28278 + Interview Questions in Maths in Class 12 Page 100 InterviewSolution

4951.	If, in triangleABC, tanA : tan B : tan C= 2:3:4, then: sec^(2)C=
Answer» `(1-COTA)(1-cot C)=2` `(1+cotA )(1+cotC)=2` cotA + cot B + cot C= cot A + cot B + cot C cotA + cot B + cot C`=sqrt(3)` ANSWER :B

Discussion

4952.	A line makes the angle alpha, beta , gamma and delta with the diagonals of a cube. The cos^2 alpha + cos^2 beta + cos^2 gamma + cos^2 delta =.............
Answer» `4/3` `2/3` `3` `1/3` ANSWER :A

Discussion

4953.	Examine the continuity of the following functions at indicated points.f(x)={((1+2x)^(1/2)if xne0),(e^2 if x=0at x=0):}
Answer» Solution :We KNOW that a function F(x) is CONTINUOUS at a point x=a if `LIM(xtoa)f(x)=f(a)` Now `lim_(xto0)f(x)=lim_(xto0)(1+2x)^(1/x)=e^2` Again `f(0)=e^2` THUS `lim_(xto0)f(x)=f(0)` So f(x) is continuous at x=0

Discussion

4954.	If A = {1,2,3,4} , define relations on A which have properties of being : Symmetric but neither reflexive nor transitive
Answer» SOLUTION :N/A

Discussion

4955.	Given that, a alpha^(2) + c ne 0 and that the system of equations (a alpha +b) x + ay + bz=0, (b alpha + c ) x + by + cz, =0, (a alpha +b) y+ (b alpha + c) z=0 has a non-trivial solution, then a,b, and c lie in
Answer» ARITHMETIC peogression GEOMETRIC progression Harmonic progression Arithmetico-grmetric progression Answer :B

Discussion

4956.	Prove that C_(1)^(2) - 2. C_(2)^(2) + 3. C_(3)^(2) - …. -2n . C_(2n)^(2) = (-1)^(n). C_(n)
Answer» Solution : We KNOW that , `(1 + x )^(2n) = C_(0)+ C_(1)x + C_(2) x^(2) + …+ C_(2n) x^(2n)` On differntiating both sides w.r.t.x, we get ` 2n (1 + x)^(2n-1) = C_(1) + 2.C_(2) x + 3. C_(3) x^(3) + …+ 2nC_(2n x^(2n-1) ` …(i) and ` (1 - (1)/(x))^(2n) = C_(0) - C_(1).(1)/(x) + C_(2) .(1)/(x^(2)) C_(3) . (1)/(x^(3)) + ...+ C_(2n). (1)/(x^(2n))`...(II) On multiplying Eqs. (i) and (ii) , we get ` 2n (1 + x)^(2n-1) (1 - (1)/(x))^(2n)` = `[C_(1) + 2C_(2)x + 3. C_(3) x^(2) +...+ 2nC_(2n)x^(2n-1)] xx[C_(0) - C_(1) ((1)/(x)) + C_(2) ((1)/(x^(3))) -...+C_(2n) ((1)/(x^(2n)))]` Coefficent of ` ((1)/(x))`on the LHS = Coefficient of ` (1)/(x) `in 2n `((1)/(x^(2n)))(1 + x)^(2n - 1) (x - 1)^(2n)` Coefficient if ` x^(2n - 1)` in 2n ` (1 - x^(2))^(2-1) (1 - x)` ` 2n (-1)^(n-1) . (2n -1) C_(n-1) (-1)` ` = (-1)^(n) (2n) ((2n -1)!)/((n-1)!n!) = (-1)^(n)n((2n)!)/((n!^(2)))n` ` = - (-1)^(n)n . C_(n)`...(iii) Again , the coefficient of `((1)/(x))` on the RHS ` = - (C_(1)^(2) - 2 C_(2)^(2) + 3C_(3)^(2)-...-2nC_(2n)^(2))`...(iv) From Eqs. (iii) and (iv), `- C_(1)^(2) - 2 C_(2)^(2) + 3C_(3)^(2)-...-2nC_(2n)^(2) = (-1)^(n) n.C_(n)`.

Discussion

4957.	Form the equation whose roots are m times the roots of the equation x^3+(x^2)/(4)-x/(16)+1/(72)=0and deduce the case when m =12 .
Answer» 3 12 9 4 Answer :2

Discussion

4958.	Evaluate the following integrals int_0^1(2x+1)^4
Answer» SOLUTION :`int_0^1(2x+1)^4dx=(1/2)[(2x+1)^5/5]_0^1` (1/2)((243-1)/5)=121/5

Discussion

4959.	Prove that Bernoulli inqeuality (1+x_(1)) [1+x_(2)).....(1+x_(n)) ge 1+x_(1)+x_(2)+......+x_(n). Where x_(1), x_(2),.....x_(n) are numbers of like sign, and 1+x_(1) gt 0(i=1,2,.....n)
Answer» ANSWER :`1+x_n GT 0, x_i . X_n gt 0 (i=1,2,.....n-1)`

Discussion

4960.	The probability that a certain kind of component will survive a electrical test is (3)/(4) . Find the probability that exactly 3 of the 5 components tested survive .
Answer» ANSWER :`(270)/(1024)`

Discussion

4961.	The value of K_(p) for the reaction NH_(2)COONH_(4)(s) hArr2NH_(3)(g)+CO_(2)(g)" is "2.9xx10^(-5)"atm"^(3). The total pressure of gases at equilibrium when NH_(2)COONH_(4)(s) is taken to start the reaction at the initial concentration of 1.0 mole is
Answer» 0.0620 atm. 0.0310 atm. 0.0582 atm. 0.2610 atm. Solution :`"The reaction is",NH_(2)COONH_(4)(s)hArr2NH_(3)(g)+CO_(2)(g)` `{:("Initial conc.",1.0"mole",,0,,0),("EQM. conc.",0,,2,,1):}` Let P be the equilibrium pressure then the PARTIAL pressure of ammonia `=(2)/(3)P` and the of carbon dioxide is `(1)/(3)P`. Or`""K_(p)=[(2P)/(3)]^(2)[(P)/(3)]=(4P^(3))/(27)` Or `""2.9xx10^(-5)=(4P^(3))/(27)" or "4P^(3)=27xx2.9xx10^(-5)` Or `""P=root(3)((27xx2.9xx10^(-5))/(4))` Or `""P=0.0582" atm. "`

Discussion

4962.	There are 4 Oranges, 4 apples and 6 mangoes in a fruit basket. In how many ways can a person makes a selection of one or more fruits from among the fruits in the basket if all the fruits of same type are identical
Answer» ANSWER :174

Discussion

4963.	There are 4 Oranges, 4 apples and 6 mangoes in a fruit basket. In how many ways can a person makes a selection of one or more fruits from among the fruits in the basket if all the fruits of same type are different
Answer» ANSWER :`2^(14)-1`

Discussion

4964.	If from a pack of 52 well shuffled cards, cards are drawn one by one without replacement and thethird card is found to be ACE. What is the probability that first two cards are not ACES ?
Answer» `260/329` `376/425` `161/329` NONE of these SOLUTION :`=((.^48C_2)/(.^52C_2)xx4/50)/((.^48C_2)/(.^52C_2)xx4/50+(.^48C_1.^4C_1)/(.^52C_2)xx3/50+(.^4C_2)/(.^52C_2)xx2/50)` `=(4.^48C_2)/(4 .^48C_2+12.^48C_1+12)`

Discussion

4965.	Expand the following (7a+3b)^6
Answer» SOLUTION :`(7A+3B)^6` = `(7a+3b)^6` = `7a^6+"^6C_1 7a^(6-1) (3b)^1 + ^6C_2 7a^(6-2)(3b^2)+...(3b)^6`

Discussion

4966.	If a square with length of each side equal to a is inscribed in the circle x ^(2) + y ^(2) + 4x + 10 y + 21 =0,then a is equal to
Answer» `SQRT2` 2 `2SQRT2` 4 Answer :D

Discussion

4967.	A boat is to be manned by 9 crew with 4 on the stroke side, 4 on the row side and one to steer. There are 11 men of which 2 can stroke only and 1 can row only while 3 can steer only. The number of ways the crew can be arranged for the boat is
Answer» 10 30 44 17280 Answer :D

Discussion

4968.	Which of the following statements (s) is/are true?
Answer» `underset(x to a)(LIM) (a^(x) - x^(a))/(x^(x) - a^(a)) = - 1` then a is 1 `underset(n to OO)(lim) log_(n - 1) n . Log_(n) (n + 1) n. log_((n + 1)) (n + 2)`………`log_((n^(5) - 1)) n^(5) = 5` `underset(x to n)(lim) log_((x^(2) + 1)/(x + 1)) (sqrt(x^(2) + 1) - x) = 1` `underset({:(x to 0),(y to 0):})(lim) (x^(2))/(y) = 0`, when (x,y) `to` (0,0) along the CURVE `y^(2) = x^(3)` Answer :A::B::C::D

Discussion

4969.	A student is instructed to answer 8 out of 12 questions. i. How many differnet ways can he choose the questions? ii. How many different ways can he choose the questions so that question number 1 will be included? iii. How many different ways can he choose the questions so that question number 1 will be included and question number 10 will be excluded?
Answer» ANSWER :i. 495 II. 330 iii. 120

Discussion

4970.	Solve as directed: abs(x-3) lt 11 , in N and in R.
Answer» Solution :`ABS(X-3) lt 11` `rArr -1 lt x - 3 lt 11 `rArr -11 + 3 lt x - 3 + 3 lt 11 + 3` ` rArr -8 lt x lt 14 ` If x `in` N the solution set is S = {1,2,3,4,5,…….12,13} If x `in` R then the solution set is : S -= {x:x `in` R and -8 `lt x lt 14} =(-8,14)

Discussion

4971.	Through the vertex O of the parabola y^(2)=4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP.OQ=
Answer» `a^(2)` `2A^(2)` `3A^(2)` `4A^(2)` ANSWER :D

Discussion

4972.	int(1-tanx)/(1+tanx)dx=.....
Answer» `LOG SEC((pi)/(4)-x)+c` `log sec((pi)/(4)+x)+c` `log sin((pi)/(4)+x)+c` NONE of these Answer :C

Discussion

4973.	A manufacturing company makes tow models A and B of product. Each piece of model A reqwuires 9 labour hours for fabricating and 1 hour labour for finishing . Each piece of model Brequires 12 labour hours for fabricating and 3 labourhours for fininshing. for fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs. 8,000 on each piece of modleA and Rs 12,000 on each piece of model B. How many pieces of model A and B should be manufactured per week to realise a maximum profit ? What is the maximum profit per week ?
Answer» ANSWER :RS. 1,68,000

Discussion

4974.	Find the area of the loop of the curve 3ay^(2)= x(x-a)^(2)
Answer» Answer :`(8sqrt(3)a^(2))/(45)` sq. units

Discussion

4975.	Let ' be the binary operation on the set {1,2,3,4,5} defined by a'b= H.C.F. of a and b. Is the operation ' same as the operation defined in Exercise 4 above ? Justify your answer.
Answer» SOLUTION :YES

Discussion

4976.	The vector equation of the line 6x-3=3y+4=2z-2 is
Answer» `VECR=hati-hatj+hatk +LAMBDA(6hati+hatj+hatk)` `vecr=6hati+3hatj+2hatk+lambda(3hati+4hatj-2hatk)` `vecr=(1/2hati-4/3hatj+hatk)+lambda(1/6 hati+1/3hatj+1/2hatk)` NONE of these ANSWER :C

Discussion

4977.	If a chord of the parabola y^(2)=4x passes through its focus and makes an angle theta with the X-axis, then its length is
Answer» `4cos^(2) theta` `4 SIN^(2) theta` `4" cosec"^(2) theta` `4 SEC^(2) theta` ANSWER :C

Discussion

4978.	If overline(a) and overline(b) are tow parallel vectors wth equal magnitude, then
Answer» `a=B` `ab=0` `ANEB` a and b MAY or may not equal Answer :D

Discussion

4979.	""^(37)C_(4)+sum_(r=1)^(5)(42-r)_(C_(r))=
Answer» `""^(38)C_(4)` `""^(39)C_(4)` `""^(41)C_(4)` `""^(42)C_(4)` ANSWER :D

Discussion

4980.	If in the triangle ABC, "tan"(A)/(2), "tan"(B)/(2) and "tan"(C )/(2) are in harmonic progression then the least value of "cot"^(2)(B)/(2) is equal to :
Answer» ANSWER :3

Discussion

4981.	Find int x sqrt(1+x-x^(2))dx as the limit of sum.
Answer» ANSWER :`-(1)/(3)(1+x-x^(2))^((3)/(2))+(1)/(8)(2x-1) sqrt(1+x-x^(2))+(5)/(16)"sin"^(-1)((2x-1)/(sqrt(5)))+C`

Discussion

4982.	If x = (1-sqrt(y))/(1+sqrt(9)), then (x+1)(d^(2)y)/(dx^(2))+((3sqrt(y)+1)/(sqrt(y)))(dy)/(dx) =
Answer» `-2Y` 0 `-y` y Answer :B

Discussion

4983.	The volume of the solid formed by revolving the area of the circle x^2+y^2=9 about y axis is :
Answer» `2PI` `24pi` `30PI` `36pi`. ANSWER :D

Discussion

4984.	If \|z + 4\| + \|z - 4\| = 10 represents an ellipse then length of its minor axis is
Answer» 3 4 6 8 Answer :C

Discussion

4985.	For matrics A and B, verify that (AB)^T=B^T .A^T, where A=[[0],[1],[2]], B=[[1,5,7]]
Answer» SOLUTION :`AB=[[1],[-4],[3]] [[-1,2,1]]=[[-1,2,1],[4,-8,-4],[-3,6,3]]` therefore `(AB)^T=[[-1,4,-3],[2,-8,6],[1,-4,3]]` `B^T A^T=[[-1],[2],[1]] [1,-4,3]]=[[-1,4,-3],[2,-8,6][1-4,3]]` , thus `(AB)^T=B^T A^T`

Discussion

4986.	Find the numerically greatest term of (2x-3y)^(12), x=1, y=(5)/(3)
Answer» SOLUTION :N/A

Discussion

4987.	The value of k for which the system of linear equations (2k+2)x+10y=k 2kx+(2k+3)y=k-1 ha sno solution is________________.
Answer» ANSWER :0.25

Discussion

4988.	I : Value of i^i=e^(-pi/2)II : z=ilog(2+sqrt3) then sinz=2which of above statement is true
Answer» only I only II Both I and II neither I nor II Answer :A

Discussion

4989.	Equation of a line passing through the point (2,-3, 2) and equally inclined to the Line L_(1) and L_(2) may be equal to :
Answer» `(x-2)/(2) = (y-3)/(-1) = (z-3)/(1)` `HATR (hati +7hatj-5 hatk)=3` `harr (hati- 7 HATJ-5 hatk)=9` `hatr (hati+ 7 hatj - 5 hatk )=9` ANSWER :D

Discussion

4990.	If int(x+1)/((x^(2)+x+1))(dx)/(sqrt(x^(2)+x+1))=K(x-1)/(sqrt(x^(2)+x+1))+C then the value of K is
Answer» 1//3 1//3 2//3 none of these Answer :C

Discussion

4991.	If four whole numbers taken at random are multiplied together. Then the chance that the last digit in the product is 1 or 3 or 7 or 9 is.(A) 16/625(B) 16/125(C) 16/625(D) NONE OF THESE
Answer» ANSWER :`(16)/(25)`

Discussion

4992.	Solve the following systems of linear inequalities graphically : x - y lt 1 , y - x = 1
Answer» SOLUTION :

Discussion

4993.	Differentiate the following w.r.t. x : e^(-x)
Answer» ANSWER :`-E^(-X)`

Discussion

4994.	Estimate the integral from above I = int_(0)^(1) (sin x)/( 1 + x^(3)) dx
Answer» ANSWER :`0 . 46`

Discussion

4995.	If the total number of ways in which 8-digit numbers can be formed by using all the digits 0, 1, 2, 3, 4, 5, 7, 9 such that no two even digits appear together is (5!)k, then k is equal to ______
Answer» ANSWER :`100`

Discussion

4996.	In the following figure, identify collinear but not equal vector
Answer» Solution :`veca "and" vecd`their LINES of ACTION are parallel and they have OPPOSITE DIRECTIONS.

Discussion

4997.	N is 50 digit number in decimal form). All digits except the 26^("th")digit (from left) are 1. If N is divisible by 13, find the 26^("th")digit.
Answer» ANSWER :3

Discussion

4998.	For any vector bar(a), the value of (bar(a)xx i)^(2)+(bar(a)xx j)^(2)+(bar(a)xx bar(k))^(2) is ………..
Answer» `\|BAR(a)\|^(2)` `3\|bar(a)\|^(2)` `4\|bar(a)\|^(2)` `2\|bar(a)\|^(2)` ANSWER :D

Discussion

4999.	Find the maximum value of the 2+3sinx+4cosx
Answer» SOLUTION :Maximum VALUE of 3sinx+4cosx is `SQRT(3^2+4^2)=5` `THEREFORE` Maximum value of 2+3sinx+4cosx is 2+5=7

Discussion

5000.	If z_(1)=a+ib,z_(2)=-a+ib then z_(1)-z_(2) lies on ………….
Answer» REAL axis imaginary axis the LINE y=x the line y=-x Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

If, in triangleABC, tanA : tan B : tan C= 2:3:4, then: sec^(2)C=

A line makes the angle alpha, beta , gamma and delta with the diagonals of a cube. The cos^2 alpha + cos^2 beta + cos^2 gamma + cos^2 delta =.............

Examine the continuity of the following functions at indicated points.f(x)={((1+2x)^(1/2)if xne0),(e^2 if x=0at x=0):}

If A = {1,2,3,4} , define relations on A which have properties of being : Symmetric but neither reflexive nor transitive

Given that, a alpha^(2) + c ne 0 and that the system of equations (a alpha +b) x + ay + bz=0, (b alpha + c ) x + by + cz, =0, (a alpha +b) y+ (b alpha + c) z=0 has a non-trivial solution, then a,b, and c lie in

Prove that C_(1)^(2) - 2. C_(2)^(2) + 3. C_(3)^(2) - …. -2n . C_(2n)^(2) = (-1)^(n). C_(n)

Form the equation whose roots are m times the roots of the equation x^3+(x^2)/(4)-x/(16)+1/(72)=0and deduce the case when m =12 .

Evaluate the following integrals int_0^1(2x+1)^4

Prove that Bernoulli inqeuality (1+x_(1)) [1+x_(2)).....(1+x_(n)) ge 1+x_(1)+x_(2)+......+x_(n). Where x_(1), x_(2),.....x_(n) are numbers of like sign, and 1+x_(1) gt 0(i=1,2,.....n)

The probability that a certain kind of component will survive a electrical test is (3)/(4) . Find the probability that exactly 3 of the 5 components tested survive .

The value of K_(p) for the reaction NH_(2)COONH_(4)(s) hArr2NH_(3)(g)+CO_(2)(g)" is "2.9xx10^(-5)"atm"^(3). The total pressure of gases at equilibrium when NH_(2)COONH_(4)(s) is taken to start the reaction at the initial concentration of 1.0 mole is

There are 4 Oranges, 4 apples and 6 mangoes in a fruit basket. In how many ways can a person makes a selection of one or more fruits from among the fruits in the basket if all the fruits of same type are identical

There are 4 Oranges, 4 apples and 6 mangoes in a fruit basket. In how many ways can a person makes a selection of one or more fruits from among the fruits in the basket if all the fruits of same type are different

If from a pack of 52 well shuffled cards, cards are drawn one by one without replacement and thethird card is found to be ACE. What is the probability that first two cards are not ACES ?

Expand the following (7a+3b)^6

If a square with length of each side equal to a is inscribed in the circle x ^(2) + y ^(2) + 4x + 10 y + 21 =0,then a is equal to

A boat is to be manned by 9 crew with 4 on the stroke side, 4 on the row side and one to steer. There are 11 men of which 2 can stroke only and 1 can row only while 3 can steer only. The number of ways the crew can be arranged for the boat is

Which of the following statements (s) is/are true?

Solve as directed: abs(x-3) lt 11 , in N and in R.

Through the vertex O of the parabola y^(2)=4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP.OQ=

int(1-tanx)/(1+tanx)dx=.....

Find the area of the loop of the curve 3ay^(2)= x(x-a)^(2)

Let **' be the binary operation on the set {1,2,3,4,5} defined by a**'b= H.C.F. of a and b. Is the operation **' same as the operation ** defined in Exercise 4 above ? Justify your answer.

The vector equation of the line 6x-3=3y+4=2z-2 is

If a chord of the parabola y^(2)=4x passes through its focus and makes an angle theta with the X-axis, then its length is

If overline(a) and overline(b) are tow parallel vectors wth equal magnitude, then

""^(37)C_(4)+sum_(r=1)^(5)(42-r)_(C_(r))=

If in the triangle ABC, "tan"(A)/(2), "tan"(B)/(2) and "tan"(C )/(2) are in harmonic progression then the least value of "cot"^(2)(B)/(2) is equal to :

Find int x sqrt(1+x-x^(2))dx as the limit of sum.

If x = (1-sqrt(y))/(1+sqrt(9)), then (x+1)(d^(2)y)/(dx^(2))+((3sqrt(y)+1)/(sqrt(y)))(dy)/(dx) =

The volume of the solid formed by revolving the area of the circle x^2+y^2=9 about y axis is :

If |z + 4| + |z - 4| = 10 represents an ellipse then length of its minor axis is

For matrics A and B, verify that (AB)^T=B^T .A^T, where A=[[0],[1],[2]], B=[[1,5,7]]

Find the numerically greatest term of (2x-3y)^(12), x=1, y=(5)/(3)

The value of k for which the system of linear equations (2k+2)x+10y=k 2kx+(2k+3)y=k-1 ha sno solution is________________.

I : Value of i^i=e^(-pi/2)II : z=ilog(2+sqrt3) then sinz=2which of above statement is true

Equation of a line passing through the point (2,-3, 2) and equally inclined to the Line L_(1) and L_(2) may be equal to :

If int(x+1)/((x^(2)+x+1))(dx)/(sqrt(x^(2)+x+1))=K(x-1)/(sqrt(x^(2)+x+1))+C then the value of K is

If four whole numbers taken at random are multiplied together. Then the chance that the last digit in the product is 1 or 3 or 7 or 9 is.(A) 16/625(B) 16/125(C) 16/625(D) NONE OF THESE

Solve the following systems of linear inequalities graphically : x - y lt 1 , y - x = 1

Differentiate the following w.r.t. x : e^(-x)

Estimate the integral from above I = int_(0)^(1) (sin x)/( 1 + x^(3)) dx

If the total number of ways in which 8-digit numbers can be formed by using all the digits 0, 1, 2, 3, 4, 5, 7, 9 such that no two even digits appear together is (5!)k, then k is equal to ______

In the following figure, identify collinear but not equal vector

N is 50 digit number in decimal form). All digits except the 26^("th")digit (from left) are 1. If N is divisible by 13, find the 26^("th")digit.

For any vector bar(a), the value of (bar(a)xx i)^(2)+(bar(a)xx j)^(2)+(bar(a)xx bar(k))^(2) is ………..

Find the maximum value of the 2+3sinx+4cosx

If z_(1)=a+ib,z_(2)=-a+ib then z_(1)-z_(2) lies on ………….

Let ' be the binary operation on the set {1,2,3,4,5} defined by a'b= H.C.F. of a and b. Is the operation ' same as the operation defined in Exercise 4 above ? Justify your answer.