14949 + Interview Questions in Maths in Class 11 Page 92 InterviewSolution

4551.	sin x + cos (x + 30^(@)) = 0, 0 ^(@) lt x lt 360^(@)
Answer» ANSWER :`120^(@) , 300^(@)`

Discussion

4552.	If A, B are acute positive angles satisfying the equations 3sin^(2)A+2sin^(2)B=1 and 3sin2A-2sin2B=0, then find A+2B.
Answer» `pi` `(2pi)/3` `(pi)/6` `(pi)/2` Answer :`(pi)/(4)`

Discussion

4553.	If (1,2,3 ), (2,3,1 ) are two vertices of an equilateral triangle then its third vertex is
Answer» (3,1,2) (-1,1,2) (3,1,4) (1,4,0) ANSWER :A

Discussion

4554.	What is the conjugate of (2-i)/((1-2i)^(2))?
Answer» ANSWER :`(-2)/(25)-(11)/(25)i`

Discussion

4555.	A metallic scale, due to heat is showing 0.99 mts as 1 meter. In this state, the radius of the base and height of a cone are measured to be 1 mts each. Find the actual volume of the cone approximately.
Answer» ANSWER :`69.84pi`

Discussion

4556.	Evaluate the following limits : Lim_(xto0) (sqrt((1+x+x^(2)))-1)/x
Answer» ANSWER :`1/2`

Discussion

4557.	4x + 3y le 60, y ge 2x, x ge 3, x, y ge 0
Answer» Solution :First inequation :` 4x + 3y le 60` Corresponding equation : `4x + 3y = 60` This line passes through the points A (15, 0) and B (0, 20). Join AB. At point (0, 0) from the inequation, `0le60` (TRUE) The solution of this inequation is that region of XY-plane DIVIDED by line AB in which (0, 0) lies. Seond inequation : `yge2x` Corresponding equation: `y = 2X` This line passes through the points O(0, 0) and C(5, 10) Join OC. At point (5, 0), from the inequation, `0 ge 10` (False) The solution of this inequation is that region of XY-plane divided byline OC in which (5, 0) does not lie. The solution of `xge 3 is x = 3` and its right side. The solution of `y ge 0 is y = 0 ` and its above. The common solution of given inequation is shown by the shaded region.

Discussion

4558.	Total numbers of 4 digits numbers using digits 5,2,3,7 and 8 are 620.
Answer» ANSWER :FALSE STATEMENT

Discussion

4559.	If (a+b+c) (b+c-a) = 3bc then find angle A .
Answer» `60 ^(@)` 0 ` 30 ^(@) ` ` 90 ^(@) ` ` 45^(@) ` ANSWER :A

Discussion

4560.	Let L be the line 2x + y - 2 = 0 . The axes rotated by 45^(0) in clockwise direction thenthe intercepts made by the line L on the new axes are respectively .
Answer» `1, SQRT(2)` `sqrt(2), 1` `-2 sqrt(2),-(2 sqrt(2))/(3)` `(2 sqrt(2))/(3), 2 sqrt(2)` Answer :C

Discussion

4561.	Find the equation of set of points P such that PA^(2)+PB^(2)=2k^(2), where A and B are the points (3, 4, 5) and (-1,3,-7), respectively.
Answer» ANSWER :`2x^(2)+2Y^(2)+2z^(2)-4x-14y+4z=2k^(2)-109`

Discussion

4562.	Find the nth term and deduce the sum of n terms of the series 4+11+22+37+56+………….
Answer» ANSWER :`(N)/(6)(4N^(2)+9n+8)`

Discussion

4563.	The odds in favour for three horses participating in a house-race are 1:3,2:5 and 3:7. Find the probability that any one can win the race.
Answer» SOLUTION :N/a

Discussion

4564.	Find the slope of a line whose inclination is 30^(@)
Answer» ANSWER : `1/sqrt(3)`

Discussion

4565.	n^( th) term of the series 4+14+ 30 + 52+ …..
Answer» `5n-1` `2N^(2) + 2n` `3n^(2) + N` `2n^(2) +2` ANSWER :C

Discussion

4566.	If (1+X+x^2)^n = Sigma_(r=0)^(2n)a_(r) x^r then prove that(a) a_(r)=a_(2n-r)(b ) Sigma_(r=0)^(n-1)a_(r)=1/2 (3^n-a_n)
Answer» Solution :We have ` (1+X+x^2)^n = UNDERSET(r=0)OVERSET(2n)Sigma a_(r) x^r` Replace x by1/x `therefore (1 +1/x+1/(x^2))^n = underset(r=0)overset(2n) Sigma a_(r)((1)/(x))^r` `rArr(x^2+x+1)^n = underset( r=0)overset(2n)Sigma a_rx^(2n-r)` `underset(r=0)overset(2n ) a_(r)x^r =underset(r=0)overset(2n ) a_(r)x^r "" {"Using (A) "}` Equating the cofficient of `x^(2n-r)` on the both sides ,we get `a_(2n-r)= a_(r) " for " 0 LE r le 2n` Hence`a_(r)=a_(2n-r)` (b) Putting x=1 in given series , then `a_(0)+a_1 +a_2+......+a_(2n)=(1+1+1)^n` `a_(0)+a_(1)+a_(2)+...... +a_(2n)=3^n` But`a^r= a_(2n-r) for 0le r le4 2 n ` `therefore ` Series (1) reduces to `2(a_(0)+a_1+a_2+.......+a_(n-1)) + a_n =3^n` `thereforea_0+a_1+a_2+........+a_(n-1)= 1/2 (3^n-a_n)`

Discussion

4567.	Solve the inequalityand represent the solution graphically on the number line ?
Answer» ANSWER :` (3(1-x)<2(x+4)`

Discussion

4568.	Draw the graphs of the following : y = \|x\| + \|x -1\| in [ -2,3]
Answer» ANSWER :`(##AKS_ELT_AI_MAT_XI_VIB_P02_C01_E01_019_A01##)`

Discussion

4569.	Illustrate in the complex plane the following set of points and explain your answer \|z-4\| lt 1
Answer» ANSWER :1

Discussion

4570.	In Delta ABC, (ab-r_1 r_2)/r_3=
Answer» ` 2r` ` R` ` 3r` ` 4R` ANSWER :B

Discussion

4571.	If 0 lt x lt pi, andcos x+ sin x =1//2, thentan x=
Answer» `((4-sqrt(7)))/(3)` `-((4 + sqrt(7)))/(3)` `((1+sqrt(7)))/(4)` `((1-sqrt(7)))/(4)` ANSWER :B

Discussion

4572.	Let f be function f(x)=cosx-(1-(x^(2))/(2)) . Then
Answer» f(X) is an INCREASING functions in `(0,OO)` f(x) is an DECREASING function in `(-oo,oo)` f(x) is an increasing function in `(-oo,oo)` f(x) is an decreasing function in `(-oo,0)` Answer :A::D

Discussion

4573.	LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {1, 2, 5} ⊂A
Answer» ANSWER :CORRECT

Discussion

4574.	If -pilexlepi,-pileylepi and the cosx+cosy=2 then cos(x-y) =
Answer» `-1` 0 1 2 Answer :C

Discussion

4575.	Find the derivatives of the function cos ^(-1) (( b + a cos x )/( a + b cos x )), (a gt 0, b gt 0)
Answer» Answer :`(SQRT (a ^(2) - b ^(2)))/( a + b cos X )`

Discussion

4576.	The value that shouldbe assigned to f (0)so that the functionf(x) =(x + 1)^(cotx)is continuous
Answer» E 1 2 `e^(-1)` ANSWER :A

Discussion

4577.	Evaluate : lim_(xto 0) (10^(x) - 2^(x) -5^(x)+1)/(sin^(2)x)
Answer» ANSWER :`[" USING "Lim_(xto0) (a^(x-1))/x = log_(e)a] `

Discussion

4578.	Find the derivative of the following functions:3 cot x +5 cosec x
Answer» ANSWER :`-3 COSEC^(2)x-5 cosecx.cotx`

Discussion

4579.	At a given instant, the sides OA and OB of a right angled triangled AOB are 8 cm and 6 cms respectively If OA increases at the rate of 2cm/sec and OB decreases at the rate of 1 cm/sec, therate of decreases of the area of DeltaAOB after 2 seconds is
Answer» 2 SQ cm/sec 1 sq cm/sec 3 sq cm/sec 4 sq cm/sec Answer :A

Discussion

4580.	Which of the following is not true about the matrix\|(1,0,0),(0,0,0),(0,0,5)\|?
Answer» a scalar matrix a DIAGONAL matrix an UPPER triangular matrix a LOWER triangular matrix Answer :B

Discussion

4581.	If f(x) = x^(n) for 0 lt a lt band na^(n-1) le (b^(n) - a^(n))/( b-a) le nb^(n-1) then n is
Answer» not LESS than one Zero n is NEGATIVE integer n is positive Answer :A

Discussion

4582.	Equation to the pair of lines passing through the origin whose sum and product of slopes are A.M. and G.M. of 4 and 9 is
Answer» `12X^(2)-13xy+2y^(2)=0` `12x^(2)+13xy+2y^(2)=0` `12x^(2)-15xy+2y^(2)=0` `12x^(2)+15xy-2y^(2)=0` ANSWER :A

Discussion

4583.	Evaluate the following limits in lim_(xrarrpi)(x-(22)/(77))
Answer» ANSWER :`(PI-(22)/(7))`

Discussion

4584.	A, B and C are foot of perpendicular from point P(-5, 3, 7) on XY, YZ, ZX planes. Then write coordinates of the point A, B and C.
Answer» Answer :A(-5, 3, 0), B(0, 3, 7), C(-5, 0, 7)

Discussion

4585.	(5, 2) is the mid point of the line segment intercepted between axes then equation of line is…..........
Answer» `5x + 2Y = 20` `2X + 5y = 20` `5x - 2y = 20` `2x - 5y = 20` Answer :B

Discussion

4586.	Statement-I : If f(theta)=(cot theta)/(1+cot theta) and alpha+ beta=(5pi)/(4) then f(alpha) f(beta)=(1)/(2) Statement-II : If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then tan alpha= tan beta+ 2tan gamm Statement-III sin^(2) alpha+ cos^(2) (alpha+ beta)+2 sin alpha beta cos (alpha+beta) is independent of alpha only
Answer» Only, I, II are true OnlyII, III true Only III, I are true I, II, III are true Answer :D

Discussion

4587.	The smallest value of x^(2)-3x+3 in the interval [-3,(3)/(2)] is
Answer» `(3)/(4)` 5 `-15` `-20` ANSWER :A

Discussion

4588.	If vecbara=2bari+3barj-4bark,vecb=bari+barj+bark,vecc=4bari+2barj+3bark then abs(vecaxx(vecbxxvecc))=
Answer» `SQRT(10)` 1 2 `SQRT5` ANSWER :D

Discussion

4589.	The verticle angleof an isosceles triangle is (2)/(3) of each od its base angle. Find it in radians.
Answer» ANSWER :`(PI)/(4)`

Discussion

4590.	Solve each of the following : x^(2)-x+2=0
Answer» ANSWER :`(-SQRT(7))/(2)i`

Discussion

4591.	The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is
Answer» `(a)/(2)COT((PI)/(2N))` `a cot((pi)/(2n))` `(a)/(4)cos((pi)/(2n))` `a cot ((pi)/(n))` Answer :A

Discussion

4592.	S-I : If f(x) is odd function and g(x) is even function then f(x)=g(x) is nether even nor odd S-II : Odd function is symmetrical in opposite quadrants and even function is symmetrical about the y-axis
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 is not a correct explanation for statement 1. Statement 1 is true, statement 2 is FALSE Statement 1 is false, statement 2 is true Answer :B

Discussion

4593.	Match the following {:("List-1","List-II"),("(A)D.C's of x-axis",(1)"1,1,1"),("(B) D.C of y-axis",(2) (1)/(sqrt(3))","(1)/(sqrt(3))","(1)/(sqrt(3))),("(C)D.C of z-axis",(3)"1,0,0"),("(D)D.C's of a line which",(4)"0,1,0"), (" makes equal",), ("angles with axes",),(,(5)"0,0,1"):}
Answer» `{:("A,B,C,D),(3,4,5,2):}` `{:("A,B,C,D),(1,2,3,4):}` `{:("A,B,C,D),(2,3,4,5):}` `{:("A,B,C,D),(5,4,3,2):}` ANSWER :A

Discussion

4594.	Simiplify :sqrt(-64).(3 + sqrt(-361))
Answer» ANSWER :`-152+24i`

Discussion

4595.	If f(x)=sin log, {(sqrt(4-x^(2)))/(1-x)}, then the domain of f(x) is _______ and its range is _
Answer» R and [0, 1] R and [-1, 1] `(0, oo)` and [-1, 1] `(0, oo)` and [0, 1] ANSWER :B

Discussion

4596.	Find the derivativ of the function w.r.to x cos [tan ^(-1) (log x)]
Answer» ANSWER :`= - (sin [ tan ^(-1) ( LOG X )])/( x [1 + (log x ) ^(2) ])`

Discussion

4597.	Find the cartesian equation of the curve whose parametric equations are : x=t, y=3t+5
Answer» ANSWER :`y=3x+5`

Discussion

4598.	The sum to infinity of the series 1+2/3+6/3^2+14/3^4+...is
Answer» 6 2 3 4 Answer :B

Discussion

4599.	If tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))=k tan^(-1)(x/a) then k=
Answer» 2 3 -2 4 Answer :B

Discussion

4600.	If R=([1+((dy)/(dx))^2]^(3/2))/((d^2y)/(dx^2)), then R^(2/3) can be put in the form of
Answer» `1/(((d^2y)/(dx^2))^(2/3))+1/(((d^2x)/(dy^2))^(2/3))` `1/(((d^2y)/(dx^2))^(3/2))+1/(((d^2x)/(dy^2))^(3/2))` `2/(((d^2y)/(dx^2))^(2/3))+2/(((d^2x)/(dy^2))^(2/3))` `1/(((d^2y)/(dx^2))^(2/3)) CDOT 1/(((d^2x)/(dy^2))^(2/3))` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

sin x + cos (x + 30^(@)) = 0, 0 ^(@) lt x lt 360^(@)

If A, B are acute positive angles satisfying the equations 3sin^(2)A+2sin^(2)B=1 and 3sin2A-2sin2B=0, then find A+2B.

If (1,2,3 ), (2,3,1 ) are two vertices of an equilateral triangle then its third vertex is

What is the conjugate of (2-i)/((1-2i)^(2))?

A metallic scale, due to heat is showing 0.99 mts as 1 meter. In this state, the radius of the base and height of a cone are measured to be 1 mts each. Find the actual volume of the cone approximately.

Evaluate the following limits : Lim_(xto0) (sqrt((1+x+x^(2)))-1)/x

4x + 3y le 60, y ge 2x, x ge 3, x, y ge 0

Total numbers of 4 digits numbers using digits 5,2,3,7 and 8 are 620.

If (a+b+c) (b+c-a) = 3bc then find angle A .

Let L be the line 2x + y - 2 = 0 . The axes rotated by 45^(0) in clockwise direction thenthe intercepts made by the line L on the new axes are respectively .

Find the equation of set of points P such that PA^(2)+PB^(2)=2k^(2), where A and B are the points (3, 4, 5) and (-1,3,-7), respectively.

Find the nth term and deduce the sum of n terms of the series 4+11+22+37+56+………….

The odds in favour for three horses participating in a house-race are 1:3,2:5 and 3:7. Find the probability that any one can win the race.

Find the slope of a line whose inclination is 30^(@)

n^( th) term of the series 4+14+ 30 + 52+ …..

If (1+X+x^2)^n = Sigma_(r=0)^(2n)a_(r) x^r then prove that(a) a_(r)=a_(2n-r)(b ) Sigma_(r=0)^(n-1)a_(r)=1/2 (3^n-a_n)

Solve the inequalityand represent the solution graphically on the number line ?

Draw the graphs of the following : y = |x| + |x -1| in [ -2,3]

Illustrate in the complex plane the following set of points and explain your answer |z-4| lt 1

In Delta ABC, (ab-r_1 r_2)/r_3=

If 0 lt x lt pi, andcos x+ sin x =1//2, thentan x=

Let f be function f(x)=cosx-(1-(x^(2))/(2)) . Then

LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {1, 2, 5} ⊂A

If -pilexlepi,-pileylepi and the cosx+cosy=2 then cos(x-y) =

Find the derivatives of the function cos ^(-1) (( b + a cos x )/( a + b cos x )), (a gt 0, b gt 0)

The value that shouldbe assigned to f (0)so that the functionf(x) =(x + 1)^(cotx)is continuous

Evaluate : lim_(xto 0) (10^(x) - 2^(x) -5^(x)+1)/(sin^(2)x)

Find the derivative of the following functions:3 cot x +5 cosec x

At a given instant, the sides OA and OB of a right angled triangled AOB are 8 cm and 6 cms respectively If OA increases at the rate of 2cm/sec and OB decreases at the rate of 1 cm/sec, therate of decreases of the area of DeltaAOB after 2 seconds is

Which of the following is not true about the matrix|(1,0,0),(0,0,0),(0,0,5)|?

If f(x) = x^(n) for 0 lt a lt band na^(n-1) le (b^(n) - a^(n))/( b-a) le nb^(n-1) then n is

Equation to the pair of lines passing through the origin whose sum and product of slopes are A.M. and G.M. of 4 and 9 is

Evaluate the following limits in lim_(xrarrpi)(x-(22)/(77))

A, B and C are foot of perpendicular from point P(-5, 3, 7) on XY, YZ, ZX planes. Then write coordinates of the point A, B and C.

(5, 2) is the mid point of the line segment intercepted between axes then equation of line is…..........

The smallest value of x^(2)-3x+3 in the interval [-3,(3)/(2)] is

If vecbara=2bari+3barj-4bark,vecb=bari+barj+bark,vecc=4bari+2barj+3bark then abs(vecaxx(vecbxxvecc))=

The verticle angleof an isosceles triangle is (2)/(3) of each od its base angle. Find it in radians.

Solve each of the following : x^(2)-x+2=0

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is

S-I : If f(x) is odd function and g(x) is even function then f(x)=g(x) is nether even nor odd S-II : Odd function is symmetrical in opposite quadrants and even function is symmetrical about the y-axis

Match the following {:("List-1","List-II"),("(A)D.C's of x-axis",(1)"1,1,1"),("(B) D.C of y-axis",(2) (1)/(sqrt(3))","(1)/(sqrt(3))","(1)/(sqrt(3))),("(C)D.C of z-axis",(3)"1,0,0"),("(D)D.C's of a line which",(4)"0,1,0"), (" makes equal",), ("angles with axes",),(,(5)"0,0,1"):}

Simiplify :sqrt(-64).(3 + sqrt(-361))

If f(x)=sin log, {(sqrt(4-x^(2)))/(1-x)}, then the domain of f(x) is _______ and its range is _

Find the derivativ of the function w.r.to x cos [tan ^(-1) (log x)]

Find the cartesian equation of the curve whose parametric equations are : x=t, y=3t+5

The sum to infinity of the series 1+2/3+6/3^2+14/3^4+...is

If tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))=k tan^(-1)(x/a) then k=

If R=([1+((dy)/(dx))^2]^(3/2))/((d^2y)/(dx^2)), then R^(2/3) can be put in the form of