14949 + Interview Questions in Maths in Class 11 Page 270 InterviewSolution

13451.	U= {x : x in N, x le 10}, A= {1, 3, 5, 7, 9}, B= {2, 4, 6, 8, 10} then (A cup B)'="…………"
Answer» `U` `{2}` `phi` `{1, 4, 7, 8}` Answer :C

Discussion

13452.	The longest side of a trangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find theminimum length of the shortest side.
Answer» Solution :Let the minimum LENGTH of the shortest side be x cm. Then, the longest side `=3x cm` and the third side `=(3x -2)` cm. `therefore x +3x +(3x-2)ge 61 rArr 7X ge 63 rArr x ge 9`. Hence, the minimum length of the shortest side is 9 cm.

Discussion

13453.	Inequality 3(x-1) + 2 (x-2) lt 5 (x +2) is true for each x in R .
Answer» ANSWER :TRUE STATEMENT

Discussion

13454.	Find the most general value of theta that satisfying both the equations Sin theta = (1)/(2) Cos theta = (sqrt(3))/(2)
Answer» ANSWER :`2N PI + (7pi)/(6)`

Discussion

13455.	If pi ltthetalt(3pi)/2 the expression sqrt(4sin^(4)theta+sin^(2)2theta)+4cos^(2)(pi/4-theta/2) is equal to
Answer» 2 `2+4 SINTHETA` `2-4 sintheta` 0 Answer :A

Discussion

13456.	If one root of 2x^(2)-5x+k=0 be double the other, find the value of k.
Answer» ANSWER :`k=2(7)/(9)`

Discussion

13457.	Describe the sample space of this experiment : (i) One die is rolled.
Answer» ANSWER :S={1,2,3,4,5,6}

Discussion

13458.	Nisha derived the polar form of (1+i)/sqrt3+i by using the polar forms of (1+i) and sqrt3 + i. Write the steps followed by Nisha.
Answer» ANSWER :`1+i=sqrt2abs(cospi/4+isinpi/4)`

Discussion

13459.	A Function defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2 Which of the following is true ?
Answer» F(X) is DECREASING on (-1,1) and has a local minimum at x=1 f(x) is increasing on (-1,1) and has a local maximum at x=1 f(x) is increasing on (-1,1) but has NEITHER a local maximum nor a localminimum at x=1 f(x) is decreasing on (-1,1) but has neither a local maximum nor a local minimum at x=1 Answer :A

Discussion

13460.	A function defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2 Which of the following is true ?
Answer» `(2+a)^(2)F''(1)+(2-a)^(2)f''(-1)=0` `(2-a)^(2)f''(1)-(2+a)^(2)f''(-1)=0` `fcancelc(1)cancelc(-1)=(2-a)^(2)` `fcancelc(1)fcancelc(-1)=-(2+a)^(2)` ANSWER :A

Discussion

13461.	Which of the following are sets? Justify your answer : The collection of first five prime minister of India.
Answer» ANSWER :it is a SET

Discussion

13462.	Compute Lt_(x to 3) (x^2 - 9)/(x^3 - 6x^2 + 9x + 1)
Answer» ANSWER :8

Discussion

13463.	{:("List-I","List -II"),((A)f(x)=x^(2)-2x+5 "is increasing in","P"phi),((B)f(x)=e^(-x) "is increasing in ","q" (-oo,1)uu(2,oo)),((C)f(x)=logx "is increasing in","r" R),((D)f(x)=(x^(3))/(3)-(3x^(2))/(2)+2x+5 " is increasing in ","s"(0,oo)),(,t(1,oo)):}
Answer» ANSWER :A-t;B-p;C-s;D-q

Discussion

13464.	If n is even then sin theta + sin ( pi + theta ) + sin (2 pi + theta) + ...........n terms =
Answer» 0 `-SIN THETA` `sin theta` `-COS theta` ANSWER :A

Discussion

13465.	If a,b,c form a GP with common ratio r, the sum of the ordinates of the points of intersection of the line ax+by+c=0 and the curvex+2y^2=0 is
Answer» `(-R)/(2)` `(-r^2)/(2)` `(r)/(2)` `(r^2)/(2)` ANSWER :A

Discussion

13466.	There are 10 persons who are to seated around a circular table . Find the probability that two particular will always sit together .
Answer» ANSWER :`=(2)/(9)`

Discussion

13467.	Let (sin(theta-alpha))/(sin(theta-beta))=(a)/(b) and (cos(theta-alpha))/(cos(theta-beta))=(c )/(d) then (ac+bd)/(ad+bc)=
Answer» `COS(alpha-beta)` `SIN(alpha-beta)` `sin(alpha+beta)` `cos(alpha+beta)` ANSWER :A

Discussion

13468.	Let bar(a), bar(b), bar(c), bar(d) be the position vectors of A, B, C and D respectively which are the vertices of a tetrahedron. Then prove that the lines joining the vertices to the centroids of the opposite faces are concurrent. (This point is called the centroid of the tetrahedron)
Answer» `BAR(a)+bar(B)=bar(C)+bar(d)` `bar(a)+bar(b)=bar(c)+bar(d)=bar(0)` `bar(a)+bar(c)=bar(b)+bar(d)` `bar(a)+bar(c)=bar(b)+bar(d)=bar(0)` ANSWER :C

Discussion

13469.	Findthe distance between the followingpairsof points (i) (2,3,5) and (4,3,1) (ii) (-3,7,2) and (2,4,-1) (iii) (-1,3,-4) and (1,-3,4) (2,-1,3) and (-2,1,3)
Answer» Answer :(i) `2sqrt(5) (II) SQRT(43) (iii) 2sqrt(26) (iv)2sqrt(5)`

Discussion

13470.	It [x] and {x} represent the integral and fractional parts of x, respectively, then the value ofsum_(r=1)^(2000) ({x+r})/(2000) is
Answer» X [x] {x} `x+2001` ANSWER :C

Discussion

13471.	If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that (A ∩ B)′ = A′ ∪ B′
Answer» ANSWER :`(A CAP B)'= A' CUP B'`

Discussion

13472.	The shortese distance between the lines (x-2)/(3) = (y-3)/(4) = (z-1)/(2) , (x-4)/(4) = (y-5)/(5) = (z-2)/(3) is
Answer» `(1)/(SQRT3)` `(1)/(SQRT6)` `(1)/(SQRT2)` `(5)/(sqrt6)` Answer :B

Discussion

13473.	Statement-I : If 0 lt alpha, beta lt pi/4, sin alpha =a/sqrt(1+a^(2)), cos beta = b/sqrt(1+b^(2)), then tan (alpha + beta) = (a+b)/(a-b) Statement-II: If tan(A + B)\m, tan(A-B) =n, then tan 2B =(m-n)/(m+n)
Answer» Only I Only II Both I & II Neither I nor II Answer :D

Discussion

13474.	Find all local maximum and local minima of the sine function.
Answer» ANSWER :maxima : `(PI)/(2), (pi)/ PM 2pi, (pi)/(2) pm 4PI`and minima: `(pi)/(2) pm pi, (pi)/(2) pm 3PI`...

Discussion

13475.	A Tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (a) subtends an angle of 60^(@) at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30°. The height of the tower is
Answer» `(2A)/(SQRT(3))` `2a sqrt(3)` `(a)/(sqrt(3))` `a sqrt(3)` ANSWER :C

Discussion

13476.	Solve the general vlaue. sin theta + sqrt3 cos theta = sqrt2
Answer» Answer :`(n - (1)/(3)) PI + (-1) ^(n) (1)/(4)pi`

Discussion

13477.	The origin is translated to (1,2) . The point (7,5) in the old systemundergoes the following transformations successively. (i) Moves to the new point under the given translation of origin (ii) Translated through 2 units along the negative direction of the new X-axis (iii) Rotated through an angle (pi)/(4)about the origin of new system in the clockwise direction The final position of the point (7,5) is
Answer» `((9)/(sqrt(2)),(-1)/(sqrt(2)))` `((7)/(sqrt(2)),(1)/(sqrt(2)))` `((7)/(sqrt(2)),(-1)/(sqrt(2)))` `((5)/(sqrt(2)),(-1)/(sqrt(2)))` Answer :C

Discussion

13478.	Find the octant in which the point (-3, 1, 2) and (-3, 1, -2) lie.
Answer» ANSWER :SIXTH

Discussion

13479.	If tan theta=0.4, when theta lies between 0^(@) and 360^(@), write down the possible values of theta and sin theta.
Answer» ANSWER :`21^(@)48',201^(@)48',0.3714,-0.3714`

Discussion

13480.	Find the component statements of the following compound statements: 0 is a positive number or a negative number.
Answer» Answer :p: 0 is a positive NUMBER. Q: 0 is a negative number

Discussion

13481.	A particle is moving on a straight line so that its distance sfrom a fixed point at any time t is proportional to t^n. If v be the velocity and 'a' the acceleration at any time , then (nas)/(n-1) equals
Answer» V `v^(2)` `v^(3)` 2v Answer :B

Discussion

13482.	If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets : C = {a, c, e, g}
Answer» ANSWER :`{ B, d , F, H }`

Discussion

13483.	If A=[(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1)] then ("Adj A")^(-1) =
Answer» I A 1 0 Answer :B

Discussion

13484.	The positive integer value of n gt 3 satisfying the equation (1)/( sin ((pi )/(n)) ) = (1)/( sin ((2pi)/(n ))) + (1)/( sin ((3pi)/( n ))) is
Answer» ANSWER :7

Discussion

13485.	Find the coordinates of the points which trisect AB given that A (2, 1, -3) and B (5,.- 8,3).
Answer» ANSWER :`(3,-2,1), (4, -5,1)`

Discussion

13486.	For 0leCos^(-1)xlepiand-pi/2leSin^(-1)xlepi/2, the value of cos(Sin^(-1)x+2Cos^(-1)x)"at "x=1/5 is
Answer» `(-2sqrt(6))/5` `(-SQRT(6))/5` `(2sqrt(6))/5` `sqrt(6)/5` ANSWER :A

Discussion

13487.	Which of the following functions from z to itself are bijections (one-one and onto )?
Answer» `F(X)=x^(3)` f(x)=x+2 f(x) = 2x+1 f(x) = `x^(2)+x` Answer :B

Discussion

13488.	Find n if : 2P( n,3) = P(n+1,3)
Answer» ANSWER :` 5`

Discussion

13489.	There are 880 boys in a school. Out of these 224 boys play cricket, 240 boys play hockey and 336 boys play basketball, 64 boys play both hockey and basketball, 80 boys play both cricket and basketball and 40 boys play both cricket and hockey. If 24 boys play all these three, then find the number of boys play none of these three game.
Answer» ANSWER :`= 240`

Discussion

13490.	If a line makes angles alpha, beta, gamma with positive axes, then the range of sin alpha sin beta+sin beta sin gamma+sin gamma sin alpha is
Answer» `[-1//2, 1]` `[1//2, 2]` [-1, 1] [-1, 2] ANSWER :D

Discussion

13491.	Find equation of the line perpendicular to the line x-7y+5=0 and having x intercept 3.
Answer» ANSWER :REQUIRED PERPENDICULAR LINE is `7x+y-21=0`.

Discussion

13492.	Consider a triangle ABC, where x, y, z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a, b, c respectively let the letters R, r, S, D denote the circumradius. inradius semi-perimeter and area of the triangle respectively. The value of (c sin B + b sin C)/x + (a sin C + c sin A)/y + (b sin A + a sin B)/zis equal to
Answer» `R/r` `S/R` 2 6 Answer :d

Discussion

13493.	Consider a triangle ABC, where x, y, z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a, b, c respectively let the letters R, r, S, D denote the circumradius. inradius semi-perimeter and area of the triangle respectively. Ifcot A + cotB + cot C = k (1/x^(2) + 1/y^(2) + 1/z^(2)) ,then the value of k is
Answer» `R^(2)` `rR` `DELTA ` `a^(2) + B^(2) + c^(2) ` Answer :c

Discussion

13494.	Consider a triangle ABC, where x, y, z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a, b, c respectively let the letters R, r, S, D denote the circumradius. inradius semi-perimeter and area of the triangle respectively. If (bx)/c + (cy)/a + (az)/b = (a^(2) + b^(2) + c^(2))/kthen the value of k is
Answer» R S 2R `3/2 R` ANSWER :C

Discussion

13495.	If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find B – C
Answer» ANSWER :`{ 20 }`

Discussion

13496.	End points of the diagonal of square are (1, -2, 3) and (2, -3, 5). Then lengh of its side is _____
Answer» `SQRT6` `SQRT3` `SQRT5` `SQRT7` ANSWER :B

Discussion

13497.	How many 3- digit even numbers are formed using the digits 0, 1, 2, …… 9, if the repetition of digit is not allowed ?
Answer» ANSWER :328

Discussion

13498.	Find the orthocenter of the triangle formed by the points (2,-1,1),(1,-3,-5),(3,-4,-4).
Answer» ANSWER :(3,-4,-4)

Discussion

13499.	Let f(x)-=(x^(2) +bx+c)/(x^(2)+b_(1)+c_(1)) where alpha,beta are the roots of the equation x^(2)+bx+c=0andalpha_(1),beta are the roots of x^(2)+b_(1)x+c_(1)=0 Now answer the following questions for f(x) A combination of graphical and analytical approach may be helpful in solving these problems If alpha_(1)andbeta_(1) are real then f(x)has vertical asymptote at x=alpha_(1),beta_(1).If the equations x^(2)+bx+c=0andx^(2)+b_(1)x+c_(1)=0 do not have real roots then
Answer» F(x) = 0 has REAL and DISTINCT roots f(x) = 0 has real equal roots f(x)=0 has imaginary roots NOTHING can be said Answer :A

Discussion

13500.	Let f(x)-=(x^(2) +bx+c)/(x^(2)+b_(1)+c_(1)) where alpha,beta are the roots of the equation x^(2)+bx+c=0andalpha_(1),beta are the roots of x^(2)+b_(1)x+c_(1)=0 Now answer the following questions for f(x) A combination of graphical and analytical approach may be helpful in solving these problems If alpha_(1)andbeta_(1) are real then f(x)has vertical asymptote at x=alpha_(1),beta_(1) If alpha_(1)ltbeta_(1)ltalphaltbeta then
Answer» f(x) has a MAXIMA in `[alpha_(1),beta_(1)]` and a minima in `[alpha,beta]` f(x) has a minima in `(alpha_(1),beta_(1))` and a maxima in `(alpha,beta)` `f(x)GT0` wherever DEFINED `f(x)lt0` wherever defined Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

U= {x : x in N, x le 10}, A= {1, 3, 5, 7, 9}, B= {2, 4, 6, 8, 10} then (A cup B)'="…………"

The longest side of a trangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find theminimum length of the shortest side.

Inequality 3(x-1) + 2 (x-2) lt 5 (x +2) is true for each x in R .

Find the most general value of theta that satisfying both the equations Sin theta = (1)/(2) Cos theta = (sqrt(3))/(2)

If pi ltthetalt(3pi)/2 the expression sqrt(4sin^(4)theta+sin^(2)2theta)+4cos^(2)(pi/4-theta/2) is equal to

If one root of 2x^(2)-5x+k=0 be double the other, find the value of k.

Describe the sample space of this experiment : (i) One die is rolled.

Nisha derived the polar form of (1+i)/sqrt3+i by using the polar forms of (1+i) and sqrt3 + i. Write the steps followed by Nisha.

A Function defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2 Which of the following is true ?

A function defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2 Which of the following is true ?

Which of the following are sets? Justify your answer : The collection of first five prime minister of India.

Compute Lt_(x to 3) (x^2 - 9)/(x^3 - 6x^2 + 9x + 1)

{:("List-I","List -II"),((A)f(x)=x^(2)-2x+5 "is increasing in","P"phi),((B)f(x)=e^(-x) "is increasing in ","q" (-oo,1)uu(2,oo)),((C)f(x)=logx "is increasing in","r" R),((D)f(x)=(x^(3))/(3)-(3x^(2))/(2)+2x+5 " is increasing in ","s"(0,oo)),(,t(1,oo)):}

If n is even then sin theta + sin ( pi + theta ) + sin (2 pi + theta) + ...........n terms =

If a,b,c form a GP with common ratio r, the sum of the ordinates of the points of intersection of the line ax+by+c=0 and the curvex+2y^2=0 is

There are 10 persons who are to seated around a circular table . Find the probability that two particular will always sit together .

Let (sin(theta-alpha))/(sin(theta-beta))=(a)/(b) and (cos(theta-alpha))/(cos(theta-beta))=(c )/(d) then (ac+bd)/(ad+bc)=

Let bar(a), bar(b), bar(c), bar(d) be the position vectors of A, B, C and D respectively which are the vertices of a tetrahedron. Then prove that the lines joining the vertices to the centroids of the opposite faces are concurrent. (This point is called the centroid of the tetrahedron)

Findthe distance between the followingpairsof points (i) (2,3,5) and (4,3,1) (ii) (-3,7,2) and (2,4,-1) (iii) (-1,3,-4) and (1,-3,4) (2,-1,3) and (-2,1,3)

It [x] and {x} represent the integral and fractional parts of x, respectively, then the value ofsum_(r=1)^(2000) ({x+r})/(2000) is

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that (A ∩ B)′ = A′ ∪ B′

The shortese distance between the lines (x-2)/(3) = (y-3)/(4) = (z-1)/(2) , (x-4)/(4) = (y-5)/(5) = (z-2)/(3) is

Statement-I : If 0 lt alpha, beta lt pi/4, sin alpha =a/sqrt(1+a^(2)), cos beta = b/sqrt(1+b^(2)), then tan (alpha + beta) = (a+b)/(a-b) Statement-II: If tan(A + B)\m, tan(A-B) =n, then tan 2B =(m-n)/(m+n)

Find all local maximum and local minima of the sine function.

A Tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (a) subtends an angle of 60^(@) at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30°. The height of the tower is

Solve the general vlaue. sin theta + sqrt3 cos theta = sqrt2

Find the octant in which the point (-3, 1, 2) and (-3, 1, -2) lie.

If tan theta=0.4, when theta lies between 0^(@) and 360^(@), write down the possible values of theta and sin theta.

Find the component statements of the following compound statements: 0 is a positive number or a negative number.

A particle is moving on a straight line so that its distance sfrom a fixed point at any time t is proportional to t^n. If v be the velocity and 'a' the acceleration at any time , then (nas)/(n-1) equals

If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets : C = {a, c, e, g}

If A=[(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1)] then ("Adj A")^(-1) =

The positive integer value of n gt 3 satisfying the equation (1)/( sin ((pi )/(n)) ) = (1)/( sin ((2pi)/(n ))) + (1)/( sin ((3pi)/( n ))) is

Find the coordinates of the points which trisect AB given that A (2, 1, -3) and B (5,.- 8,3).

For 0leCos^(-1)xlepiand-pi/2leSin^(-1)xlepi/2, the value of cos(Sin^(-1)x+2Cos^(-1)x)"at "x=1/5 is

Which of the following functions from z to itself are bijections (one-one and onto )?

Find n if : 2P( n,3) = P(n+1,3)

If a line makes angles alpha, beta, gamma with positive axes, then the range of sin alpha sin beta+sin beta sin gamma+sin gamma sin alpha is

Find equation of the line perpendicular to the line x-7y+5=0 and having x intercept 3.

If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find B – C

End points of the diagonal of square are (1, -2, 3) and (2, -3, 5). Then lengh of its side is _____

How many 3- digit even numbers are formed using the digits 0, 1, 2, …… 9, if the repetition of digit is not allowed ?

Find the orthocenter of the triangle formed by the points (2,-1,1),(1,-3,-5),(3,-4,-4).