14949 + Interview Questions in Maths in Class 11 Page 45 InterviewSolution

2201.	If alpha,beta are the roots of the equation x^(2)-2x-1=0, then what is the value of alpha^(2)beta^(-2)+alpha^(-2)beta^(2) ?
Answer» `-2` 0 30 34 Answer :D

Discussion

2202.	If x = sint , y = cos pt , then
Answer» `(1-x^2)y_2+xy_(1)+p^2y=0` `(1-x^2)y_2+xy_(1)-p^2y=0` `(1-x^2)y_2 -xy_(1)-p^2y=0` `(1-x^2)y_2-xy_(1)+p^2y=0` ANSWER :D

Discussion

2203.	Find the area (in square units) of the quadrilateral formed by the two pairs of lines l^2x^2-m^2y^2-n(lx+my)=0 and l^2x^2-m^2y^2+ n(lx-my) = 0
Answer» ANSWER :`(n^2)/(2\|lm\|)`

Discussion

2204.	Write down the types of waves.
Answer» Solution :(a) Mechanical wave: WAVES which REQUIRE a medium for propagation are known as mechanical waves. Examples : sound waves, ripples formed on the surface of water, etc. (b) Non-mechanical wave: Waves which do not require any medium for propagation are known as non-mechanical waves. Example : light Further, waves can be classified into TWO TYPES a. TRANSVERSE waves b. Longitudinal waves

Discussion

2205.	There are 20 students in a Chemistry class and 30 students in a Physics class . Findthe number of students which are either in Physics class or Chemistry class in the following cases : (i) the classes meet at the same hour (ii) the two claeese meet at rolled in both the subjects.
Answer» ANSWER :`=40`.

Discussion

2206.	4sin27^@ =
Answer» `SQRT(5+sqrt5)+sqrt(3-sqrt5)` `sqrt(5-sqrt5)+sqrt(3+sqrt5)` `sqrt(5+sqrt5)-sqrt(3-sqrt5)` `sqrt(5+sqrt5)+sqrt(3+sqrt5)` ANSWER :C

Discussion

2207.	Convert the following in the polar form(1+3i)/(1-2i)
Answer» ANSWER :(i) `SQRT(2)(COS (3pi)/4 + ISIN(3pi)/4)`, (ii) `sqrt(2)(cos (3pi)/4 + isin(3pi)/4)`

Discussion

2208.	Find distance of the point (3, 4, 5) from Y-axis.
Answer» ANSWER :`sqrt34` UNIT

Discussion

2209.	Find the value of : (i) antilog 0.654(ii) antilog 1.204 (iii) antilog bar(1).3612(iv) antilog bar(3).4568
Answer» Solution :We have (i) ANTILOG (0.654) = 4.508 (ii) antilog (1.204) = 16.00 (III) antilog `(bar(1).3612) = 0.2297` (iv) antilog `(bar(3).4568) = 0.002863`

Discussion

2210.	IFX to B (n,p) andY=n-Xthen: Y to
Answer» <P>`B(p,N)` `B (n,1,-p)` `N(0,1)` NONEOF these ANSWER :B

Discussion

2211.	If 2x+3y=5 is the perpendicular bisector of the line segment joining the points A (1, (1)/(3)) and B, then B is equal to
Answer» `(21/13,49/39)` `(17/13,31/39)` `(7/13,49/39)` `(21/13,31/39)` ANSWER :A

Discussion

2212.	Determine the values of m for which the equations 3x^(2)+4mx+2=0 and 2x^(2)+3x-2=0 may have a common root.
Answer» ANSWER :`m=(-11)/(8) or (7)/(4)`

Discussion

2213.	Let f be the subset of Z xx Z defined by f={(ab,a+b) : a,b in Z}. Is f a function from Z to Z? Justify your answer.
Answer» ANSWER :3 and `-3`

Discussion

2214.	Show that the coefficient of the middle term in the expansion of (1+x)^(2n) is equal to the sum of the coefficients of the two middle terms in the expansion of (1+x)^(2n-1)
Answer» ANSWER :`= "" ^(2N)C_(N)`

Discussion

2215.	The ratio in which the line joining (2, -4 ,3) and (-4,5,-6) is divided by the plane 3x + 2y + z-4 =0 is
Answer» `1:4` `2:3` `-1:4` `4:1` ANSWER :C

Discussion

2216.	The locus of the point (r sec alpha cos beta, r sec alpha beta, r tan alpha) is
Answer» `x^(2)+y^(2)-Z^(2) = R^(2)` `x^(2)+y^(2)+z^(2) = r^(2)` `x^(2)+y^(2)-z^(2) = r^(2)` `x^(2)-y^(2)+z^(2) = r^(2)` Answer :C

Discussion

2217.	Show that the function f(x)={{:(1,if x is "rational"),(-1, if x is "rational"):}(Dirichlet’s function ) is discontinuous everywhere.
Answer» ANSWER :APPROACH ` - 1 NE F(a)`

Discussion

2218.	Express each of the following complex number in the form a+ib: i^(29)+((1)/(i))^(50)
Answer» ANSWER :`-1+i`

Discussion

2219.	Solve sinx-5sin3x +sin5x =cosx -5cos3x +cos5x
Answer» ANSWER :`x=pi/12 +(NPI)/3`

Discussion

2220.	Eliminating theta from the following(iii) m = cosec theta - s in theta, n cosec theta + sin theta
Answer» ANSWER :4

Discussion

2221.	Each of the digits 1, 1, 2, 3, 3 and 4 is written to consonants. on a separate card. The six cards are then laidout in a row to form a 6-digit number.Q How many of these 6-digit numbers are divisible by 4?
Answer» ANSWER :12

Discussion

2222.	Each of the digits 1, 1, 2, 3, 3 and 4 is written to consonants. on a separate card. The six cards are then laidout in a row to form a 6-digit number.Q How many distinct 6-digit numbers are there?
Answer» ANSWER :180

Discussion

2223.	Each of the digits 1, 1, 2, 3, 3 and 4 is written to consonants. on a separate card. The six cards are then laidout in a row to form a 6-digit number.Q How many of these 6-digit numbers are even?
Answer» ANSWER :60

Discussion

2224.	Find the radius and centre of the circle z bar(z) + (1-i) z + (1+ i) bar(z)- 7 = 0
Answer» ANSWER :CENTRE is `(-1, -1)`; RADIUS =3

Discussion

2225.	Find the coordinates of the focus , axis, the equation of the directrix and latus rectum of the parabola y^(2)=8x.
Answer» ANSWER :`4a=4xx2=8`

Discussion

2226.	Which of the following sentences are statements? Justify Every square is a rectangle.
Answer» ANSWER :It is STATEMENT.

Discussion

2227.	If [(x-1,2,5-y),(0,z-1,7),(1,0,a-5)]=[(1,2,3),(0,4,7),(1,0,0)] find x,y,z,a
Answer» ANSWER :`x=2,y=2,z=5,a=5`

Discussion

2228.	The values of a,b such that x^3+3ax^2+3a^2x+b is increasing on R-{-a} are
Answer» ANSWER :`therefore f(X)` is INCREASING on R for all VALUES of a and B.

Discussion

2229.	Using the results abs(z^2) = absz^2 and abs(z_1/z_2) = (abs(z_1))/abs(z_2), find the modulus of (3-i)^2/(2+i)
Answer» ANSWER :`2SQRT5`

Discussion

2230.	ABCD is a quadrilateral with vec(AB)= vec(a), vec(AD)= vec(b) and vec(AC)= 2 vec(a) + 3vec(b). If its area is alpha times the area of the parallelogram with AB, AD as adjacent sides, then alpha=
Answer» `(5)/(2)` `(3)/(2)` `(9)/(2)` `(7)/(2)` Answer :A

Discussion

2231.	If (b-c)cos A/2 = a ( sin k )then k =
Answer» `(B + C)/( 2) ` ` B+ C ` ` (B - C) /( 2) ` ` B- C ` ANSWER :C

Discussion

2232.	x tan (theta - (pi)/(6)) = y tan (theta + (2pi)/(3)) implies (x + y)/(x -y) =
Answer» `COS 2 theta ` `2 cos 2 theta ` `sin 2 theta ` `2 sin 2 theta ` ANSWER :B

Discussion

2233.	If f(x)=x^(3)+4x^(2)+lambdax+1is a monotonically decreasingfunction of x in the largest possible interval (-2,-2//3) . Then
Answer» `LAMBDA=4` `lambda=2` `lambda=-1` `lambda` has no REALVALUE ANSWER :A

Discussion

2234.	Find the slope of a line whose inclination is 45^(@)
Answer» ANSWER :1

Discussion

2235.	If Ax+By=C and x"cos"alpha+y"sin"alpha=p represent the same line, find p in terms of A, B, C.
Answer» <P> Answer :`p=(\|C\|)/SQRT((A^(2)+B^(2))`

Discussion

2236.	If the increase in the side of square is 2% then find approximate percentage of increase in its area
Answer» ANSWER :4

Discussion

2237.	If sinh(x)=(3)/(4) then sinh(3x) =
Answer» `(61)/(16)` `(63)/(16)` `(61)/(63)` `(65)/(16)` ANSWER :B

Discussion

2238.	If P(-1,5) is hormonic conjugate of Q(-13,9) with respect to A and B. If A=(5,3) then find the length AB
Answer» ANSWER :`3sqrt10`

Discussion

2239.	Prove that the area of triangle remains invariant on transforming the axes.
Answer» SOLUTION :Let `A(x_(1),y_(1))`, `B(x_(2),y_(2))` and `C(x_(3),y_(3))` are the VERTICES of `DeltaABC`. `:. "Area of" DeltaABC` `DELTA=(1)/(2)[x_(1)(y_(2)-y_(3))+x_(2)(y_(3)-y_(1))+x_(3)(y_(1)-y_(2))]` ……..`(1)` Let origin is shifted to the point `(h,k)`. Now, the new co-ordinates of the vertices `A(x_(1)-h,y_(1)-k)`, `B(x_(2)-h,y_(2)-k)`, `C(x_(3)-h,y_(3)-k)`

Discussion

2240.	Let f : R to R be a differentiable function such that f(2) = -40 ,f^1(2) =- 5 then lim_(x to 0)((f(2 - x^2))/(f(2)))^(4/(x^2)) is equal to
Answer» `E^(32)` `sqrt(e)` `1/(sqrt(e))` `e` Answer :C

Discussion

2241.	If sin theta=(21)/(29), prove that sectheta+tan theta=2(1)/(2) if theta lies between 0 and (pi)/(2). What will be the value of the expression when theta lies (i) between (pi)/(2) and pi and (ii) between pi and (3pi)/(2) ?
Answer» ANSWER :(i) `(-5)/(2)`

Discussion

2242.	The solution set of the equation sin3theta=4sintheta(sin^(2)x-sin^(2)theta),thetanenpi,ninz is
Answer» `{npipm(pi)/(2)}` `{npipm(pi)/(3)}` `{npipm(pi)/(4)}` `{npipm(pi)/(6)}` ANSWER :B

Discussion

2243.	Consider the statements: p : You will work hardq : You will become wealthy. Translate each of the symbolic statements into an English sentence. qimplies p
Answer» ANSWER :If you will BECOME WEALTHY, then you will workhard.

Discussion

2244.	Consider the statements: p : You will work hardq : You will become wealthy. Translate each of the symbolic statements into an English sentence. p implies q
Answer» ANSWER :If you WORK HARD, then you will BECOME WEALTHY.

Discussion

2245.	Consider the statements: p : You will work hardq : You will become wealthy. Translate each of the symbolic statements into an English sentence. (~q)implies(~p)
Answer» ANSWER :If you will not BECOME WEALTHY, then you will not WORK HARD.

Discussion

2246.	Consider the statements: p : You will work hardq : You will become wealthy. Translate each of the symbolic statements into an English sentence. (~p)implies(~q)
Answer» ANSWER :If you will not WORK HARD , then you will not BECOME WEALTHY.

Discussion

2247.	Letf : N to Rbe a function satisfying the following conditions: f(1) =1 and f(1) +2f( 2)+ 3 f(3) + ………n f(n )""f(n ) = n (n+1) , f(n) "for " n ge 2 f(1), f(2) , f(3) , f(4) ,…………. represent a series of
Answer» an AP a GP an HP an arithmetico-geometric progression Answer :C

Discussion

2248.	Letf : N to Rbe a function satisfying the following conditions: f(1) =1 and f(1) +2f( 2)+ 3 f(3) + ………n f(n )""f(n ) = n (n+1) , f(n) "for " n ge 2 The value of f(999)is(1)/(K)where K equals
Answer» 999 1000 1998 2000 Answer :C

Discussion

2249.	Letf : N to Rbe a function satisfying the following conditions: f(1) =1 and f(1) +2f( 2)+ 3 f(3) + ………n f(n )""f(n ) = n (n+1) , f(n) "for " n ge 2 The value of f(1003)is (1)/(K) . Where K equals
Answer» 1003 2003 2005 2006 Answer :D

Discussion

2250.	Assertion (A) : If the area of triangle formed by (0,0), (-1,2),(1,2) is 2 square units. Then the area triangle on shfting the origin to a point (2,3) is 2 units Reason (R) : By the change of axes area does not change Choose the correct answer
Answer» Both A and R are TRUE and R is the correct EXPLANATION of A BOTHA and R are trueand R is not the correct explanation of A A is true but R is FALSE A is false but R is true Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

If alpha,beta are the roots of the equation x^(2)-2x-1=0, then what is the value of alpha^(2)beta^(-2)+alpha^(-2)beta^(2) ?

If x = sint , y = cos pt , then

Find the area (in square units) of the quadrilateral formed by the two pairs of lines l^2x^2-m^2y^2-n(lx+my)=0 and l^2x^2-m^2y^2+ n(lx-my) = 0

Write down the types of waves.

There are 20 students in a Chemistry class and 30 students in a Physics class . Findthe number of students which are either in Physics class or Chemistry class in the following cases : (i) the classes meet at the same hour (ii) the two claeese meet at rolled in both the subjects.

4sin27^@ =

Convert the following in the polar form(1+3i)/(1-2i)

Find distance of the point (3, 4, 5) from Y-axis.

Find the value of : (i) antilog 0.654(ii) antilog 1.204 (iii) antilog bar(1).3612(iv) antilog bar(3).4568

IFX to B (n,p) andY=n-Xthen: Y to

If 2x+3y=5 is the perpendicular bisector of the line segment joining the points A (1, (1)/(3)) and B, then B is equal to

Determine the values of m for which the equations 3x^(2)+4mx+2=0 and 2x^(2)+3x-2=0 may have a common root.

Let f be the subset of Z xx Z defined by f={(ab,a+b) : a,b in Z}. Is f a function from Z to Z? Justify your answer.

Show that the coefficient of the middle term in the expansion of (1+x)^(2n) is equal to the sum of the coefficients of the two middle terms in the expansion of (1+x)^(2n-1)

The ratio in which the line joining (2, -4 ,3) and (-4,5,-6) is divided by the plane 3x + 2y + z-4 =0 is

The locus of the point (r sec alpha cos beta, r sec alpha beta, r tan alpha) is

Show that the function f(x)={{:(1,if x is "rational"),(-1, if x is "rational"):}(Dirichlet’s function ) is discontinuous everywhere.

Express each of the following complex number in the form a+ib: i^(29)+((1)/(i))^(50)

Solve sinx-5sin3x +sin5x =cosx -5cos3x +cos5x

Eliminating theta from the following(iii) m = cosec theta - s in theta, n cosec theta + sin theta

Each of the digits 1, 1, 2, 3, 3 and 4 is written to consonants. on a separate card. The six cards are then laidout in a row to form a 6-digit number.Q How many of these 6-digit numbers are divisible by 4?

Each of the digits 1, 1, 2, 3, 3 and 4 is written to consonants. on a separate card. The six cards are then laidout in a row to form a 6-digit number.Q How many distinct 6-digit numbers are there?

Each of the digits 1, 1, 2, 3, 3 and 4 is written to consonants. on a separate card. The six cards are then laidout in a row to form a 6-digit number.Q How many of these 6-digit numbers are even?

Find the radius and centre of the circle z bar(z) + (1-i) z + (1+ i) bar(z)- 7 = 0

Find the coordinates of the focus , axis, the equation of the directrix and latus rectum of the parabola y^(2)=8x.

Which of the following sentences are statements? Justify Every square is a rectangle.

If [(x-1,2,5-y),(0,z-1,7),(1,0,a-5)]=[(1,2,3),(0,4,7),(1,0,0)] find x,y,z,a

The values of a,b such that x^3+3ax^2+3a^2x+b is increasing on R-{-a} are

Using the results abs(z^2) = absz^2 and abs(z_1/z_2) = (abs(z_1))/abs(z_2), find the modulus of (3-i)^2/(2+i)

ABCD is a quadrilateral with vec(AB)= vec(a), vec(AD)= vec(b) and vec(AC)= 2 vec(a) + 3vec(b). If its area is alpha times the area of the parallelogram with AB, AD as adjacent sides, then alpha=

If (b-c)cos A/2 = a ( sin k )then k =

x tan (theta - (pi)/(6)) = y tan (theta + (2pi)/(3)) implies (x + y)/(x -y) =

If f(x)=x^(3)+4x^(2)+lambdax+1is a monotonically decreasingfunction of x in the largest possible interval (-2,-2//3) . Then

Find the slope of a line whose inclination is 45^(@)

If Ax+By=C and x"cos"alpha+y"sin"alpha=p represent the same line, find p in terms of A, B, C.

If the increase in the side of square is 2% then find approximate percentage of increase in its area

If sinh(x)=(3)/(4) then sinh(3x) =

If P(-1,5) is hormonic conjugate of Q(-13,9) with respect to A and B. If A=(5,3) then find the length AB

Prove that the area of triangle remains invariant on transforming the axes.

Let f : R to R be a differentiable function such that f(2) = -40 ,f^1(2) =- 5 then lim_(x to 0)((f(2 - x^2))/(f(2)))^(4/(x^2)) is equal to

If sin theta=(21)/(29), prove that sectheta+tan theta=2(1)/(2) if theta lies between 0 and (pi)/(2). What will be the value of the expression when theta lies (i) between (pi)/(2) and pi and (ii) between pi and (3pi)/(2) ?

The solution set of the equation sin3theta=4sintheta(sin^(2)x-sin^(2)theta),thetanenpi,ninz is

Consider the statements: p : You will work hardq : You will become wealthy. Translate each of the symbolic statements into an English sentence. qimplies p

Consider the statements: p : You will work hardq : You will become wealthy. Translate each of the symbolic statements into an English sentence. p implies q

Consider the statements: p : You will work hardq : You will become wealthy. Translate each of the symbolic statements into an English sentence. (~q)implies(~p)

Consider the statements: p : You will work hardq : You will become wealthy. Translate each of the symbolic statements into an English sentence. (~p)implies(~q)

Letf : N to Rbe a function satisfying the following conditions: f(1) =1 and f(1) +2f( 2)+ 3 f(3) + ………n f(n )""f(n ) = n (n+1) , f(n) "for " n ge 2 f(1), f(2) , f(3) , f(4) ,…………. represent a series of

Letf : N to Rbe a function satisfying the following conditions: f(1) =1 and f(1) +2f( 2)+ 3 f(3) + ………n f(n )""f(n ) = n (n+1) , f(n) "for " n ge 2 The value of f(999)is(1)/(K)where K equals

Letf : N to Rbe a function satisfying the following conditions: f(1) =1 and f(1) +2f( 2)+ 3 f(3) + ………n f(n )""f(n ) = n (n+1) , f(n) "for " n ge 2 The value of f(1003)is (1)/(K) . Where K equals

Assertion (A) : If the area of triangle formed by (0,0), (-1,2),(1,2) is 2 square units. Then the area triangle on shfting the origin to a point (2,3) is 2 units Reason (R) : By the change of axes area does not change Choose the correct answer