in the fourth quadrant and cos A=(5)/(13), find the value of (13 sin A+5 secA)/(5tanA+6" cosec"A).

Find the condition that the slope of one of the lines represented by ax^2 + 2xy +by^2 = 0 is square of slope the other

The reflection of the plane 2x - 3y + 4z - 3=0 in the plane x - y + z -3 =0 is the plane

Which of the following statements is true for the funiction f(x)={{:(sqrt(x)",",xge1),(x^(3)",",olexle1),((x^(3))/(3)-4x",",xle0):}

(""^(8) C_(0) )/(6) - ""^(8) C_1 + ""^(8) C_(2) . 6-""^(8) C_3 . 6^2 + ... + ""^(8) C_(8) .6^(7) is equal to(i) 0(ii) 6^7(iii) 6^5(iv) (5^8)/(6)

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

If the equation a_(n)x^(n) + a_(n-1) x^(n-1)+"......" + a_(1) x= 0(a_(1) cancel(=)0,nge 2)has a positive root x = alpha then the equation na_(n) x^(n-1)+(n-1)a_(n-1)x^(n-2)+"......"+a_(1) =0 has a positive root, which is

The value of (sqrt(5)+1)^(5)-(sqrt(5)-1)^(5) is ………

If 4 sin 27^@ = sqrt(alpha) + sqrt(beta) then the sum of the digits in (alpha + beta + alpha beta + 2)^4

If barx.bara=barx.barb=barx.barc=0 for some non-zero vector barx and abs(bara)=abs(barb)=abs(barc)=1 then the volume of parallelopiped with bara,barb,barc is

Let A = (2,5) and B = (4, -1) are two vertices of a AABC. Third vertex C moves along L=9x+7y+4=0. The locus of the centroid of triangle ABC is the line

Write the negation of the following simple statements. sqrt(5) is a rational number.

The y intercept of the line through the point (1,-2) making an angle of 135^(@) with the x - axis is

25x^(2)-9y^(2)=225

Show that, (1 xx 2^(2) + 2 xx 3^(2) + ….+ n xx (n+1)^(2))/(1^(2) xx 2 + 2^(2) xx 3 + ….+ n^(2) xx (n+1))= (3n+ 5)/(3n+ 1)

Write the first five terms of each of the sequences whose n^(th) terms are: a_(n)= 2^(n)

Show that Lim_(x to 2) log_(10){x^(6) +sqrt((x^(2)+1292))}=2

Find out which of the following sentences are statements and which are not ?JustifyStand up

A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn baJI is white, is

A(1, - 1, 2) B(1, 0, 2) C(2, -2, 3) and D(4, 2, 1) are the vertices of a tetrahedron then find the distance of the plane ABC from the vertex D.

If bar(a) = bar(i) + 2bar(j) + 3bar(k), bar(b) = 3bar(i) +5bar(j) -bar(k) are 2 sides of a triangle, find its area.

Find sum: (1)/(2) + (1)/(3^(2)) + (1)/(2^(3)) + (1)/(3^(4)) + (1)/(2^(5)) + (1)/(3^(6))+ …..oo

If tan.(C-A)/(2)=k cot.(B)/(2) then find k .

Find the number of terms of the series 21, 18, 15, 12...which must be taken to give a sum of zero.

Match the following from List - I to List - II {:(,"List - I",,"List - II"),(I.,[(1,1),(1,0)],(a),0),(II.,[(1,1),(1,1)],(b),1),(III.,[(0,0),(0,0)],(c),2),(IV.,[(1,0,0),(0,1,0),(0,0,1)],(d),3):}

Identify the Quantifiers in the following statements: There exists a statemen in above statements which is not true.

Find the value of sum_(n=1)^(oo)(1)/(2n-1)((1)/(9^(n-1))+(1)/(9^(2n-1))).

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

Orthocentre of the triangle formed by line 3x^(2)-xy-2y^(2)=0 and 2x+3y-5=0 is