14949 + Interview Questions in Maths in Class 11 Page 245 InterviewSolution

12201.	Assertion (A) : P(3,4,5), Q(-1,7,9) are two given points, length of projection of PQ on xyplane is 5 units Reason ( R ): The projection of (x_(1),y_(1),z_(1)) " onXY PLANEis (x_(1),y_(1),0)
Answer» Both A and R are true and R is the CORECT explanation of A Both A and R are tru and R is not the CORRECT explanation of A a is true but Ris false A is false but R is true Answer :A

Discussion

12202.	Two dice are thrown.Find the probability of an odd number on one die and 5 on the other
Answer» ANSWER :`(1)/(12)`

Discussion

12203.	Consider the family of lines 5x+3y-2+lambda_(1)(3x-y-4)=0 andx-y+1+lambda_(2)(2x-y-2)=0. Equation of a straight line that belong to both families is
Answer» `25x-62y+86=0` `62x-25y+86=0` `25x-62y=86` `5x-2y-7=0` ANSWER :D

Discussion

12204.	If (1, 1, a) is the centroid of the triangle formed by the points (1, 2, -3) (b, 0, 1) and (-1, 1, -4), then a-b=
Answer» `-5` `-7` 5 1 Answer :a

Discussion

12205.	E is a point on the side AD of a rectangle ABCD, so that DE = 6, DA = 8, DC = 6. If CE is extended to meet the circumcircle of rectangle at F. Then DF = FB =
Answer» `5 SQRT2` `5 SQRT3` `2 SQRT5` None Answer :a

Discussion

12206.	Find the sum to n terms of the series , 5+11+19+29+41…
Answer» ANSWER :`=(N(n+2)(n+4))/3`

Discussion

12207.	Identify the quantifier in the following statements and write the negation of the statements. For every real number x, x is less than x + 1.
Answer» ANSWER : ''For EVERY''. The NEGATION is There exists a real number x such that x is not less than x + 1.

Discussion

12208.	Prove that C_1/C_0+(2c_(2))/C_1+(3C_3)/(C_2)+......+(n.C_n)/(C_(n-1))=(n(n+1))/2 2.C_0+(2^2.C_1)/(2)+(2^(3).C_(3))/(3)+.....(2^(4).C_3)/4+....(2^(n-1).C_(n))/(n+1)=(3^(n+1)-1)/(n+1) C_(0)-(C_(1))/2+C_(2)/3-.....+(-1)^a(C_n)/(n+1)=(1)/(n+1)
Answer»

Discussion

12209.	1+2+3+…….+(n+1)= ((n+1) (n+2))/(2) , n in N.
Answer» <P>For P(1) , L.H.S = 7 = R.H.S. For P(1) , L.H.S = 3 = R.H.S. `P(k) rArr P(k+1) , k in N` is not true By the principle of mathematical INDUCTION P(n) is true for all `n in N` . Which is not true . ANSWER :B

Discussion

12210.	If A ge 0, B ge 0, A + B = (pi)/(3) and y = tan A. tan B then
Answer» the MINIMUM VALUE of y is 3 the minimum value of is 1/3 the MAXIMUM value of y is 1/3 the minimum value of y is 0 Answer :D

Discussion

12211.	Evaluate : (2 tan 22 (1^(@))/( 2 ))/(1 - tan ^(2) 22 (1^(@))/( 2))
Answer» ANSWER :1

Discussion

12212.	Two adjacent sides of cyclic quadrilateral are 2 and 5 and angle between them is60 ^(@) .If the third side is 3 then the remaining side is
Answer» ` 2` ` 3` ` 4` ` 5` ANSWER :A

Discussion

12213.	Find the sum of (x + (1)/(x))^(2), (x^(2) + (1)/(x^(2)))^(2), (x^(3) + (1)/(x^(3)))^(2), ……..to n terms
Answer» ANSWER :`((X^(2N)-1)/(x^(2)-1)) (x^(2) + (1)/(x^(2n)))+ 2n`

Discussion

12214.	Evaluate the following limits : Lim_(x to 1) (x^(2) - x log x + log x - 1)/(x-1)
Answer» Answer :`1+1 - LOG 1 = 2 -0 = 2 "" [ :' X to 1 :. x != :. x - 1 != 0 ] `

Discussion

12215.	Let f(x)=ln(2x-x^(2))+sin((pi x)/(2)) then
Answer» GRAPHOF is SYMMETRICAL about the LINE x=1 Maximum value of f is 1 Absolute minimum value of f does not exist f(x) is a periodic function Answer :A::B::C::D

Discussion

12216.	If vec(a)= vec(i) + vec(j)+ vec(k), vec(c )= vec(j)- vec(k), then find vector vec(b) such that vec(a) xx vec(b)= vec(c ) and vec(a).vec(b)= 3
Answer» ANSWER :`(1)/(3) (5vec(i) + 2vec(J) + 2vec(K))`

Discussion

12217.	Write the sample space in each of the following : A coin is tossed and a die is thrown.
Answer» Answer :{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

Discussion

12218.	Solve graphically and compare your answer with algebraic solution either by factorization or formula method: (i) y=x^(2)-5x+6 (ii) y=-x^(2)+2x+3 (iii) y=x^(2)-4x+4 (iv) y=x^(2)-x-6 (v) y=x^(2)-6x+9 (vi) y=-x^(2)-x+12 (vii) y=x^(2)-4x+5=0 (viii) y=x^(2)+2x+2=0.
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C10_E05_004_A01##)`

Discussion

12219.	A straight line through origin O meets the lines 3y=10-4x and 8x+6y+5=0 at points A and B respectively. Then O divides the segment AB in the ratio.
Answer» `2:3` `1:2` `4:1` `3:4` ANSWER :C

Discussion

12220.	If si 4 A - cos 2A = cso 4A - sin 2A (0 lt A lt (pi)/(4)), then the value of tan 4A=
Answer» 1 `(1)/(SQRT3)` `sqrt3` `(sqrt3-1)/(sqrt3+1)` ANSWER :C

Discussion

12221.	Expand (2+ x)^(5) - (2- x)^(5) in ascending powers of x and simplify your result.
Answer» ANSWER :`160x+ 80X^(3) + 2X^(5)`

Discussion

12222.	The most general value of theta satisfying both the equations sintheta=1//2,tantheta=1//sqrt(3) is
Answer» `npi+(pi)/(6)` `(npi)/(2)+(-1)^(N)(7pi)/(6)` `2npi+(7pi)/(6)` `2npi+(11pi)/(4)` ANSWER :C

Discussion

12223.	Compute the first quartile and third deciles from the following data : {:("Weekly Income (in Rs.)",58,59,60,61,62,63,64,65,66),("No. of workers",2,3,6,15,10,5,4,3,1):}
Answer» ANSWER :`Q_(1) = Rs. 6, D_(3) = Rs. 61`

Discussion

12224.	If tan^(2)(pi-A)/4 + tan^(2)(pi-B)/2 + tan^(2) (pi-C)/4=1, then triangleABC is:
Answer» equilateral isoceles scalene obtuse angle Answer :A

Discussion

12225.	Length of the arc of circle with radius 5 cm and angle at centre is 15^@ ...........cm.
Answer» ANSWER :`(5PI)/12` CM

Discussion

12226.	Obtain the equation of the ellipse whose focus is the point (-1, 1), and the corresponding directrix is the line x-y+3=0, and the eccentricity is 1/2.
Answer» ANSWER :`7X^(2)+2xy+7y^(2)+10x-10y+7=0`

Discussion

12227.	If the d.c's of a line are (1//c,1//c,1c) then find c.
Answer» ANSWER :`PM SQRT(3)`

Discussion

12228.	A coin is tossed three times. Find the number of elemnts in 'Sample space '?
Answer» Answer :{HHH, HHT, HTH, TTH, HTT, THT, TTT}

Discussion

12229.	cos(2pi -x) cos (-x) - sin(2pi +x) sin (-x) = 0
Answer» ANSWER :FALSE STATEMENT

Discussion

12230.	If f:[1, oo)rarr[2, oo) is given by f(x)=x+(1)/(x) then f^(-1)(x)=
Answer» `((X+sqrt(x^(2)-4)))/(2)` `(x)/(1+x^(2))` `((x-sqrt(x^(2)-4))/(2))` `1+sqrt(x^(2)-4)` ANSWER :A

Discussion

12231.	If tanx = (2b)/(a-c) , a ne c, y = a cos^2 x + 2b sinx.cos x + c sin^2 x z = a sin^2 x -2b sinx.cos x+"c" cos ^2x then
Answer» y = Z `y - z = a +C` `y - z = a - c` `y - z = (a-c)^2 + 4b^2` ANSWER :C

Discussion

12232.	Find the mean deviation about the mediam for the data 13, 17,16,14,11,13,10,16,11,18,12,17.
Answer» ANSWER :2.33

Discussion

12233.	If the eccentricity of an ellipse is (5)/(8) and ht distance between its foci is 10, then find latus rectum of the ellipse.
Answer» ANSWER :`(39)/(4)`

Discussion

12234.	Let f={(1,1),(2,3),(0,-1),(-1,-3)} be a function from Z to Z defined by f(x)= ax + b, for some integers a, b. Determine a, b,
Answer» ANSWER :`a= 2, B= - 1`

Discussion

12235.	For given set A and B if A sub B and A ne Bthen set A is …..of set B.
Answer» ANSWER :SET A is CALLED PROPER SUBSET of set A.

Discussion

12236.	How far apart are the points (2, 0, 0) and (-3, 0, 0) ?
Answer» ANSWER :5

Discussion

12237.	Evaluate : 7!
Answer» ANSWER :5040

Discussion

12238.	If bara, barb, barc represents three concurrent edges of a rectangular parallelopiped whose lengths are 4, 3, 2 then (bara+ barb+barc). (baraxx barb+ barb xx barc + barc xx bara) =
Answer» 0 48 36 72 Answer :D

Discussion

12239.	Find the derivative of the function (a-b cos x)/(a +b cos x)
Answer» ANSWER :`(2AB SIN X)/( (a + b COS x) ^(2))`

Discussion

12240.	A unit vector parallel to the intersection of the planes vecr.(hati - hatj + hatk) =5 and vecr.( 2 hati + hatj - 3 hatk) =4 is
Answer» `(2 hati + 5 HATJ - 3 HATK)/(sqrt38)` `(2 hati - 5 hatj + 3 hatk)/(sqrt38) ` `(-2 hati - 5 hatj - 3 hatk)/(sqrt38)` `(- 2 hati + 5 hatj - 3 hatk)/(sqrt38)` ANSWER :C

Discussion

12241.	Let A = { a, e, i, o, u} and B = { a, b, c, d}. Is A a subset of B ? No. (Why?). Is B a subset ofA? No. (Why?)
Answer» ANSWER :A is not SUBSET of B and B is not subset of A

Discussion

12242.	If Tan8A - Tan5A - Tan3A = K Tan8A Tan5A.Tan3A then K =
Answer» 1 2 3 4 Answer :A

Discussion

12243.	Find the distance of the point P from the lines ABin the following cases : P(0, 0),AB is h(x+h)+k(y+k)=0
Answer» ANSWER :`SQRT((H^(2)+K^(2))`

Discussion

12244.	L and L' are end points of latus rectum of parabola y^2 = 4ax and M' and M are foot of perpendiculars from there points to line x = 0 then are of LL'M'M = .........
Answer» ANSWER :`4a^2`

Discussion

12245.	Solve: x^((2)/(3))+x^((1)/(3))-2=0.
Answer» ANSWER :CUBING both SIDES, we GET x=1 and -8.

Discussion

12246.	If the direction ratios of a line are (3,4,0) find its direction cosines and also the angles made with the coordinate axes.
Answer» ANSWER :`((3)/(5),(4)/(4),0),COS^(1)((3)/(5)),cos^(-1)((4)/(5)),(PI)/(2)`

Discussion

12247.	The maximum area of a right angled triangle with hypotenuse h is
Answer» `H^(2)//2 SQRT(2)` `h^(2)//2` `h^(2)//sqrt(2)` `h^(2)//4` ANSWER :D

Discussion

12248.	If f(x)=1+x+x^(2)+…………+x^(100), then find f'(1).
Answer» 5025 5050 5321 5060 Answer :B

Discussion

12249.	Assertion (A) : In Delta ABCif angle B = pi//2then the diameterof the incircleof the triangleis c+a-b. Reasons( R ) :In a rightangled triangle,hypotenuseis equalto circumradius of circumcircle.
Answer» A is true , R is true and R is CORRECT explanationof A A is true , R is true and R is not correct explanation of A A is true R is false A is false , R is true Answer :C

Discussion

12250.	Write the following sets in the roaster from. E= {w}(w-2)/(w+3)=3, w in R}
Answer» ANSWER :`={-(11)/(2)}`

Discussion

Explore topic-wise InterviewSolutions in .

Assertion (A) : P(3,4,5), Q(-1,7,9) are two given points, length of projection of PQ on xyplane is 5 units Reason ( R ): The projection of (x_(1),y_(1),z_(1)) " onXY PLANEis (x_(1),y_(1),0)

Two dice are thrown.Find the probability of an odd number on one die and 5 on the other

Consider the family of lines 5x+3y-2+lambda_(1)(3x-y-4)=0 andx-y+1+lambda_(2)(2x-y-2)=0. Equation of a straight line that belong to both families is

If (1, 1, a) is the centroid of the triangle formed by the points (1, 2, -3) (b, 0, 1) and (-1, 1, -4), then a-b=

E is a point on the side AD of a rectangle ABCD, so that DE = 6, DA = 8, DC = 6. If CE is extended to meet the circumcircle of rectangle at F. Then DF = FB =

Find the sum to n terms of the series , 5+11+19+29+41…

Identify the quantifier in the following statements and write the negation of the statements. For every real number x, x is less than x + 1.

Prove that C_1/C_0+(2c_(2))/C_1+(3C_3)/(C_2)+......+(n.C_n)/(C_(n-1))=(n(n+1))/2 2.C_0+(2^2.C_1)/(2)+(2^(3).C_(3))/(3)+.....(2^(4).C_3)/4+....(2^(n-1).C_(n))/(n+1)=(3^(n+1)-1)/(n+1) C_(0)-(C_(1))/2+C_(2)/3-.....+(-1)^a(C_n)/(n+1)=(1)/(n+1)

1+2+3+…….+(n+1)= ((n+1) (n+2))/(2) , n in N.

If A ge 0, B ge 0, A + B = (pi)/(3) and y = tan A. tan B then

Evaluate : (2 tan 22 (1^(@))/( 2 ))/(1 - tan ^(2) 22 (1^(@))/( 2))

Two adjacent sides of cyclic quadrilateral are 2 and 5 and angle between them is60 ^(@) .If the third side is 3 then the remaining side is

Find the sum of (x + (1)/(x))^(2), (x^(2) + (1)/(x^(2)))^(2), (x^(3) + (1)/(x^(3)))^(2), ……..to n terms

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

Let f(x)=ln(2x-x^(2))+sin((pi x)/(2)) then

If vec(a)= vec(i) + vec(j)+ vec(k), vec(c )= vec(j)- vec(k), then find vector vec(b) such that vec(a) xx vec(b)= vec(c ) and vec(a).vec(b)= 3

Write the sample space in each of the following : A coin is tossed and a die is thrown.

Solve graphically and compare your answer with algebraic solution either by factorization or formula method: (i) y=x^(2)-5x+6 (ii) y=-x^(2)+2x+3 (iii) y=x^(2)-4x+4 (iv) y=x^(2)-x-6 (v) y=x^(2)-6x+9 (vi) y=-x^(2)-x+12 (vii) y=x^(2)-4x+5=0 (viii) y=x^(2)+2x+2=0.

A straight line through origin O meets the lines 3y=10-4x and 8x+6y+5=0 at points A and B respectively. Then O divides the segment AB in the ratio.

If si 4 A - cos 2A = cso 4A - sin 2A (0 lt A lt (pi)/(4)), then the value of tan 4A=

Expand (2+ x)^(5) - (2- x)^(5) in ascending powers of x and simplify your result.

The most general value of theta satisfying both the equations sintheta=1//2,tantheta=1//sqrt(3) is

Compute the first quartile and third deciles from the following data : {:("Weekly Income (in Rs.)",58,59,60,61,62,63,64,65,66),("No. of workers",2,3,6,15,10,5,4,3,1):}

If tan^(2)(pi-A)/4 + tan^(2)(pi-B)/2 + tan^(2) (pi-C)/4=1, then triangleABC is:

Length of the arc of circle with radius 5 cm and angle at centre is 15^@ ...........cm.

Obtain the equation of the ellipse whose focus is the point (-1, 1), and the corresponding directrix is the line x-y+3=0, and the eccentricity is 1/2.

If the d.c's of a line are (1//c,1//c,1c) then find c.

A coin is tossed three times. Find the number of elemnts in 'Sample space '?

cos(2pi -x) cos (-x) - sin(2pi +x) sin (-x) = 0

If f:[1, oo)rarr[2, oo) is given by f(x)=x+(1)/(x) then f^(-1)(x)=

If tanx = (2b)/(a-c) , a ne c, y = a cos^2 x + 2b sinx.cos x + c sin^2 x z = a sin^2 x -2b sinx.cos x+"c" cos ^2x then

Find the mean deviation about the mediam for the data 13, 17,16,14,11,13,10,16,11,18,12,17.

If the eccentricity of an ellipse is (5)/(8) and ht distance between its foci is 10, then find latus rectum of the ellipse.

Let f={(1,1),(2,3),(0,-1),(-1,-3)} be a function from Z to Z defined by f(x)= ax + b, for some integers a, b. Determine a, b,

For given set A and B if A sub B and A ne Bthen set A is …..of set B.

How far apart are the points (2, 0, 0) and (-3, 0, 0) ?

Evaluate : 7!

If bara, barb, barc represents three concurrent edges of a rectangular parallelopiped whose lengths are 4, 3, 2 then (bara+ barb+barc). (baraxx barb+ barb xx barc + barc xx bara) =

Find the derivative of the function (a-b cos x)/(a +b cos x)

A unit vector parallel to the intersection of the planes vecr.(hati - hatj + hatk) =5 and vecr.( 2 hati + hatj - 3 hatk) =4 is

Let A = { a, e, i, o, u} and B = { a, b, c, d}. Is A a subset of B ? No. (Why?). Is B a subset ofA? No. (Why?)

If Tan8A - Tan5A - Tan3A = K Tan8A Tan5A.Tan3A then K =

Find the distance of the point P from the lines ABin the following cases : P(0, 0),AB is h(x+h)+k(y+k)=0

L and L' are end points of latus rectum of parabola y^2 = 4ax and M' and M are foot of perpendiculars from there points to line x = 0 then are of LL'M'M = .........

Solve: x^((2)/(3))+x^((1)/(3))-2=0.

If the direction ratios of a line are (3,4,0) find its direction cosines and also the angles made with the coordinate axes.

The maximum area of a right angled triangle with hypotenuse h is

If f(x)=1+x+x^(2)+…………+x^(100), then find f'(1).

Assertion (A) : In Delta ABCif angle B = pi//2then the diameterof the incircleof the triangleis c+a-b. Reasons( R ) :In a rightangled triangle,hypotenuseis equalto circumradius of circumcircle.

Write the following sets in the roaster from. E= {w}(w-2)/(w+3)=3, w in R}