14949 + Interview Questions in Maths in Class 11 Page 228 InterviewSolution

11351.	A student writes the formula sqrt(ab) = sqrtasqrtb. Then he substitutes a = -1, b = -1 and finds 1 = -1. Explain where heis wrong?
Answer» Answer :SINCE a and B are NEGATIVE, he can't write `SQRT(ab) = sqrtasqrtb`

Discussion

11352.	The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then P(A')+P(B') is
Answer» 0.4 0.8 1.2 1.6 Answer :C

Discussion

11353.	Determine the slope and y- intercept of the following lines: y=x+5
Answer» ANSWER :5

Discussion

11354.	If the angles of elevation of the top of a tower from three collinear points A, B and C on a line leading to the foot of the tower, are 30^(@), 45^(@) and 60^(@) respectively, then the ratio, AB : BC, is
Answer» `SQRT(3) : 1` `sqrt(3) : sqrt(2)` `1 :sqrt(3)` `2 : 3` ANSWER :A

Discussion

11355.	If a half line bar(OP)where bar(OP)=rmakes an angle alphawith the positive X-axis bar(OX)and lies in the XZ plane, then the coordinates of P are:
Answer» `(0, 4 cos alpha, 0)` `(R cos alpha, 0, RSIN alpha)` `(r SIN alpha, 0, rcos alpha)` `(0, r sin alpha, 0)` Answer :B

Discussion

11356.	If sec 4 theta - sec 2 theta = 2 " then " theta=
Answer» `(N + (1)/(2) ) pi, n in Z` `(n*+(1)/(3))pi,n in Z` `(n + (1)/(4))pi, n in Z` `(n + (1)/(5))pi, n in Z` ANSWER :A

Discussion

11357.	Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 4. . . A
Answer» ANSWER :`in`

Discussion

11358.	Find the derivatives of the following : tan^(-1)((cosx+sinx)/(cosx-sinx))
Answer» ANSWER :1

Discussion

11359.	A= {0, 2, 4, 6, 8, 10}. Insert the appropriate symbol in" or "notin in the blank space. -4"………"A
Answer» ANSWER :`NOTIN`

Discussion

11360.	Find the mean, variance and standard deviation for the numbers 4, 6, 10, 12, 7, 8, 13, 12.
Answer» ANSWER :MEAN = 9, VARIANCE = 9.25 and SD = 3.04

Discussion

11361.	The value of c so that all real 'x' the vectors cxbari - 6barj+3bark, xbari+2barj+2cxbark make an obtuse angle, are
Answer» `clt0` `0ltclt4/3` `-4/3ltcle0` `cgt0` ANSWER :C

Discussion

11362.	x and y are two + ve numbers sucbs that xy=1 Then the minimum value of x+y is
Answer» 4 `(1)/(4)` `(1)/(2)` 2 Answer :D

Discussion

11363.	Show that x^3-6x^2+15xge0AAxge0
Answer» ANSWER :`x^3-6x^2+15xge0AAxge0`

Discussion

11364.	Number of solutions of the equation 4 ( cos ^(2) 2 x + cos 2 x + 1) + tan x ( tan x - 2 sqrt(3)) = 0i n [ 0, 2 pi]is
Answer» 0 1 2 3 Answer :C

Discussion

11365.	If the planes barr.(bari+barj-3bark) = 7 and barr.(bari -tbarj+bark) = 9 are perpendicular to each other, find the value of t.
Answer» ANSWER :-2

Discussion

11366.	A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done ? How many of these committees would consist of 1 man and 2 women ?
Answer» ANSWER :10, 6

Discussion

11367.	Find the distance of the point (-1, 1) from the line 12(x+6) = 5(y-2).
Answer» ANSWER :`= (65)/(13) =5` UNITS

Discussion

11368.	In the Parallelogram ABCD, bar(AC)^(2)-bar(BD)^(2) =
Answer» 1)`4bar(AB). ("PROJECTION of " bar(AD) " on " bar(AB))` 2)`2bar(AB). ("projection of " bar(AD) " on " bar(AB))` 3)`bar(AC). ("projection of " bar(BD) " on " bar(AC))` 4)`2bar(AB). ("projection of " bar(BD) " on " bar(AC))` ANSWER :A

Discussion

11369.	Calculate weighted index number for 2001 from the following data:
Answer» ANSWER :`=148.77`.

Discussion

11370.	Evaluate Lt_(xtoy)(x^(y)-y^(x))/(x^(x)-y^(y))
Answer» ANSWER :`(1-logy)/(1+logy)`

Discussion

11371.	If alpha and beta are the roots of ax^(2)+bx+c=0 andif px^(2)+qx+r=0 has roots (1-alpha)/(alpha) and (1-beta)/(beta) then r=
Answer» `a+2b` `a+B+c` `ab+bc+ca` `ABC` ANSWER :A::B

Discussion

11372.	Points A(3,2,4), B (33/8,28/5,38/5) and C(9,8,10) are given. The ratio in which B divides bar(AC) is
Answer» " 5:3 " " 2: 1 " " 1:3 " " 3 : 2 " ANSWER :D

Discussion

11373.	Prove that lim_(thetararr0)(sin theta)/(theta)=1.
Answer» ANSWER :`lim_( THETA to 0) (sin theta)/(theta)=1`.

Discussion

11374.	How many numbers greater than 7000 can be formed with the digits 2, 5, 6, 8, 9 without repetition ?
Answer» ANSWER :168

Discussion

11375.	(A) If tanh alpha=(2)/(3), tan h beta=(3)/(5) then tanh(alpha-beta)=p_(1) (B) sinh(cosh^(-1)3+sinh^(-1)7)=p_(2) (C ) tanh["tanh"^(-1)(2)/(3)+"tanh"^(-1)(3)/(5)]=p_(3)
Answer» `p_(1) gtp_(3) gt p_(2)` `p_(2) gt p_(3) gt p_(1)` `p_(1) gt p_(2) gt p_(3)` `p_(2) gt p_(1) gt p_(3)` Answer :B

Discussion

11376.	(iv) Let y= (1)/( ax^(2) + bx + c)then find dy/dx
Answer» ANSWER :`= (-(2ax +B))/((ax^(2) + BX+ C)^2)`

Discussion

11377.	( r_1 (r_2+ r_3))/( sqrt( r_1r_2+r_2r_3+ r_1r_3)) =
Answer» ` a` ` B` ` C` `1` ANSWER :A

Discussion

11378.	lim_(xtopi)(tanx)/(pi-x)=………
Answer» 1 -1 0 Does not exists Answer :B

Discussion

11379.	Iff(x)=cos [pi ^(2)] x+cos [-pi ^(2) ] x, where [x] stands for the greatest integer functions , then
Answer» `F(PI/2)= -1` `f(pi)=1` `f(-pi)=1` `f(pi/4)=1` ANSWER :A::C

Discussion

11380.	Solve the equation for0 le x le 2pi. 2 sin ^(2) theta = 3 cos theta
Answer» ANSWER :`(PI)/(3) , (5PI)/(3)`

Discussion

11381.	If [n(A)]^(3) = 8 and {0,1,0} in A^3 then a = {0,1}
Answer» ANSWER :TRUE STATEMENT

Discussion

11382.	Identify the pair(s) of functions which are identical
Answer» `y=TAN(cos^(-1)X),y=(sqrt(1-x^(2)))/x` `y=tan(COT^(-1)x),y=1/x` `y=sin(arc ta x),y=x/(sqrt(1+x^(2)))` `y=cos(tan^(-1)x),y=sin(cot^(-1)x)` ANSWER :A::B::C::D

Discussion

11383.	Identify the quantifier in the following statements and write the negation of the statements. There exists a capital for every state in India.
Answer» ANSWER : ''There exists''. The negation is There exists a state in India which does not have a CAPITAL.

Discussion

11384.	Identify the quantifier in the following statements and write the negation of the statements. There exists a number which is equal to its square.
Answer» ANSWER : ''There EXISTS''. The negation is There does not exist a number which is EQUAL to its SQUARE.

Discussion

11385.	Evaluate the following limits : Lim_(x to 0) (e^(x) -1)/(sqrt(1-cos x))
Answer» ANSWER :`SQRT(2)`

Discussion

11386.	Write the negation of the following statements: All triangles are not equilateral triangle.
Answer» ANSWER :All TRIANGLES are EQUILATERAL TRIANGLE.

Discussion

11387.	The value of Sin^(-1)(Cos((33pi)/5)) is
Answer» `(3PI)/5` `(7pi)/5` `PI/10` `(-pi)/10` ANSWER :D

Discussion

11388.	Let f(x) and g(x) be differentiable functions for 0 lex le 1such thatf(0) = 2, g(0) = 0, f(1) = 6. Let there exist a real number c in (0,1) such that f ’(c) = 2 g ’(c), then g(1) =
Answer» 1 2 `-2` `-1` ANSWER :B

Discussion

11389.	Prove that the aea of the triangle formed by y=x+c and the pair of lines ax^(2)+2hxy=by^(2)=0 is (e^(2)sqrt(h^(2)-ab))/(\|a+b+2h\|) sq. units.
Answer» ANSWER :`(e^(2)sqrt(H^(2)-AB))/(\|a+b+2h\|)`

Discussion

11390.	Show that the statement . p : 'If x is a real number such thatx^(3)+ 4x=0, then x=0' is true by Direct method
Answer» ANSWER :DIRECT method : `x^(3)+4x=0=>x(x^(2) + 4)=0.` But `x^(2)+4,x in R ≠ 0,` THEREFORE, x=0.

Discussion

11391.	Find the orthocentre of the triangle formed by the lines x+2y=0,4x+3y=5 and 3x+y=0
Answer» ANSWER :(-4,-3)

Discussion

11392.	The projection of a vector on the three coordinate axes are 6,-3,2 respectively. The direction cosines of the vector are
Answer» 6,-3,2 `(6)/(5),(-3)/(5),(2)/(5)` `(6)/(7),(-3)/(7),(2)/(7)` `(-6)/(7),(-3)/(7),(2)/(7)` ANSWER :C

Discussion

11393.	Let f be twice differentiable function such that f^11(x) = -f(x) "and " f^1(x) = g(x), h(x) = (f(x))^2 + (g(x))^2), if h(5) = 11, then h(10) is
Answer» ANSWER :11

Discussion

11394.	Q_(3) is always equal to
Answer» <P>`P_(1)` `P_(25)` `P_(75)` `D_(3)` ANSWER :C

Discussion

11395.	Let P be the pressure and V the volume of a gas such that PV = constant. If percentage error in P is k then percentage error in V is
Answer» K `(1)/(k)` `-k` 2k Answer :C

Discussion

11396.	A person of height 180 cm starts from a lamp post height 450 cm and walks at the constant rate of4 km per hour. Find the rate at which his shadow increases.
Answer» ANSWER :8/3 kmp/h

Discussion

11397.	If bar(a), bar(b) represent bar(AB), bar(BC) respectively of a regular hexagon ABCDEF then bar(CD), bar(DE), bar(EF), bar(FA)
Answer» `BAR(B)-bar(a),-bar(a), -bar(b), bar(a)-bar(b)` `bar(a)-bar(b), bar(a), bar(b), bar(b)-bar(a)` `bar(b)-bar(a), bar(a), bar(b), bar(a)-bar(b)` `bar(a)-bar(b), -bar(a), -bar(b), bar(b)-bar(a)` ANSWER :A

Discussion

11398.	Fill in the blanks of the following The number ((1-i)^(2))/(1-i^(3)) is equal to....
Answer» ANSWER :`-2`

Discussion

11399.	If 2sin^(2)x-5sinxcosx-8cos^(2)x=-2 5 then
Answer» `X={N pi +tan^(-1)(2),n inn Z}uu{n pi +tan^(-1)(-3/4),minZ}` `x=npi+tan^(-1)(3),n in Z` `x=n pi +tan^(-1)((-4)/3), n in Z` `x=n pi +tan^(-1)(4),n in Z` Answer :A

Discussion

11400.	If x=a + b, y= a alpha + b beta, z= a beta + b alpha, where alpha and beta are complex cube roots of unity, then show that xyz = a^(3) + b^(3)
Answer» ANSWER :`a^(3) + B^(3)`

Discussion

Explore topic-wise InterviewSolutions in .

A student writes the formula sqrt(ab) = sqrtasqrtb. Then he substitutes a = -1, b = -1 and finds 1 = -1. Explain where heis wrong?

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then P(A')+P(B') is

Determine the slope and y- intercept of the following lines: y=x+5

If the angles of elevation of the top of a tower from three collinear points A, B and C on a line leading to the foot of the tower, are 30^(@), 45^(@) and 60^(@) respectively, then the ratio, AB : BC, is

If a half line bar(OP)where bar(OP)=rmakes an angle alphawith the positive X-axis bar(OX)and lies in the XZ plane, then the coordinates of P are:

If sec 4 theta - sec 2 theta = 2 " then " theta=

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

Find the derivatives of the following : tan^(-1)((cosx+sinx)/(cosx-sinx))

A= {0, 2, 4, 6, 8, 10}. Insert the appropriate symbol in" or "notin in the blank space. -4"………"A

Find the mean, variance and standard deviation for the numbers 4, 6, 10, 12, 7, 8, 13, 12.

The value of c so that all real 'x' the vectors cxbari - 6barj+3bark, xbari+2barj+2cxbark make an obtuse angle, are

x and y are two + ve numbers sucbs that xy=1 Then the minimum value of x+y is

Show that x^3-6x^2+15xge0AAxge0

Number of solutions of the equation 4 ( cos ^(2) 2 x + cos 2 x + 1) + tan x ( tan x - 2 sqrt(3)) = 0i n [ 0, 2 pi]is

If the planes barr.(bari+barj-3bark) = 7 and barr.(bari -tbarj+bark) = 9 are perpendicular to each other, find the value of t.

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done ? How many of these committees would consist of 1 man and 2 women ?

Find the distance of the point (-1, 1) from the line 12(x+6) = 5(y-2).

In the Parallelogram ABCD, bar(AC)^(2)-bar(BD)^(2) =

Calculate weighted index number for 2001 from the following data:

Evaluate Lt_(xtoy)(x^(y)-y^(x))/(x^(x)-y^(y))

If alpha and beta are the roots of ax^(2)+bx+c=0 andif px^(2)+qx+r=0 has roots (1-alpha)/(alpha) and (1-beta)/(beta) then r=

Points A(3,2,4), B (33/8,28/5,38/5) and C(9,8,10) are given. The ratio in which B divides bar(AC) is

Prove that lim_(thetararr0)(sin theta)/(theta)=1.

How many numbers greater than 7000 can be formed with the digits 2, 5, 6, 8, 9 without repetition ?

(A) If tanh alpha=(2)/(3), tan h beta=(3)/(5) then tanh(alpha-beta)=p_(1) (B) sinh(cosh^(-1)3+sinh^(-1)7)=p_(2) (C ) tanh["tanh"^(-1)(2)/(3)+"tanh"^(-1)(3)/(5)]=p_(3)

(iv) Let y= (1)/( ax^(2) + bx + c)then find dy/dx

( r_1 (r_2+ r_3))/( sqrt( r_1r_2+r_2r_3+ r_1r_3)) =

lim_(xtopi)(tanx)/(pi-x)=………

Iff(x)=cos [pi ^(2)] x+cos [-pi ^(2) ] x, where [x] stands for the greatest integer functions , then

Solve the equation for0 le x le 2pi. 2 sin ^(2) theta = 3 cos theta

If [n(A)]^(3) = 8 and {0,1,0} in A^3 then a = {0,1}

Identify the pair(s) of functions which are identical

Identify the quantifier in the following statements and write the negation of the statements. There exists a capital for every state in India.

Identify the quantifier in the following statements and write the negation of the statements. There exists a number which is equal to its square.

Evaluate the following limits : Lim_(x to 0) (e^(x) -1)/(sqrt(1-cos x))

Write the negation of the following statements: All triangles are not equilateral triangle.

The value of Sin^(-1)(Cos((33pi)/5)) is

Let f(x) and g(x) be differentiable functions for 0 lex le 1such thatf(0) = 2, g(0) = 0, f(1) = 6. Let there exist a real number c in (0,1) such that f ’(c) = 2 g ’(c), then g(1) =

Prove that the aea of the triangle formed by y=x+c and the pair of lines ax^(2)+2hxy=by^(2)=0 is (e^(2)sqrt(h^(2)-ab))/(|a+b+2h|) sq. units.

Show that the statement . p : 'If x is a real number such thatx^(3)+ 4x=0, then x=0' is true by Direct method

Find the orthocentre of the triangle formed by the lines x+2y=0,4x+3y=5 and 3x+y=0

The projection of a vector on the three coordinate axes are 6,-3,2 respectively. The direction cosines of the vector are

Let f be twice differentiable function such that f^11(x) = -f(x) "and " f^1(x) = g(x), h(x) = (f(x))^2 + (g(x))^2), if h(5) = 11, then h(10) is

Q_(3) is always equal to

Let P be the pressure and V the volume of a gas such that PV = constant. If percentage error in P is k then percentage error in V is

A person of height 180 cm starts from a lamp post height 450 cm and walks at the constant rate of4 km per hour. Find the rate at which his shadow increases.

If bar(a), bar(b) represent bar(AB), bar(BC) respectively of a regular hexagon ABCDEF then bar(CD), bar(DE), bar(EF), bar(FA)

Fill in the blanks of the following The number ((1-i)^(2))/(1-i^(3)) is equal to....

If 2sin^(2)x-5sinxcosx-8cos^(2)x=-2 5 then

If x=a + b, y= a alpha + b beta, z= a beta + b alpha, where alpha and beta are complex cube roots of unity, then show that xyz = a^(3) + b^(3)