14949 + Interview Questions in Maths in Class 11 Page 49 InterviewSolution

2401.	With the help of tables, find the values, correct to places of decimals, of each of the following : tan(2015^(@)24').
Answer» ANSWER :`0.7107`

Discussion

2402.	Show that the four points with position vectors bara,barb,barc,bard are coplaner if [barb barc bard]+[barc bara bard]+[bara barb bard]=[bara barb barc]
Answer» `[[BARABARBBARC]` `2[barabarbbarc]` `3[barabarbbarc]` 0 Answer :A

Discussion

2403.	If f(x)= (x-1)/(x+1), Then show that f(-(1)/(x))= (-1)/(f(x))
Answer» ANSWER :`-(1)/(F(X))`

Discussion

2404.	If tanx=(b)/(a) then acos(2x)+bsin(2x) = ……….
Answer» `a-B` a b `a+b` ANSWER :B

Discussion

2405.	If (baraxxbarb)xx(barcxxbard)=[barabarbbard]barc +kbard then k =
Answer» `[barbbarabarc]` `[BARABARBBARC]` `[barbbarcbard]` `[barcbarbbard]` ANSWER :A

Discussion

2406.	A point P(x, y) moves so that the product of the slopes of the two lines joining P to the two points (-2, 1) and (6, 5) is -4. Show that the locus is an ellipse and locate its centre.
Answer» ANSWER :`4X^(2)+y^(2)-16x-6y-43=0`, CENTRE (2, 3)

Discussion

2407.	The probability of happening of an event is 0.6 for one experiment. In three such experiments, find the probability of happening the event at least one time.
Answer» SOLUTION :N/a

Discussion

2408.	If n(U)= 700, n(A)= 200, n(B)= 300, n(A cap B)= 100" then"n(A' cap B')="………."
Answer» 400 600 300 200 Answer :C

Discussion

2409.	Let vec(a) + m vec(b) + n vec(c )= vec(0).vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a)= vec(0) for
Answer» `m + N = -1` `m + n = 1` `m + 2N= 1` `m-2n =1` ANSWER :A

Discussion

2410.	If sin h^(-1) (2) + sin h^(-1) (3) = x then cos h(x) =
Answer» `(1)/(2) (3 sqrt(5) + 2 sqrt(10))` `(1)/(2) (3 sqrt(5) - 2 sqrt(10))` `(1)/(2) (12 + 2 sqrt(50))` `(1)/(2) (12 - 2 sqrt(50))` ANSWER :C

Discussion

2411.	Check whether the given sentence is a statement or not : "5 is a prime number"
Answer» ANSWER :STATEMENT

Discussion

2412.	Solve \|x-1\|+\|x-2\|ge4,x in R.
Answer» Solution : Putting `x -1=0 and x-2=0`, we get `x =1 and x =2` as the critical points, These points DIVIDE the whole realline into three parts, namely`(-oo,1),[1,2) and [2,oo)`. So, we consider the following three CASES. Case I When `-ooltxlt1`. In this case, `x-1lt0 and x-2lt0`. `THEREFORE \|x-1\|=-(x-1)=-x+1 and\|x-2\|=-(x-2)=-x+2`. Now, `\|x-1\|+\|x-2\|ge4` `rArr-x+1-x+2ge4` `rArr -2x+3ge4rArr-2xge4-3rArr=-2xge1rArrxle(-1)/(2)` `rArr x in(-oo,(-1)/(2)]`. But, `-ooltxlt1.` `therefore` solution set in this case `=(-oo,(-1)/(2)]cap(-oo,1)=(-oo,(-1)/(2)]`. Case II When `1le x lt 2`. In this, case, `x-1ge0 and x-2lt0`. `therefore \|x-1\|=x-1and\|x-2\|=-(x-2)=-x+2`. Now, `\|x-1\|+\|x-2\|ge4` `rArr x-1-x+2ge4rArr-1ge4`, which is absured. So, the given inequation has no solution in `[1,2)`. Case III When `2 le x lt oo`. In this case, `x-2ge0and x-1gt0`. `therefore \|x-2\|=x-2 and \|x-1\|=x-1.` Now, `\|x-1\|+\|x-2\|ge4` `rArr x-1+x-2ge4rArr2x-3ge4 rArr2xge7 rArrxge(7)/(2)`. ALSO, in this case, we have `XGE 2`. `therefore` solution set in this case `=[(7)/(2),oo)nn[2,oo),=[(7)/(2),oo)`. Hence, from all the above cases, we have Solution set `=(-oo,(-1)/(2)]uu[(7)/(2),oo)`.

Discussion

2413.	Find (dy)/(dx) for the function (using logarithms). y = (x ^(3) sqrt ( 2+ 3x))/( (1- x ) (2 + x))
Answer» ANSWER :`y [ (3)/(x) + (3)/( 2 (2 + 3x))+ ( 1)/( 1-x) - (1)/( 2 +x)]`

Discussion

2414.	Let f(x) = sqrt(x-1) + sqrt(x+ 24-10sqrt(x-1)),1 lt x lt 26 be real valued function. Then f'(x)for 1 lt x lt 26 is
Answer» 0 `(1)/( sqrt(x-1))` `2 sqrt(x-1) -5` 5 Answer :A

Discussion

2415.	The nearest point on the line 2x-y+5=0 from the origin is
Answer» (2,1) (2,-1) (-2,1) (0,5) ANSWER :C

Discussion

2416.	The origin is shifted to (2,3) by the translation of axes. If a point P has changed as (i) (4, -3), find the coordinates of P in the originalsystem. (ii) (4, 5), find the coordinates of P in the original system.
Answer» ANSWER :(i) (6,0) (II) (6, 8)

Discussion

2417.	Consider the A.P. 18,15,12.... Find the sum to n terms of the A.P.
Answer» SOLUTION :`N/2[39-3N]`

Discussion

2418.	A square matrix (a_(ij)) where a_(ij)=0 for i!=j and a_(ij)=k (constant) for i=j is called
Answer» UNIT matrix Scalar matrix Null matrix Diagonal matrix Answer :B

Discussion

2419.	Number of functions defined from f{1,2,3,4,5,6} rarr {7,8,9,10} such that the sum f(1)+f(2)+f(3)+f(4)+f(5)+f(6) is odd is ______
Answer» `2^(11)` `2^(12)` `2^(11)-1` `2^(12)-1` ANSWER :A

Discussion

2420.	If (1+x)^n=C_(0)+C_(1)x+C_(2)x^2+….+C_(n)x^n then prove that(SigmaSigma)_(0 le i lt j le n ) C_(i)C_(j)^2=(n-1)^(2n)C_(n)+2^(2n)
Answer» Solution :L.H.S =`underset(0 LE i lt j le n )(SigmaSigma) C_(i)C_(j)^2=(n-1)^(2n)C_(n)+2^(2n)` `(C_(0)+C_(1))^2+(C_(0)+C_2)^2+....+(C_(0)+C_(n))^2+(C_1C_2)^2+(C_1+C_3)^2+....+(C_1+C_c)^2+(C_2+C_3)^2+(C_(2)+C_4)^2+....+(C_2+C_n)^2+......+(C_(n-1)+C_n)^2` `=n(C_(0)^2+C_1^2+C_2^2+....+C_n^2)+2underset(0 le i lt j le n )(SigmaSigma) C_(i)C_(j)` `n.""^(2n)C_(n)+2{2^(2n-1)-(2n !)/(2.n!n!)} "" {"from Illustration 17 "}` `=n.""^(2n)C_n+2^(2n)-""^(2n)C_n= (n-1).""^(2n)C_(n)+2^(2n)= R.H.S`

Discussion

2421.	Obtain the equation of the parabola with given conditions:Vertex (6, -3) equation of the directrix 3x - 5y + 1 =0.
Answer» Answer :`25X^(2) + 9Y^(2) - 618x + 554y + 30xy + 4929 = 0`

Discussion

2422.	The standard deviation of some centigrade (""^@C) temperature is 5. if it is convert in Fahrenheit temperature, then find its variance.
Answer» 81 57 36 25 Answer :A

Discussion

2423.	Find the slope and inclination of the line through each pair of the following points: (0, 0) and (-sqrt(3), 3)
Answer» ANSWER : `-SQRT(3), 120^(@)`

Discussion

2424.	cot^(2) theta ((sec theta -1)/(1+ sin theta ))+ sec^(2) theta ((sin theta -1)/( 1+ sec theta ))=
Answer» 0 1 2 -2 Answer :D

Discussion

2425.	Find sin""(x)/(2),cos""(x)/(2)andtan""(x)/(2) in each of the following. cosx=-(1)/(3),x in quadrant III.
Answer» ANSWER :`(SQRT6)/( 3),-(SQRT3)/(3), -SQRT2`

Discussion

2426.	Differentiate w.r.t.x Let y= (ax^(2) + bx + c)/( px^(2) + qx+ f)
Answer» Answer :`= ((aq - BP)X^(2)+ 2 (af -pc) x+bf - CQ)/((px^(2) +qx+f)^(2) )`

Discussion

2427.	Ifx log_(e) (log _(e) x) - x^(2) + y^(2) = 4 (y gt 0), then (dy)/(dx) atx = eis equal to
Answer» SOLUTION :`( 2e-1)/(2Y)`

Discussion

2428.	If origin is shifted to point (1,-2) then find the new transformed form of the following equation. (i) 2x^(2) + y^(2) - 4x+ 4y =0 (ii) y^(2) - 4x + 4y + 8=0
Answer» ANSWER :(i) `2x^(2) + y^(2) = 6` (ii) `y^(2) = 4x`

Discussion

2429.	If 4 sin^(2)x-8 sinx+3 le 0,0 le x le 2pi, x in
Answer» `[0,(PI)/(6)]` `[0,(5pi)/(6)]` `[(5pi)/(6),2PI]` `[(pi)/(6),(5pi)/(6)]` Answer :D

Discussion

2430.	From a pack of 52 cards , 3 cards are drawn at random . Findthe probability of drawing exactly two aces .
Answer» ANSWER :`(72)/(5525)`

Discussion

2431.	What is Kinematics?
Answer» SOLUTION :KINEMATICS is the branch of MECHANICS which deals with the MOTION of objects without taking force into ACCOUNT. The Greek word “kinema" means “motion”.

Discussion

2432.	If sin A=1//sqrt(10), sin B= 1//sqrt(5)where A and B are positive and acute , then A +B=
Answer» `(PI)/(2)` `(pi)/(3)` `(pi)/(4)` `(pi)/(5)` Answer :C

Discussion

2433.	The orbit of the earth around the sum is an ellipse. The sun is at one of the focus of this ellipse. If the length of its major axis of this ellipse. If the leght of its major axis of this ellipse is 30 million. Km. and eccentricity is 0,.0167 then find minimum and maximum distance of the earth from the sun.
Answer» ANSWER :MAXIMUM DISTANCE 152505000 KM. MINIMUM distance 147495000 km.

Discussion

2434.	Consider the G.p 3, 6, 12…Find its n^th term and sum to n terms
Answer» SOLUTION :`3xx2^(n-1)3(2^n-1)`

Discussion

2435.	If bara,barb,barc are any three vectors such that (bara+ barb) . barc = (bara - barb) . barc = 0 then (baraxx barb)xxbarc =
Answer» `BAR0` `BARA` `BARB` `BARC` ANSWER :A

Discussion

2436.	Given : f(x)=x^((1)/(x)),(xgt0) has the maximum value at x=e , then
Answer» `E^(X)gtpi^(e)` `e^(pi)gtpi^(pi)` `e^(pi)=pi^(e)` `e^(pi)lepi^(e)` ANSWER :A

Discussion

2437.	The turning values of x^3-3px+q(p gt 0) are
Answer» <P> ANSWER :`Q - 2psqrt(p), 2psqrt(p) + q`

Discussion

2438.	If b +c =3a , then find the value of cot.(B)/(2)cot.(C)/(2)
Answer» ANSWER :` 2`

Discussion

2439.	The value of tan840^(@) is equal to
Answer» `(1)/(SQRT(3))` `-(1)/(sqrt(3))` `sqrt(3)` `-sqrt(3)` ANSWER :D

Discussion

2440.	If a line through A(1, 0) meets the lines of the pair 2x^2 - xy = 0 at P and Q. If the point R is on the segment PQ such that AP, AR, AQ are in H.P then find the locus of the point R.
Answer» ANSWER :4x+y = 0

Discussion

2441.	A car starts from and attains the speed of 1 km/hr nad 2,ms/hr at the end of 1st and 2nd minutes. IF the car moves onstraight road, the distance travelled in 2 minutes is
Answer» `(1)/(4)` km `(1)/(30)` km 15 km 20 km Answer :B

Discussion

2442.	Solve: x^(2)+x+1=0.
Answer» Answer :Hence, the EQUATION have COMPLEX ROOTS `(-1+sqrt(3)i)/(2) and (-1-sqrt(3)i)/(2)`.

Discussion

2443.	A= {a, b {c, d}, e} which of the following statements are correct? phi in A
Answer» ANSWER :INCORRECT

Discussion

2444.	If \| cos theta{ sin theta + sqrt( sin^(2) theta + sin^(2) alpha)}\|le k, then the value of k is
Answer» `sqrt(1+ COS^(2) alpha)` `sqrt(1+ SIN^(2) alpha)` `sqrt(2+sin^(2) alpha)` `sqrt(2+cos^(2) alpha)` ANSWER :B

Discussion

2445.	Triangle ABC is isosceles with AB=AC and BC=65 cm. P is a point on BC such that the perpendicular distances from P to AB and AC are 24 cm and 36 cm, respectively. The area of triangle ABC (in sq.cm is)
Answer» 1254 1950 2535 5070 Answer :C

Discussion

2446.	Prove that the product of the 2^(nd) and 3^(rd) terms of an arithmetic progression exceeds the product of the first and fourth by twice the square of the difference between the 1^(st) and 2^(nd).
Answer» ANSWER :`= 2D^(2)`

Discussion

2447.	Solve the equation: 2^(2x+3)+2^(x+3)=1+2^(x).
Answer» ANSWER :`-3`

Discussion

2448.	Simplify (""^(n)P_(4))/(""^(n-1)P_(3))
Answer» ANSWER :10

Discussion

2449.	If tan.(A)/(2)=(5)/(6)andtan.(C)/(2)=(2)/(5) then determine the relation between a, b,c
Answer» ANSWER :HENCE a,B,C are in A.P .

Discussion

2450.	If y = log {((1 +x)/(1-x )) ^(1//4) } -1/2 Tan ^(-1) (x ), then (dy)/(dx)=
Answer» `X/(1-x^2)` `x^2/(1-x^4)` `x/(1+x^4)` `x/(1-x^4)` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

With the help of tables, find the values, correct to places of decimals, of each of the following : tan(2015^(@)24').

Show that the four points with position vectors bara,barb,barc,bard are coplaner if [barb barc bard]+[barc bara bard]+[bara barb bard]=[bara barb barc]

If f(x)= (x-1)/(x+1), Then show that f(-(1)/(x))= (-1)/(f(x))

If tanx=(b)/(a) then acos(2x)+bsin(2x) = ……….

If (baraxxbarb)xx(barcxxbard)=[barabarbbard]barc +kbard then k =

A point P(x, y) moves so that the product of the slopes of the two lines joining P to the two points (-2, 1) and (6, 5) is -4. Show that the locus is an ellipse and locate its centre.

The probability of happening of an event is 0.6 for one experiment. In three such experiments, find the probability of happening the event at least one time.

If n(U)= 700, n(A)= 200, n(B)= 300, n(A cap B)= 100" then"n(A' cap B')="………."

Let vec(a) + m vec(b) + n vec(c )= vec(0).vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a)= vec(0) for

If sin h^(-1) (2) + sin h^(-1) (3) = x then cos h(x) =

Check whether the given sentence is a statement or not : "5 is a prime number"

Solve |x-1|+|x-2|ge4,x in R.

Find (dy)/(dx) for the function (using logarithms). y = (x ^(3) sqrt ( 2+ 3x))/( (1- x ) (2 + x))

Let f(x) = sqrt(x-1) + sqrt(x+ 24-10sqrt(x-1)),1 lt x lt 26 be real valued function. Then f'(x)for 1 lt x lt 26 is

The nearest point on the line 2x-y+5=0 from the origin is

The origin is shifted to (2,3) by the translation of axes. If a point P has changed as (i) (4, -3), find the coordinates of P in the originalsystem. (ii) (4, 5), find the coordinates of P in the original system.

Consider the A.P. 18,15,12.... Find the sum to n terms of the A.P.

A square matrix (a_(ij)) where a_(ij)=0 for i!=j and a_(ij)=k (constant) for i=j is called

Number of functions defined from f{1,2,3,4,5,6} rarr {7,8,9,10} such that the sum f(1)+f(2)+f(3)+f(4)+f(5)+f(6) is odd is ______

If (1+x)^n=C_(0)+C_(1)x+C_(2)x^2+….+C_(n)x^n then prove that(SigmaSigma)_(0 le i lt j le n ) C_(i)C_(j)^2=(n-1)^(2n)C_(n)+2^(2n)

Obtain the equation of the parabola with given conditions:Vertex (6, -3) equation of the directrix 3x - 5y + 1 =0.

The standard deviation of some centigrade (""^@C) temperature is 5. if it is convert in Fahrenheit temperature, then find its variance.

Find the slope and inclination of the line through each pair of the following points: (0, 0) and (-sqrt(3), 3)

cot^(2) theta ((sec theta -1)/(1+ sin theta ))+ sec^(2) theta ((sin theta -1)/( 1+ sec theta ))=

Find sin""(x)/(2),cos""(x)/(2)andtan""(x)/(2) in each of the following. cosx=-(1)/(3),x in quadrant III.

Differentiate w.r.t.x Let y= (ax^(2) + bx + c)/( px^(2) + qx+ f)

Ifx log_(e) (log _(e) x) - x^(2) + y^(2) = 4 (y gt 0), then (dy)/(dx) atx = eis equal to

If origin is shifted to point (1,-2) then find the new transformed form of the following equation. (i) 2x^(2) + y^(2) - 4x+ 4y =0 (ii) y^(2) - 4x + 4y + 8=0

If 4 sin^(2)x-8 sinx+3 le 0,0 le x le 2pi, x in

From a pack of 52 cards , 3 cards are drawn at random . Findthe probability of drawing exactly two aces .

What is Kinematics?

If sin A=1//sqrt(10), sin B= 1//sqrt(5)where A and B are positive and acute , then A +B=

Consider the G.p 3, 6, 12…Find its n^th term and sum to n terms

If bara,barb,barc are any three vectors such that (bara+ barb) . barc = (bara - barb) . barc = 0 then (baraxx barb)xxbarc =

Given : f(x)=x^((1)/(x)),(xgt0) has the maximum value at x=e , then

The turning values of x^3-3px+q(p gt 0) are

If b +c =3a , then find the value of cot.(B)/(2)cot.(C)/(2)

The value of tan840^(@) is equal to

If a line through A(1, 0) meets the lines of the pair 2x^2 - xy = 0 at P and Q. If the point R is on the segment PQ such that AP, AR, AQ are in H.P then find the locus of the point R.

A car starts from and attains the speed of 1 km/hr nad 2,ms/hr at the end of 1st and 2nd minutes. IF the car moves onstraight road, the distance travelled in 2 minutes is

Solve: x^(2)+x+1=0.

A= {a, b {c, d}, e} which of the following statements are correct? phi in A

If | cos theta{ sin theta + sqrt( sin^(2) theta + sin^(2) alpha)}|le k, then the value of k is

Triangle ABC is isosceles with AB=AC and BC=65 cm. P is a point on BC such that the perpendicular distances from P to AB and AC are 24 cm and 36 cm, respectively. The area of triangle ABC (in sq.cm is)

Prove that the product of the 2^(nd) and 3^(rd) terms of an arithmetic progression exceeds the product of the first and fourth by twice the square of the difference between the 1^(st) and 2^(nd).

Solve the equation: 2^(2x+3)+2^(x+3)=1+2^(x).

Simplify (""^(n)P_(4))/(""^(n-1)P_(3))

If tan.(A)/(2)=(5)/(6)andtan.(C)/(2)=(2)/(5) then determine the relation between a, b,c

If y = log {((1 +x)/(1-x )) ^(1//4) } -1/2 Tan ^(-1) (x ), then (dy)/(dx)=