14949 + Interview Questions in Maths in Class 11 Page 275 InterviewSolution

13701.	Obtain the area of equilateral triangle inscribed in circle x^(2) + y^(2) + 2gx + 2fy + c = 0.
Answer» Answer :`(3sqrt(3))/(4)(G^(2)+F^(2)-c)` Sq. UNIT

Discussion

13702.	A point P(x,y) moves so that the sum of its distances from point (4,2) and (-2,2) is 8. If the locus of P is an ellipse then its length of semi-major axis is
Answer» 8 2 4 None of these ANSWER :C

Discussion

13703.	2x + y ge 0
Answer» SOLUTION :

Discussion

13704.	Iftan "" (A ) /(2) = (5)/(6), tan "" ( B)/(2)= ( 20 )/( 37)" then "a,b,care in
Answer» A.P. G.P. H.P. A.G.P Answer :A

Discussion

13705.	Solve :\|x-1/4\|lt\|1/2x-3/4\|
Answer» ANSWER :`-1 LT X lt 2/3`

Discussion

13706.	Evaluate the following limits : Lim_(x to 0) (sin x cos x)/(3x)
Answer» ANSWER :`1/3`

Discussion

13707.	If H is the orthocentre of a acute-angled triangle ABC whose circumcircle is x^(2)+y^(2)=16 then circum diameter of the triangle HBC is
Answer» 1 2 4 8 Answer :D

Discussion

13708.	If sin theta, 1, cos2 thetaare in G.P. then the general values of theta
Answer» `theta=n PI +(-1)^(n)(pi)/2, n in Z` `theta=n pi +(-1)^(n)(pi)/2, n in Z` `theta=n pi +(-1)^(n)(pi)/6,n in Z` `theta=n pi +(-1)^(n-1)(pi)/6, n in Z` ANSWER :B

Discussion

13709.	If in a triangle PQR , sin P, sin Q, sin R are in A.P., then
Answer» the ALTITUDE are in A.P the ALTITUDES are in H.P the altitudes are in G.P the MEDIANS are in A.P Answer :B

Discussion

13710.	Which of the following sentences is a statement?
Answer» A. 5 is LESS than 7 B. Where are you going? C. Close the door D. How FUNNY he is ! ANSWER :A

Discussion

13711.	Derive the formula to find the co-ordinates of a point which divide the line joining the points A(x_1,y_1,z_1) and B(x_2,y_2,z_2)internally in the ratio m:n.
Answer» Answer :` R= ((mx_(2)+nx_(1))/(m+n),(my_(2)+ny_(1))/(m+n),(mz_(2)+nz_(1))/(m+n))`

Discussion

13712.	If angleBAC=120^(@) then measure of angleRPQ will be
Answer» `60^(@)` `90^(@)` `120^(@)` `150^(@)` ANSWER :B

Discussion

13713.	Write the expansion of (a-b)^n, n is a positive integer
Answer» SOLUTION :`(a+B)^n=a^n-"^nC_1a^(n-1)b+...+(-1)^nb^n`

Discussion

13714.	Let O be the circumcentre, H be the orthocentre, I be the incentre and I_(1)I_(2),I_(3) be the excentres of acuteangled DeltaABC
Answer» ANSWER :A::B::C::D

Discussion

13715.	Which of the following sentences are statements? Justify sin^(2)x+cos^(2)x=0
Answer» ANSWER :It is STATEMENT.

Discussion

13716.	The minimum value ofcos^(3) x+ cos^(3) (120^(@) + x) + cos^(3) (120^(@) -x)is
Answer» `1/4` `1/2` `3/4` 1 Answer :C

Discussion

13717.	Derive cosine formula using the law of sines in a triangleABC.
Answer» ANSWER :`(1+COS (A-B) cos C)/(1+cos (A-C) cos B)`

Discussion

13718.	If p=(sinA)/(sinB) and q=(cos A)/(cos B)
Answer» Solution :`p=(sinA)/(sinB)` and `therefore p/q=(sinA//sinB)/(cosA//COSB)= (sinA)/(sinB).(cosB)/(sinB)` `=tanA. cotB=tanA. 1/(TANB)=(tanA)/(tanB)` `RARR (tanA)/p = (tanB)/(q)=k` (say) `rArr tanA=p.k` and `tan B=q.k` Now `(sinA)/(sinB)=p` `rArr sinA=sinB` `rArr (sinA)/(cosA. secA)= (p.sinA)/(cosB.secB)` `rArr (tanA)/(sqrt(sec^(2)A))= (p.tanB)/(sqrt(sec^(2)B))` `rArr (tanA)/(sqrt(1+tan^(2)A))= (ptanB)/(sqrt(sec^(2)B))` `rArr (tanA)/(sqrt(1+tan^(2)A))=(ptanB)/(sqrt(1+tan^(2)B))` `rArr (pk)/(sqrt(1+p^(2)k^(2)))= (p.qk)/(sqrt(1+q^(2)k^(2)))` `rArr sqrt(1+q^(2)k^(2))=qsqrt(1+p^(2)k^(2))` `rArr 1+q^(2)k^(2)=q^(2)(1+p^(2)k^(2))` `= q^(2)+p^(2)q^(2)k^(2)` `rArr q^(2)k^(2)(1-p^(2))=q^(2)-1` `rArr k^(2)=(q^(2)-1)/(q^(2)(1-p^(2))` `rArr k= +-1/qsqrt((q^(2)-1)/(1-p^(2)))` `therefore tan A = +- p/q sqrt((q^(2)-1)/(1-p^(2)))` and `tan B=+-sqrt((q^(2)-1)/(1-p^(2)))`Ans.

Discussion

13719.	In the hyperbola x ^(2) - y ^(2) = 4, find the length of the axes, the coordinates of the foci, the ecentricity, and the latus rectum, and the equations of the directrices.
Answer» ANSWER :`sqrt5 x pm 4 =0`

Discussion

13720.	Find the derivatives of the function x tan ^(-1) x
Answer» Answer :`COS x ; (tan ^(-1) x) ^(2) + (2SIN x tan ^(-1))/( 1 + x ^(2))`

Discussion

13721.	If sum of the n terms of a G.P be S, their product P and the sum of their reciprocals R, then prove that P^(2)=((S)/(R ))^(n)
Answer» <P> ANSWER :`P^(2)=((S)/(R ))^(N)`

Discussion

13722.	For DeltaABC , sinA + sinB + sinC
Answer» ANSWER :`GE`

Discussion

13723.	y co - ordinate of the point lies on X - axis is ..........
Answer» ANSWER :ZERO

Discussion

13724.	Find the value of (i) sin 765^(@) (ii) " cosec"(-1410^(@)) (iii) cot ((-15pi)/(4))
Answer» ANSWER :1

Discussion

13725.	Let f(theta)=(cot theta)/(1+cot theta) and alpha+beta = (5pi)/(4), then the value of f(alpha), f(beta) is
Answer» `(1)/(2)` `-(1)/(2)` 2 3 Answer :A

Discussion

13726.	Write the following statement in five different ways, conveying the same meaning. p: If a triangle is equiangular, then it is an obtuse angled triangle.
Answer» ANSWER :EQUAL MEASURE.

Discussion

13727.	Find sets A, B and C such that A∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B∩ C = φ.
Answer» Answer :We MAY TAKE `A = { 1, 2 }, B = { 1, 3 }, C = { 2 , 3 }`

Discussion

13728.	If A=60 ^(@)" then "( b) / ( c+ a)+ ( c ) /( a+ b)=
Answer» `1` `2` `3` `4` ANSWER :A

Discussion

13729.	Show that the relative error in the n^(th) power of a number is 'n' times the relative error in that number
Answer» ANSWER :`F(X)=x^(N)`

Discussion

13730.	A rod AB of length 15 cm rests in between two coordinate axes is such a way that the end point A lies on x-axis and end Point B lies on y-axis. A point P (x,y) is taken on the rod in such a way that AP=6cm . Show that the locus of P is an ellipse.
Answer» <P> ANSWER :THUS the LOCUS P is an ELLIPSE.

Discussion

13731.	( cot ""(A)/(2) + cot ""(B)/(2)+ cot ""( C )/( 2))/(cot A + cot B + cot C ) =
Answer» ` (( a+B+C)^(2))/( a^(2) + b^(2) +c^(2))` ` ( a+b+c)/( a^(2) + b^(2) +c^(2))` ` ( a+b+c)/( a^(3) + b^(3) +c^(3))` ` ( a^(2) +b^(2) +c^(2) )/(( a + b +c)^(2))` ANSWER :A

Discussion

13732.	If f(x)=(x^(2)+1)/([x]), ([.] denotes the greatest integer function), 1 le x lt 4, then
Answer» RANGE of F is `[2, (17)/(3))` f is monotonically increasing in [1, 4] the maximumvalue of f(X) is `(17)/(3)` the maximum value of `f(x)` is `(17)/(4)` ANSWER :A

Discussion

13733.	For the equation 2x=tan(2tan^(-1)a)+2tan(tan^(-1)a+tan^(-1)a^(3)), which of the following is valid ?
Answer» `a^(2)x+2a=x` `a^(2)+2ax+1=0` `a!=0` `a=-2,2` ANSWER :A

Discussion

13734.	Show that \|{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}\|=2\|{:(a,b,c),(b,c,a),(c,a,b):}\|
Answer» ANSWER :`=2\|{:(a,B,C),(b,c,a),(c,a,b):}\|`

Discussion

13735.	If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find A ∪ B
Answer» Answer :`{ 1, 2, 3, 4, 5, 6 }`

Discussion

13736.	If vec(u)= vec(a)- vec(b), vec(v)= vec(a) + vec(b) and \|vec(a)\| =\|vec(b)\|=2, (vec(a), vec(b)) =(pi)/(3), then \|vec(u) xx vec(v)\|=
Answer» `SQRT3` `2 sqrt3` `3 sqrt3` `4 sqrt3` ANSWER :D

Discussion

13737.	If barA=(1,a,a^(2)),barB=(1,b,b^(2)),barC=(1,c,c^(2)) are non-coplanar vectors and abs({:(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))}:)=0 then abc=
Answer» `-2` `-1` 2 1 Answer :B

Discussion

13738.	Find the derivative of the function wrt x. Sec ^(-1) ((1)/( sqrt (1 - x ^(2))))
Answer» ANSWER :`(1)/( SQRT (1 - X ^(2)))`

Discussion

13739.	d/dx{Tan ^(-1) (( sqrt ( 1 + x ^(2)) - sqrt (1 - x ^(2)))/( sqrt (1 + x ^(2)) + sqrt (1 - x ^(2))))} =
Answer» `(X^2)/(SQRT(1 - x^4))` `(x^2)/(sqrt(1 + x^4))` `(x)/(sqrt(1 + x^4))` `(x)/(sqrt(1 - x^4))` ANSWER :D

Discussion

13740.	Discuss the continuity of f(x)={{:(2x=-1,if x le1),(x^(2),if 1 lt x lt 2),(3x-4,if 2lt x lt 4),(x^(3/2),if x ge4):} on R
Answer» ANSWER :CONTINOUS on R-(2) discontinous at 2

Discussion

13741.	If bara.bari = 4 then (bara xx barj).(2barj - 3bark) =
Answer» `-12` 0 2 12 Answer :A

Discussion

13742.	Statement-I : If the equation 4x^(2)+mxy-3y^(2)=0 represents a pair of real and distinct lines then m in R. Statement-II : If the difference of the slopes of the lines kx^(2)-12xy + y^(2) = 0 is 2 then k is 30 Which of the above statement is correct :
Answer» only I only II Both I and II NEITHER I nor II Answer :A

Discussion

13743.	If an angle alpha is divided into two parts A and B such that A-B=x and Tan : Tan B=k:then sin x=
Answer» `(K+1)/(k-1) SIN ALPHA` `(k)/(k+1) sin alpha` `(k-1)/(k+1) sin alpha` `(k+1)/(k) sin alpha` ANSWER :C

Discussion

13744.	cosec x =-2
Answer» Answer :`(7pi)/( 6), (11pi)/(6) , N PI + (-1) ^(n) (7pi)/(6), n in Z`

Discussion

13745.	If log_(2)x ge 0" then "log_(1/pi)(sin^(-1)((2x)/(1+x^(2)))+2Tan^(-1)x)=lambda" then "abs(lambda)=
Answer» 1 2 3 4 Answer :A

Discussion

13746.	At the point (2,3) on the curve y = x^(3) - 2x + 1, the gradient of the curve increases
Answer» 6 times as FAST as x 10 times as fast as x 12 times s fast as x 8 times as fast as x Answer :C

Discussion

13747.	Write the negation of the following statements: r: For every real number x, either x > 1 or x < 1.
Answer» Answer :There exists a REAL NUMBER X such that NEITHER `x > 1` nor `x < 1`.

Discussion

13748.	If the angle between two lines is (pi)/(4) and slope of one of the lines is (1)/(2), find the slope of the other line.
Answer» ANSWER :3 OR `- (1)/(3)`

Discussion

13749.	If the point (0,4) and (0,2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.
Answer» ANSWER :32

Discussion

13750.	If A={a,b,c,d,e} , B ={a,c,e,g} and C= { b,e,f,g}, verify that:(i)A cup B =B cup A (ii) A cup C= Ccup A (iii) Bcup C = C cup B (iv) A cap B= B cap A (v)B capC = C cap B (vi) A capC= C cap A (vii)(A cup B) cup C A cup (B cup C) (viii) A cap C= Ccap A .
Answer»

Discussion

Explore topic-wise InterviewSolutions in .

Obtain the area of equilateral triangle inscribed in circle x^(2) + y^(2) + 2gx + 2fy + c = 0.

A point P(x,y) moves so that the sum of its distances from point (4,2) and (-2,2) is 8. If the locus of P is an ellipse then its length of semi-major axis is

2x + y ge 0

Iftan "" (A ) /(2) = (5)/(6), tan "" ( B)/(2)= ( 20 )/( 37)" then "a,b,care in

Solve :|x-1/4|lt|1/2x-3/4|

Evaluate the following limits : Lim_(x to 0) (sin x cos x)/(3x)

If H is the orthocentre of a acute-angled triangle ABC whose circumcircle is x^(2)+y^(2)=16 then circum diameter of the triangle HBC is

If sin theta, 1, cos2 thetaare in G.P. then the general values of theta

If in a triangle PQR , sin P, sin Q, sin R are in A.P., then

Which of the following sentences is a statement?

Derive the formula to find the co-ordinates of a point which divide the line joining the points A(x_1,y_1,z_1) and B(x_2,y_2,z_2)internally in the ratio m:n.

If angleBAC=120^(@) then measure of angleRPQ will be

Write the expansion of (a-b)^n, n is a positive integer

Let O be the circumcentre, H be the orthocentre, I be the incentre and I_(1)I_(2),I_(3) be the excentres of acuteangled DeltaABC

Which of the following sentences are statements? Justify sin^(2)x+cos^(2)x=0

The minimum value ofcos^(3) x+ cos^(3) (120^(@) + x) + cos^(3) (120^(@) -x)is

Derive cosine formula using the law of sines in a triangleABC.

If p=(sinA)/(sinB) and q=(cos A)/(cos B)

In the hyperbola x ^(2) - y ^(2) = 4, find the length of the axes, the coordinates of the foci, the ecentricity, and the latus rectum, and the equations of the directrices.

Find the derivatives of the function x tan ^(-1) x

If sum of the n terms of a G.P be S, their product P and the sum of their reciprocals R, then prove that P^(2)=((S)/(R ))^(n)

For DeltaABC , sinA + sinB + sinC

y co - ordinate of the point lies on X - axis is ..........

Find the value of (i) sin 765^(@) (ii) " cosec"(-1410^(@)) (iii) cot ((-15pi)/(4))

Let f(theta)=(cot theta)/(1+cot theta) and alpha+beta = (5pi)/(4), then the value of f(alpha), f(beta) is

Write the following statement in five different ways, conveying the same meaning. p: If a triangle is equiangular, then it is an obtuse angled triangle.

Find sets A, B and C such that A∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B∩ C = φ.

If A=60 ^(@)" then "( b) / ( c+ a)+ ( c ) /( a+ b)=

Show that the relative error in the n^(th) power of a number is 'n' times the relative error in that number

A rod AB of length 15 cm rests in between two coordinate axes is such a way that the end point A lies on x-axis and end Point B lies on y-axis. A point P (x,y) is taken on the rod in such a way that AP=6cm . Show that the locus of P is an ellipse.

( cot ""(A)/(2) + cot ""(B)/(2)+ cot ""( C )/( 2))/(cot A + cot B + cot C ) =

If f(x)=(x^(2)+1)/([x]), ([.] denotes the greatest integer function), 1 le x lt 4, then

For the equation 2x=tan(2tan^(-1)a)+2tan(tan^(-1)a+tan^(-1)a^(3)), which of the following is valid ?

Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}|

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find A ∪ B

If vec(u)= vec(a)- vec(b), vec(v)= vec(a) + vec(b) and |vec(a)| =|vec(b)|=2, (vec(a), vec(b)) =(pi)/(3), then |vec(u) xx vec(v)|=

If barA=(1,a,a^(2)),barB=(1,b,b^(2)),barC=(1,c,c^(2)) are non-coplanar vectors and abs({:(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))}:)=0 then abc=

Find the derivative of the function wrt x. Sec ^(-1) ((1)/( sqrt (1 - x ^(2))))

d/dx{Tan ^(-1) (( sqrt ( 1 + x ^(2)) - sqrt (1 - x ^(2)))/( sqrt (1 + x ^(2)) + sqrt (1 - x ^(2))))} =

Discuss the continuity of f(x)={{:(2x=-1,if x le1),(x^(2),if 1 lt x lt 2),(3x-4,if 2lt x lt 4),(x^(3/2),if x ge4):} on R

If bara.bari = 4 then (bara xx barj).(2barj - 3bark) =

Statement-I : If the equation 4x^(2)+mxy-3y^(2)=0 represents a pair of real and distinct lines then m in R. Statement-II : If the difference of the slopes of the lines kx^(2)-12xy + y^(2) = 0 is 2 then k is 30 Which of the above statement is correct :

If an angle alpha is divided into two parts A and B such that A-B=x and Tan : Tan B=k:then sin x=

cosec x =-2

If log_(2)x ge 0" then "log_(1/pi)(sin^(-1)((2x)/(1+x^(2)))+2Tan^(-1)x)=lambda" then "abs(lambda)=

At the point (2,3) on the curve y = x^(3) - 2x + 1, the gradient of the curve increases

Write the negation of the following statements: r: For every real number x, either x > 1 or x < 1.

If the angle between two lines is (pi)/(4) and slope of one of the lines is (1)/(2), find the slope of the other line.

If the point (0,4) and (0,2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.

If A={a,b,c,d,e} , B ={a,c,e,g} and C= { b,e,f,g}, verify that:(i)A cup B =B cup A (ii) A cup C= Ccup A (iii) Bcup C = C cup B (iv) A cap B= B cap A (v)B capC = C cap B (vi) A capC= C cap A (vii)(A cup B) cup C A cup (B cup C) (viii) A cap C= Ccap A .