14949 + Interview Questions in Maths in Class 11 Page 294 InterviewSolution

14651.	Find the square root of the complex number -4-3i
Answer» ANSWER :`+- ((1)/(SQRT2)- (3)/(sqrt2)i)`

Discussion

14652.	The sides of a triangle are OA, OB, AB and have equations 2x-y=0, 3x+y=0, x-3y+10=0, respectively. Find the equation of the three medians of the triangle and verify that they are concurrent.
Answer» ANSWER :`7x-y=0,x-y+2=0,x+2y-5=0`

Discussion

14653.	x^(2) + 3x +9=0
Answer» ANSWER :`(-3 +-3sqrt(3)i)/2`

Discussion

14654.	Solve the general vlaue. tan 2x + 2 tan x =0
Answer» ANSWER :`N pi, n pi PM alpha ` when ` TAN ^(2) alpha = 2`

Discussion

14655.	Find the derivative of x at x = 1.
Answer» ANSWER :1

Discussion

14656.	Two dice are thrown together. The probability that the sum of the numbers obtained on both the dice is prime is ....
Answer» ANSWER :`5/12`

Discussion

14657.	Find n, if the ratio of the fifth term from beginning to the fifth term from the end in the expansion of (root(4)(2) + 1/root(4)(3))^n id sqrt6:1.
Answer» ANSWER :N = 10

Discussion

14658.	Solve sin^(2)theta-costheta=1/4 for theta and write the values of theta in the interval 0 lethetale2pi
Answer» Solution :The GIVEN equation can be written as `1-cos^(2)theta-costheta=1/4 rArr cos^(2)theta+costheta-3//4=0` `rArr 4cos^(2)theta+4costheta-3=0 rArr (2costheta-1)(2costheta+3)=0` `rArr costheta=1/2,-3/2` Since, `costheta=-3//2` is not POSSIBLE as `-1 LE costhetale1` `therefore costheta=1/2 rArr costheta=cospi/3 rArr theta=2npi+-pi/3, n in I` For the given interval, n=0 and n=1 `rArr theta=pi/3, (5pi)/(3)`Ans.

Discussion

14659.	Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 10. . .A
Answer» ANSWER :`∉`

Discussion

14660.	If sum _(r=1)^(n) t_(r) = (1)/( 12) n (n+1) (n+2) then sum_(r=1)^(n)(1)/( t_r)
Answer» `(2N)/( n+1)` `(4N)/( n+1)` `(3N)/( n+2)` `(3n)/( n+1)` ANSWER :B

Discussion

14661.	Evaluate the following limits : Lim_(xto oo) x tan (1/x)
Answer» ANSWER :1

Discussion

14662.	If a,c,b are in G.P then the line ax+by+c=0
Answer» has fixed DIRECTION always PASSES through a fixed point forms a triangle with the axes whose AREA is constant always CUTS intercepts on the axes such that their SUM is zero Answer :C

Discussion

14663.	Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+ 2/3 +4/9 +............
Answer» ANSWER :`(211)/81`

Discussion

14664.	1^(2)+ 3^(2)x+ 5^(2)x^(2)+ 7^(2)x^(3)+.....
Answer» ANSWER :`(1+7x)/((1-x)^(2))+(8X^(2))/((1-x)^(3)`

Discussion

14665.	If A and B are two sets such that A sub B,then A uu B is a)A b)Null set c)Bd){O/}
Answer» A Null set B `{O/}` ANSWER :B

Discussion

14666.	If bara, barb, barc are non-coplanar, non zero vectors then (baraxxbarb)xx(baraxxbarc)+(barb xxbarc)xx(barbxxbara)+ (barcxxbara)xx(barcxxbarb) =
Answer» `[BARABARBBARC]^(2)(bara+barb+barc)` `[barabarbbarc](bara+barb+barc)` `BAR0` 0 Answer :B

Discussion

14667.	A rectangle is inscribed in a equilaternal triangle of side length 2a units . The maximum area of this rectangle can be
Answer» `SQRT(3)a^(2)` `(sqrt(3)a^(2))/(4)` `a^(2)` `(sqrt(3)a^(2))/(2)` ANSWER :D

Discussion

14668.	If P, Q, R and S are points whose position vectors are bari-bark, -bari+2barj, 2barj-3bark and 3bari - 2barj- bark respectively, then find the component of bar(RS) " on " bar(PQ).
Answer» ANSWER :`-4/3`

Discussion

14669.	Evaluate the following limits : Lim_( x to 1^(-)) (x^(2) -1)/(\|x-1\|)
Answer» ANSWER :`-2`

Discussion

14670.	If y = Sin ^(-1) (1 - x ^(2))/(1+ x ^(2))then (dy)/(dX)=
Answer» ANSWER :`(-2)/( 1 + X ^(2))`

Discussion

14671.	if y = Tan^(-1)(sec x + tanx) then (dy)/(dx) =
Answer» `1` `1/2` `-1` `0` ANSWER :B

Discussion

14672.	If (tan3A)/(tanA)=arArr (sin3A)/(sinA)=
Answer» `(2A)/(a-1)` `(2a)/(a+1)` `a/(a+1)` `a/(a-1)` ANSWER :A

Discussion

14673.	The polar form of 1+isqrt(3) is
Answer» `2( cos ""(pi)/(6) + isin""(pi)/(6))` `2( cos ""(pi)/(3) + isin""(pi)/(3))` `2(cos ""(2PI)/(3)+isin""(2pi)/(3))` `2( cos (-(pi)/(6))+ isin (-(pi)/(6)))` ANSWER :B

Discussion

14674.	Statement-1: If a = 3, b = 7, c = 8, and internal angle bisector Al meets BC at D (where I is incenter), then AI/ID = 11/2 Statement-2 : Internal angle bisector of angle A divides the side BC in the ratio AB/AC
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 :D

Discussion

14675.	Evaluate the following limits. Lt_(xtooo)(sqrt(x^(2)+ax+b)-x)
Answer» ANSWER :a/2

Discussion

14676.	Using properties of sets, show that A ∩ ( A ∪ B ) = A.
Answer» ANSWER :`= A`

Discussion

14677.	A particle moves along the X-axis with velocity v = (dx)/(dt)=f(x) then the acceleration of the particle is
Answer» F''(X) f(x) f(x),f(x) f(x) ANSWER :C

Discussion

14678.	Let ABC be a triangle. If P is a point such that AP divides BC in the ratio 2:3, BP divides CA in the ratio 3:5 then the ratio in which CP divides AB is
Answer» `2:5` `2:-5` `5:2` `5:-2` ANSWER :C

Discussion

14679.	Find the derivatives from the left and from the right at x=1 (if they exist) of the following functions. Are the functions differentiable at x=1? f(x)=abs(x-1)
Answer» ANSWER :1

Discussion

14680.	If the sides a, b, c of a triangle are in G..P. and largest angle exceeds the smallest by 60^(@), then cos B =
Answer» 1 `(sqrt(13) - 1)/4 ` `1/2` `(1- SQRT13)/4` ANSWER :B

Discussion

14681.	If the linea_1x+b_1y=1,a_2x+b_2y=1,a_3x+b_3y=1 are concurrent then the points (a_1,b_1),(a_2,a_2),(a_3,b_3),
Answer» FORMS equlateral triangle forms RIGHT ANGLED triangle forms SCALENE triangle lie on a STRAIGHT line Answer :D

Discussion

14682.	If tan theta + tan phi =a, and cot theta + cot phi =b, and theta - phi = alpha ne 0, then
Answer» `AB gt 4` `ab=4` `TAN^(2)ALPHA =(ab(ab-4))/(a+b)^(2)` `cot^(2)alpha =(ab(ab+4))/(a-b)^(2)` Answer :A::C

Discussion

14683.	A firm manufactures PVC pipes in three plants viz, X,Y and Z. The daily production volumes from the three firms X,Y and Z are respectively 2000 units, 3000 units and 5000 units. It is known from the past experience that 3% of the output from plant X,4% form plant Y and 2% from plant Z are defective. A pipe is selected at random from a days total production,(i)find the probability that the selected pipe is a defective one(ii)if the selected pipe is a defective ,then what is the probability that it was produced by plant Y?
Answer» ANSWER :(i)`(7)/(250)` (II)`(3)/(7)`

Discussion

14684.	If f(x)={{:(\|x\|+1",",xlt0),(0",",x=0),(\|x\|-1",",xgt0):} For what value(s) of a does lim_(xrarra)f(x) exists?
Answer» ANSWER :`lim_(xrarra)f(X)` EXISTS for all `ANE0`.

Discussion

14685.	Evaluate Lt_(xto0)(1+ax)^(b//x) where a, b are constants.
Answer» ANSWER :`E^(AB)`

Discussion

14686.	The most general value of theta which satisfies both equations tantheta=-1 and costheta=(1)/(sqrt(2)) is
Answer» `NPI+(7pi)/(4)` `2npi+(7pi)/(4)` `npi+(-1)^(N)(7pi)/(4)` `(7pi)/(4)` Answer :B

Discussion

14687.	Find the valule (s) of k so that the line 2x + y + k =0 may touch the hyperbola 3x ^(2) - y ^(2) = 3
Answer» ANSWER :` K = pm1 `

Discussion

14688.	A line passing through the point P(1,2) meets the line x+y=7 at the distance of 3 units from P. Then theslope of this line satisfies the equation :
Answer» `8x^(2)-9x+1=0` `7x^(2)-18x+7=0` `16x^(2)-39x+16=0` `7x^(2)-6x-7=0` Solution :The equation of a line through P(1,2) is `(x-1)/(cos theta)=(y-2)/(sin theta)` The COORDINATES of point of this line at a distance of 3 units from P(1,2) are given by `(x-1)/(cos theta)=(y-2)/(sin theta)=PM3` . Letthe coordinates of the points be `(1 pm 3 cos theta, 2 pm sin theta)` . Thesepoints lie on `x+y=7`. `(1 pm 3 cos theta)+(2 pm 3 sintheta)=7` `IMPLIES pm3(cos theta + sin theta)=4` `implies 9(1+sin 2theta)=16` `implies (18tan theta)/(1+tan^(2)theta)=7` `implies 7 tan^(2)theta-18 tan theta +7=0` `implies tan theta ` is a root of `7x^(2)-18x+7=0`

Discussion

14689.	Find the square roots of the following : -8-6i
Answer» ANSWER :`+-(1-3i)`

Discussion

14690.	If f_(n)(x) = (sin x)/(cos3x)+(sin 3x)/(cos 3^(2)x) +(sin 3^(2)x)/(cos 3^(3)x) +....+ (sin 3^(n-1)x)/(cos 3^(n)x)"Then" f_(2) ((pi)/(4)) + f_(3) ((pi)/(4))=
Answer» 0 1 -1 2 Answer :C

Discussion

14691.	If x=sin(2tan^(-1)2) and y=sin(1/2"tan"^(-1)4/3) then
Answer» `x=y` `x GT y` `2/sqrt(5)` `x lt y` Answer :B

Discussion

14692.	Express (1- 2i)/(2+i) + (3+i)/(2-i) in the form a + bi
Answer» ANSWER :`1+ 0I`

Discussion

14693.	Assertion : The distance between the straight lines y=mx+c_(1),y=mx+c_(2) is \|c_(1)-c_(2)\|impliesm=0 Reason : The distance between parallel lines ax+by+c_(1)=0,ax+by+c_(2)=0 is (\|c_(1)-c_(2)\|)/(sqrt(a^(2)+b^(2))) Then the correct answer
Answer» A, R are correct, R is correct EXPLANATION of A A,R are correct, R is not correct explanation of A A is true, R is FALSE A is false, R is true Answer :A

Discussion

14694.	The point (-2, -3, -4) lies in the _____
Answer» FIRST octant Seventh octant Second octant Eighth octant Answer :B

Discussion

14695.	One bisector of a(x-1)^(2)+2h(x-1)y+by^(2)=0 is 2x+y-2=0 is then other bisector is
Answer» 2x+y+2=0 x – 2Y + 1 = 0 x – 2y – 1 = 0 2x + y = 1 Answer :C

Discussion

14696.	Find the derivative of the following functions: "cosec"x
Answer» ANSWER :`-"COSEC"X COTX`

Discussion

14697.	If x,y = 12 then the minimum value of x^2+y^2 is
Answer» 72 144 49y 7y Answer :A

Discussion

14698.	If f[1, oo)rarr[1, oo) is defined by f(x)=2^(x(x-1)) then f^(-1)(x)=
Answer» `(1/2)^(x(x-1))` `1/2 (1+ SQRT(1+4 log_(2)x))` `1/2 (1-sqrt(1+4log_(2)x))` `1/2 (1 PM sqrt(1+4 log_(2)x))` Answer :B

Discussion

14699.	The two equal sides of an isoceles triangle with fixed base b are decreasing at the rate of 3cm /s. How fast is the tea decreasing when the two equal to the base ?
Answer» `sqrt(3)b CM^(2)//s` `sqrt(3)b cm^(2)//s` `sqrt((3)/(2))cm^(2)//s` `sqrt(3)b^(2)cm^(2)//s` ANSWER :A

Discussion

14700.	If x + y = (2pi)/3 then equation cosx +cosy = 3/2 has empty solution set.
Answer» ANSWER :TRUE STATEMENT

Discussion

Explore topic-wise InterviewSolutions in .

Find the square root of the complex number -4-3i

The sides of a triangle are OA, OB, AB and have equations 2x-y=0, 3x+y=0, x-3y+10=0, respectively. Find the equation of the three medians of the triangle and verify that they are concurrent.

x^(2) + 3x +9=0

Solve the general vlaue. tan 2x + 2 tan x =0

Find the derivative of x at x = 1.

Two dice are thrown together. The probability that the sum of the numbers obtained on both the dice is prime is ....

Find n, if the ratio of the fifth term from beginning to the fifth term from the end in the expansion of (root(4)(2) + 1/root(4)(3))^n id sqrt6:1.

Solve sin^(2)theta-costheta=1/4 for theta and write the values of theta in the interval 0 lethetale2pi

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 10. . .A

If sum _(r=1)^(n) t_(r) = (1)/( 12) n (n+1) (n+2) then sum_(r=1)^(n)(1)/( t_r)

Evaluate the following limits : Lim_(xto oo) x tan (1/x)

If a,c,b are in G.P then the line ax+by+c=0

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+ 2/3 +4/9 +............

1^(2)+ 3^(2)x+ 5^(2)x^(2)+ 7^(2)x^(3)+.....

If A and B are two sets such that A sub B,then A uu B is a)A b)Null set c)Bd){O/}

If bara, barb, barc are non-coplanar, non zero vectors then (baraxxbarb)xx(baraxxbarc)+(barb xxbarc)xx(barbxxbara)+ (barcxxbara)xx(barcxxbarb) =

A rectangle is inscribed in a equilaternal triangle of side length 2a units . The maximum area of this rectangle can be

If P, Q, R and S are points whose position vectors are bari-bark, -bari+2barj, 2barj-3bark and 3bari - 2barj- bark respectively, then find the component of bar(RS) " on " bar(PQ).

Evaluate the following limits : Lim_( x to 1^(-)) (x^(2) -1)/(|x-1|)

If y = Sin ^(-1) (1 - x ^(2))/(1+ x ^(2))then (dy)/(dX)=

if y = Tan^(-1)(sec x + tanx) then (dy)/(dx) =

If (tan3A)/(tanA)=arArr (sin3A)/(sinA)=

The polar form of 1+isqrt(3) is

Statement-1: If a = 3, b = 7, c = 8, and internal angle bisector Al meets BC at D (where I is incenter), then AI/ID = 11/2 Statement-2 : Internal angle bisector of angle A divides the side BC in the ratio AB/AC

Evaluate the following limits. Lt_(xtooo)(sqrt(x^(2)+ax+b)-x)

Using properties of sets, show that A ∩ ( A ∪ B ) = A.

A particle moves along the X-axis with velocity v = (dx)/(dt)=f(x) then the acceleration of the particle is

Let ABC be a triangle. If P is a point such that AP divides BC in the ratio 2:3, BP divides CA in the ratio 3:5 then the ratio in which CP divides AB is

Find the derivatives from the left and from the right at x=1 (if they exist) of the following functions. Are the functions differentiable at x=1? f(x)=abs(x-1)

If the sides a, b, c of a triangle are in G..P. and largest angle exceeds the smallest by 60^(@), then cos B =

If the linea_1x+b_1y=1,a_2x+b_2y=1,a_3x+b_3y=1 are concurrent then the points (a_1,b_1),(a_2,a_2),(a_3,b_3),

If tan theta + tan phi =a, and cot theta + cot phi =b, and theta - phi = alpha ne 0, then

If f(x)={{:(|x|+1",",xlt0),(0",",x=0),(|x|-1",",xgt0):} For what value(s) of a does lim_(xrarra)f(x) exists?

Evaluate Lt_(xto0)(1+ax)^(b//x) where a, b are constants.

The most general value of theta which satisfies both equations tantheta=-1 and costheta=(1)/(sqrt(2)) is

Find the valule (s) of k so that the line 2x + y + k =0 may touch the hyperbola 3x ^(2) - y ^(2) = 3

A line passing through the point P(1,2) meets the line x+y=7 at the distance of 3 units from P. Then theslope of this line satisfies the equation :

Find the square roots of the following : -8-6i

If f_(n)(x) = (sin x)/(cos3x)+(sin 3x)/(cos 3^(2)x) +(sin 3^(2)x)/(cos 3^(3)x) +....+ (sin 3^(n-1)x)/(cos 3^(n)x)"Then" f_(2) ((pi)/(4)) + f_(3) ((pi)/(4))=

If x=sin(2tan^(-1)2) and y=sin(1/2"tan"^(-1)4/3) then

Express (1- 2i)/(2+i) + (3+i)/(2-i) in the form a + bi

Assertion : The distance between the straight lines y=mx+c_(1),y=mx+c_(2) is |c_(1)-c_(2)|impliesm=0 Reason : The distance between parallel lines ax+by+c_(1)=0,ax+by+c_(2)=0 is (|c_(1)-c_(2)|)/(sqrt(a^(2)+b^(2))) Then the correct answer

The point (-2, -3, -4) lies in the _____

One bisector of a(x-1)^(2)+2h(x-1)y+by^(2)=0 is 2x+y-2=0 is then other bisector is

Find the derivative of the following functions: "cosec"x

If x,y = 12 then the minimum value of x^2+y^2 is

If f[1, oo)rarr[1, oo) is defined by f(x)=2^(x(x-1)) then f^(-1)(x)=

The two equal sides of an isoceles triangle with fixed base b are decreasing at the rate of 3cm /s. How fast is the tea decreasing when the two equal to the base ?

If x + y = (2pi)/3 then equation cosx +cosy = 3/2 has empty solution set.