28278 + Interview Questions in Maths in Class 12 Page 42 InterviewSolution

2051.	If a complex number z satisfies \|z\|^(2)+1=\|z^(2)-1\|, then the locus of z is
Answer» the REAL AXIS the imaginary axis y = x a circle ANSWER :B

Discussion

2052.	By vector method prove that altitudes of a triangle are concurrent.
Answer» ANSWER :The 3 ALTITUDES are CONCURRENT at O.

Discussion

2053.	A fair coin is tossed10 times. The probability of getting as many heads in the first 5 tosses as in the last 5 tosses is
Answer» `(1)/(2^(10))` `(1)/(2^(9))` `(""^(10)C_(5))/(2^(10))` `(1)/(2)` ANSWER :C

Discussion

2054.	If a,b,c are sides of a triangle and \|(a^(2),b^(2),c^(2)),((a+1)^(2),(b+1)^(2),(c+1)^(2)),((a-1)^(2),(b-1)^(2),(c-1)^(2))\|=0 then
Answer» `(a-b)(b-c)(c-a)` `2(a-b)(b-c)(c-a)` `3(a-b)(b-c)(c-a)` `-4(a-b)(b-c)(c-a)` ANSWER :D

Discussion

2055.	If 0ltxltpiand x ne(pi)/(2) , " then:" tan^(-1) (tanx)=...
Answer» `X-PI` `pi+x` `x-(pi)/(2)` `pi/2-x` ANSWER :D

Discussion

2056.	The volume of a tetrahedron (in cubic units) whose vertices are 4overset(^)i+5overset(^)j+overset(^)k, -overset(^)j+overset(^)k,3overset(^)i+9overset(^)j+4overset(^)k and -2overset(^)i+4overset(^)j+4overset(^)k is
Answer» `14/3` 5 6 30 Answer :B

Discussion

2057.	\|{:(5^2,5^3,5^4),(5^1,5^2,5^3),(5^3,5^4,5^4):}\|=.......
Answer» `5^9` `5^(12)` `5^0` 0 Answer :D

Discussion

2058.	If n is a positive integer, show that ( P + iQ)^(1//n) + ( P - iQ)^(1//n) = 2 ( P^(2) + Q^(2))^(1//2n)cos (1/n , tan . Q/P).
Answer»

Discussion

2059.	A and B are two events such that P(A)=1/5 and P(AuuB)=2/5Find P(B) if they are mutually exclusive. a)1/5 b)2/5 c)3/5 d)4/5
Answer» `1/5` `2/5` `3/5` `4/5` ANSWER :A

Discussion

2060.	Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]]=0
Answer» SOLUTION :`[[1,bc,a(B+C)],[1,ca,b(c+a)],[1,AB,c(a+b)]] C_3rarrC_3+C_2` `[[1,bc,ab+bc+ca],[1,ca,ab+bc+ca],[1,ab,ab+bc+ca]]` =`(ab+bc+ca)[[1,bc,1],[1,ca,1],[1,ab,1]]`=0 `(therefore C_1 and C_3 are identical)`

Discussion

2061.	If matrix A_(lamda)=[(lamda+1,lamda-2),(lamda-1,lamda)], lamda epsilonN then the valueof \|A_(1)\|+\|A_(2)\|+\|A_(3)\|+…………….+\|A_(300)\|is
Answer» `(299)^(2)` `(300)^(2)` `2(300)^(2)` `(301)^(2)` Solution :`\|A_(2)\|=LAMDA(lamda+1)-(lamda-1)(lamda-2)=4lamda-2` `\|A_(1)\|+\|A_(2)\|+\|A_(3)\|+……+\|A_(300)\|` `implies4{1+2+3+…….+300\|-600` `implies4.(300.301)/2-600=2(300)^(2)`

Discussion

2062.	Danielle is a civil enginner for Dastis Dynamic Construction, Inc. She must create blueprints for a wheelchair accessible ramp leading up to the entrance of amall that she and her group are building. The ramp must be exactly 100 meters in length and make a 20^@ angle with the level ground. What is the horizontal distance, in meters, from the start of the ramp to the point level with the start of the ramp immediately below the entrance of the mall, rounded to the nearest meter? (Disregard units when inputting your answer)
Answer» ANSWER :94

Discussion

2063.	A and B are two events such that P(A) = (1)/(4), P(A \| B)= (1)/(2) , P(B \| A)= (2)/(3), then P(B)= ………….
Answer» `(1)/(2)` `(1)/(6)` `(1)/(3)` `(2)/(3)` Answer :C

Discussion

2064.	If the roots of x^(3) - 42x^(2) + 336x - 512 = 0 , are in increasing geometric progression, its common ratio is
Answer» 2 3 4 6 Answer :C

Discussion

2065.	1/(2!)-1/(3!)+1/(4!) .....oo =
Answer» `E^(1/2)` `e^(-2)` `e^(-1)` `e^((-1)/2)` ANSWER :C

Discussion

2066.	Let S is the region of points which satisfies y^(2)lt16x,x lt4 and (xy(x^(2)-3x+2))/(x^(2)-7x+12)gt0. Its area is
Answer» `(8)/(3)` `(64)/(3)` `(32)/(3)` none of these Solution :`(xy(x^(2)-3x+2))/(x^(2)-7x+12)gt0` `rArr""(xy(x-1)(x-2))/((x-3)(x-4))gt0` `rArr""{{:(ygt0",","if",(x(x-1)(x-2))/((x-3)(x-4))gt0),(ylt0",","if",(x(x-1)(x-2))/((x-3)(x-4))lt0):}` `rArr""{{:(ygt0",","if",x in(0,1)uu(2,3)uu(4,oo)),(ylt0",","if",x in(-oo,0)uu(1,2)uu(3,4)):}` `y^(2)lt16x" is interior of the parabola "y^(2)=16x` Region is as shown in the following FIGURE: From the figure, required AREA = HALF of the area of the region bounded by `y^(2)=16x and x=4`

Discussion

2067.	I= int ( sqrt( alpha^(2) - x^(2) ) )/( x^4) dx.
Answer» Answer :`I= - ((a^(2) -X^(2) )^(3//2) )/( 3A^(2) x^(3) ) + C`.

Discussion

2068.	If z and omega are two nonzero complex numbers such that \|zomega\|=1 and "Arg" (z)-Arg "(omega) =pi//2 " then " barzomega =
Answer» 1 `-1` i `-i` ANSWER :D

Discussion

2069.	Evaluate: inte^(x)((x-1)/x^(2)) dx
Answer» ANSWER :`= E^(X) (1)/( x) + C`

Discussion

2070.	which of the following is true for x in [0,1]?
Answer» `sin^(-1)x+x^(2)-x(9-x^(2))/(3)le0` `sin^(-1)x+x^(2)-x(9-x^(2))/(3)ge0` `sin^(-1)x+x^(2)-x(9-x^(2))/(3)le0` `sin^(-1)x+x^(2)-x(9-x^(2))/(3)ge0` Solution :Let `f(x)=sin^(-1)x+x^(2)-3x+(x^(3))/(3)` `THEREFORE f(X)=(1)/sqrt(1-x^(2))+2x-3+x^(2)` Thus f(X)=0 for some x=`x_(1) in (0,1)` `f(x)=(x)/(1-x^(2))^(3//2)+2+2xgt 0 forall x in (0,1)` Thus x=`x_(1)`is the point of MINIMUM f(0)=0,f(1)=`pi//2-5//3lt0` f(X) is global maxima `forall x in [0,1]`.Thus `f(X)lef(X)XIN [0,1]or sin ^(-1)x+x^(2)-3x+x^(3)//3le0` or `sin^(-1)x+x^(2)LEX(9-x^(2))/(3)forall x in [0,1]`

Discussion

2071.	\|{:(1,a,bc),(1,b,ca),(1,c,ab):}\|
Answer» ANSWER :`= ( a-b)(b-c) (c-a) `

Discussion

2072.	Find the area of the surface obtained by revolving a loop of the curve 9ax^(2)= y (3a-y)^(2) about the y-axis
Answer» ANSWER :`= 3PI a^(2)`

Discussion

2073.	State which of the following are positive ?cosec 159^@
Answer» SOLUTION :`COSEC 159^@` is +ve as `159^@` lies in 2ND QUANDRANT and cosec is +ve there.

Discussion

2074.	Let f(x+2)=3x -4,then find f^(-1) (1)
Answer»

Discussion

2075.	(3x^(2)+x+1)/((x-1)^(4))=(A)/(x-1)+(B)/((x-1)^(2))+(C)/((x-1)^(3))+(D)/((x-1)^(4)) then A+B-C+D=
Answer» 0 15 1 10 Answer :C

Discussion

2076.	If \|a.b\| = \|a xx b\| then (a,b) = pi //4
Answer»

Discussion

2077.	For \|x\| lt 1/2 , the value of the fourth term of (1 - 2x)^(-3//4) is
Answer» `-77/16 x^3` `16/77 x^3` `77/16 x^3` `-16/77x^3` ANSWER :C

Discussion

2078.	State the order of [a b c] matrices.
Answer» SOLUTION :`(1xx3)`

Discussion

2079.	The values of k for which each root of the equation, x^(2)-6kx+2-2k+9k^(2)=0 is greater than 3, salways satisfy the inequality :
Answer» `7-9y GT0` `11-9ylt0` `29-11ygt0` `29-11ylt0` ANSWER :B

Discussion

2080.	If z (x,y) = x tan ^(-1) (xY), x = t ^(2), t y = se ^(t), s , t in R. Find (del z)/( del s) and (del z)/(del t) at s = t =1.
Answer» Answer :`= (3e)/( 1 + E ^(2)) + 2 tan ^(-1) e `

Discussion

2081.	Obtain the equation of a hyperbola with coordinate axes as principal axes given that the distances of one of its vertices from the foci are 9 and 1 units.
Answer» ANSWER :12X^(2)-4Y^(2)-24x+32y-127=0`

Discussion

2082.	Evaluate int(x + (1)/(x))^(3) dx, x gt 0
Answer» Answer :`(x^(4))/(4)+3.(x^(2))/(2)+3log\|x\|-(1)/(2x^(2))+C`

Discussion

2083.	Evaluate int e^(-2x) [2 tanx - sec^(2) x]dx
Answer» ANSWER :`-E^(-2X)tanx+c`

Discussion

2084.	If x ge 0, y ge 0, 2x le x +y le 8, 2x+y le 10, then the minimum value of F=5x+7y is
Answer» 10 14 6 5 Answer :A

Discussion

2085.	A plane meets the co-ordinate axes at A,B,C and (alpha,beta,gamma) is the centroid of the triangle ABC. Then the equation of the plane is
Answer» `alphax+betay+gammaz=1` `(x)/(alpha)+(y)/(beta)+(Z)/(gamma)=1` `(x)/(alpha)+(y)/(beta)+(z)/(gamma)=3` `(3X)/(alpha)+(3y)/(beta)+(3Z)/(gamma)=1` Answer :C

Discussion

2086.	Solve system of linear equations, using matrix method in examples 7 to 14 5x+2y=3 3x+2y=5
Answer» ANSWER :x=-1 and y=4

Discussion

2087.	The three equations: x + y +z = 3, x^(3) + y^(3) + z^(3) = 15 and x^(4) + y^(4) + z^(4) = 35 has a real solution x,y,z for which x^(2) + y^(2) + z^(2) lt 10. Find the value of (x^(5) + y^(5) + z^(5))
Answer» ANSWER :83

Discussion

2088.	Given that the two numbers appearing on throwing two dice are different. Find the probability of the event 'the sum of numbers on the dice is 4.
Answer» ANSWER :`(1)/(15)`

Discussion

2089.	Classify 10 Newton measures as scalar and vector.
Answer» SOLUTION :Force-vector

Discussion

2090.	Let P(n) denote the statement that n^(2)+n is odd. It is seen that P(n) = P(n + 1). P(n) is true for all.
Answer» `NGT1` N `ngt2` NONE of these Answer :D

Discussion

2091.	int_(0)^(1) cot^(-1) (1-x+x^(2)) dx=?
Answer» `(PI)/(2) +LOG 2` `(pi)/(2) -log 2` `-(pi)/(2) - log 2` ANSWER :C

Discussion

2092.	A line passes through (2,2) and is perpendicular to the line 3x+y=3, its y-intercepts is__________
Answer» 1 `(4)/(3)` `(2)/(3)` `(1)/(3)` Answer :B

Discussion

2093.	Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B)=36, then find n(A ∩ B).
Answer» ANSWER :12

Discussion

2094.	Giventhe continuousfuunctiony= f(x) ={{:( x^(2) +10x+8, x le -2),( ax^(2)+bx +c, -2ltxlt 0","a ne 0) ,( x^(2) + 2x, xge 0):} if a line L touches the graph of y=f(x)at three points , thenthe slope of theline L is equal to
Answer» 1 2 4 6 Answer :C

Discussion

2095.	Giventhe continuousfuunctiony= f(x) ={{:( x^(2) +10x+8, x le -2),( ax^(2)+bx +c, -2ltxlt 0","a ne 0) ,( x^(2) + 2x, xge 0):} if a line L touches the graph of y=f(x)at three points , then thevalueof ( a+b+c) is equal to
Answer» `5sqrt(2)` 5 6 7 Answer :D

Discussion

2096.	Giventhe continuousfuunctiony= f(x) ={{:( x^(2) +10x+8, x le -2),( ax^(2)+bx +c, -2ltxlt 0","a ne 0) ,( x^(2) + 2x, xge 0):} if a line L touches the graph of y=f(x)at three points , then ify= f(x)isdifferentiableat x=0, thenthe valueof B
Answer» is -1 is 2 is 4 connot bedetermined ANSWER :B

Discussion

2097.	The point equidistant to the lines 4x+3y+10=0, 5x-12y+26=0, 7x+24y-50=10 is
Answer» (1, -1) (1, 1) (0, 0) (0, 1) ANSWER :C

Discussion

2098.	The set of values of alpha (alpha gt 0) for which the inequality int_(-alpha)^(alpha) e^x dx gt 3/2 holds true is :
Answer» `(0, oo)` `(2,oo)` `(ln2, oo)` None of these SOLUTION :`2e^(2ALPHA) - 3e^(alpha) - 2 gt 0 RARR E^(alpha) lt -1/2 " or " e^(alpha) gt 2` But `e^(alpha) gt 0 AA alpha in R rArr e^alpha gt 2` `i.e. alpha in (log2, oo)`

Discussion

2099.	Statement I If f (x) = int_(0)^(1) (xf(t)+1) dt, then int_(0)^(3) f (x) dx =12 Statement II f(x)=3x+1
Answer» Statement I is true, Statement II is ALSO true, Statement II is the correct explanation of Statement 1. Statement I is true, Statement II is also true , Statement II is not the correct explanation of Statement II. Statement I is true, Statement II is FALSE Statement I is false , STATEMENTII is true Answer :C

Discussion

2100.	Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t. tan^(-1) ((x)/(sqrt(1-x^(2)))).
Answer» ANSWER :`(SQRT(1-x^(2)))/(2(1+x^(2)))`

Discussion

Explore topic-wise InterviewSolutions in .

If a complex number z satisfies |z|^(2)+1=|z^(2)-1|, then the locus of z is

By vector method prove that altitudes of a triangle are concurrent.

A fair coin is tossed10 times. The probability of getting as many heads in the first 5 tosses as in the last 5 tosses is

If a,b,c are sides of a triangle and |(a^(2),b^(2),c^(2)),((a+1)^(2),(b+1)^(2),(c+1)^(2)),((a-1)^(2),(b-1)^(2),(c-1)^(2))|=0 then

If 0ltxltpiand x ne(pi)/(2) , " then:" tan^(-1) (tanx)=...

The volume of a tetrahedron (in cubic units) whose vertices are 4overset(^)i+5overset(^)j+overset(^)k, -overset(^)j+overset(^)k,3overset(^)i+9overset(^)j+4overset(^)k and -2overset(^)i+4overset(^)j+4overset(^)k is

|{:(5^2,5^3,5^4),(5^1,5^2,5^3),(5^3,5^4,5^4):}|=.......

If n is a positive integer, show that ( P + iQ)^(1//n) + ( P - iQ)^(1//n) = 2 ( P^(2) + Q^(2))^(1//2n)cos (1/n , tan . Q/P).

A and B are two events such that P(A)=1/5 and P(AuuB)=2/5Find P(B) if they are mutually exclusive. a)1/5 b)2/5 c)3/5 d)4/5

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]]=0

If matrix A_(lamda)=[(lamda+1,lamda-2),(lamda-1,lamda)], lamda epsilonN then the valueof |A_(1)|+|A_(2)|+|A_(3)|+…………….+|A_(300)|is

A and B are two events such that P(A) = (1)/(4), P(A | B)= (1)/(2) , P(B | A)= (2)/(3), then P(B)= ………….

If the roots of x^(3) - 42x^(2) + 336x - 512 = 0 , are in increasing geometric progression, its common ratio is

1/(2!)-1/(3!)+1/(4!) .....oo =

Let S is the region of points which satisfies y^(2)lt16x,x lt4 and (xy(x^(2)-3x+2))/(x^(2)-7x+12)gt0. Its area is

I= int ( sqrt( alpha^(2) - x^(2) ) )/( x^4) dx.

If z and omega are two nonzero complex numbers such that |zomega|=1 and "Arg" (z)-Arg "(omega) =pi//2 " then " barzomega =

Evaluate: inte^(x)((x-1)/x^(2)) dx

which of the following is true for x in [0,1]?

|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

Find the area of the surface obtained by revolving a loop of the curve 9ax^(2)= y (3a-y)^(2) about the y-axis

State which of the following are positive ?cosec 159^@

Let f(x+2)=3x -4,then find f^(-1) (1)

(3x^(2)+x+1)/((x-1)^(4))=(A)/(x-1)+(B)/((x-1)^(2))+(C)/((x-1)^(3))+(D)/((x-1)^(4)) then A+B-C+D=

If |a.b| = |a xx b| then (a,b) = pi //4

For |x| lt 1/2 , the value of the fourth term of (1 - 2x)^(-3//4) is

State the order of [a b c] matrices.

The values of k for which each root of the equation, x^(2)-6kx+2-2k+9k^(2)=0 is greater than 3, salways satisfy the inequality :

If z (x,y) = x tan ^(-1) (xY), x = t ^(2), t y = se ^(t), s , t in R. Find (del z)/( del s) and (del z)/(del t) at s = t =1.

Obtain the equation of a hyperbola with coordinate axes as principal axes given that the distances of one of its vertices from the foci are 9 and 1 units.

Evaluate int(x + (1)/(x))^(3) dx, x gt 0

Evaluate int e^(-2x) [2 tanx - sec^(2) x]dx

If x ge 0, y ge 0, 2x le x +y le 8, 2x+y le 10, then the minimum value of F=5x+7y is

A plane meets the co-ordinate axes at A,B,C and (alpha,beta,gamma) is the centroid of the triangle ABC. Then the equation of the plane is

Solve system of linear equations, using matrix method in examples 7 to 14 5x+2y=3 3x+2y=5

The three equations: x + y +z = 3, x^(3) + y^(3) + z^(3) = 15 and x^(4) + y^(4) + z^(4) = 35 has a real solution x,y,z for which x^(2) + y^(2) + z^(2) lt 10. Find the value of (x^(5) + y^(5) + z^(5))

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event 'the sum of numbers on the dice is 4.

Classify 10 Newton measures as scalar and vector.

Let P(n) denote the statement that n^(2)+n is odd. It is seen that P(n) = P(n + 1). P(n) is true for all.

int_(0)^(1) cot^(-1) (1-x+x^(2)) dx=?

A line passes through (2,2) and is perpendicular to the line 3x+y=3, its y-intercepts is__________

Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B)=36, then find n(A ∩ B).

Giventhe continuousfuunctiony= f(x) ={{:( x^(2) +10x+8, x le -2),( ax^(2)+bx +c, -2ltxlt 0","a ne 0) ,( x^(2) + 2x, xge 0):} if a line L touches the graph of y=f(x)at three points , thenthe slope of theline L is equal to

Giventhe continuousfuunctiony= f(x) ={{:( x^(2) +10x+8, x le -2),( ax^(2)+bx +c, -2ltxlt 0","a ne 0) ,( x^(2) + 2x, xge 0):} if a line L touches the graph of y=f(x)at three points , then thevalueof ( a+b+c) is equal to

Giventhe continuousfuunctiony= f(x) ={{:( x^(2) +10x+8, x le -2),( ax^(2)+bx +c, -2ltxlt 0","a ne 0) ,( x^(2) + 2x, xge 0):} if a line L touches the graph of y=f(x)at three points , then ify= f(x)isdifferentiableat x=0, thenthe valueof B

The point equidistant to the lines 4x+3y+10=0, 5x-12y+26=0, 7x+24y-50=10 is

The set of values of alpha (alpha gt 0) for which the inequality int_(-alpha)^(alpha) e^x dx gt 3/2 holds true is :

Statement I If f (x) = int_(0)^(1) (xf(t)+1) dt, then int_(0)^(3) f (x) dx =12 Statement II f(x)=3x+1

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t. tan^(-1) ((x)/(sqrt(1-x^(2)))).