14949 + Interview Questions in Maths in Class 11

1.	Find the distance between each of pair of point: (0,3,0) and (6,0,2)
Answer» ANSWER :`3sqrt11`

Discussion

2.	A real valued function f(x) satisfies the functional equation f(x-y) = f(x)f(y)-f(a - x)f(a + y) where a is a given constant and f(0)=1, f(2a-x) is equal to:
Answer» `F(a)+f(a-X)` `f(-x)` `-f(x)` `f(x)` ANSWER :C

Discussion

3.	Find n in the Binomial (root3(2)+1/(root3(3)))^(n) , if the ratio of 7th term from the beginning to the 7th term from the end is 1/6.
Answer» ANSWER :` :. N =9`

Discussion

4.	State whether each of the following set is finite or infinite: The set of lines which are parallel to the x-axis
Answer» ANSWER :it is an INFINITE SET

Discussion

5.	Find the distance from the origin to each of the point: (4, -1, 2)
Answer» ANSWER :`sqrt21`

Discussion

6.	Let the statement m^(2) gt 100, the statement P(k+1) will be true if
Answer» `P(1)` is TRUE `P(2)` is true `P(k)` is true none of these Answer :C

Discussion

7.	Alamp post is situated at the middle point M of the side AC of triangular plot ABC with BC = 7m , CA = 8m and AB = 9m. Lamp post subtends an angle15 ^(@)at the point. Find the height of the lamp post
Answer» ANSWER :` therefore MN = 7 tan 15 ^(@)= 7 (2-sqrt3) mts `

Discussion

8.	For the proposition P(n), given by, 1+3+5+ldots+(2n-1)=n^(2)+2prove that P(k) is true implies P(k + 1) is true. But, P(n) is not true for all n in N
Answer» ANSWER :`NIN N`

Discussion

9.	A point Q is at a distance 3 from the point P (1,1,1) lying on the line joining the points A(0,-1,3) and P, has the coordinates
Answer» (2,3,-1) (4,7,-5) (0,0,3) (-2,-5,7) ANSWER :A

Discussion

10.	Let f(x) = {{:("sin"("cos"^(-1) x) + "cos"("sin"^(-1)x),x le 0),("sin"("cos"^(-1)x) -"cos"("sin"^(-1)x),x gt 0):} and g(x) = f(\|x\|) + \|f(x)\| g'(1/2) =
Answer» `0` `2` `3` `1` ANSWER :A

Discussion

11.	What are the cartesian co-ordinates of the points1+i, 2+i, 2+3i, 1+3i?
Answer» ANSWER :(1,1), (2,1), (2,3), (1,3)

Discussion

12.	Draw a quadrilateral in the Cartesian plane, whose vertices are (- 4, 5), (0, 7), (5, - 5) and (- 4, -2). Also, find its area.
Answer» ANSWER :`= ( 121)/(2)` SQ. UNIT

Discussion

13.	Pis any point inside a Delta^("le")ABC. lines are drawn through P parallel to the sides and the area of new triangle formed are Delta_(1),Delta_(2),Delta_(3), then sqrt(Delta_(1))+sqrt(Delta_(2))+ sqrt(Delta_(3))=
Answer» `SQRT(DELTA)` `(sqrt(Delta))/(2)` `Delta` `Delta^(2)` ANSWER :A

Discussion

14.	Evaluate the following limits : Lim_(x to pi/4) (1- tan x)/(x - pi/4 )
Answer» ANSWER :`-2`

Discussion

15.	Variance of first n natural number is…………
Answer» `(n^2 -1)/(12)` `(n^2 -1)/(6)` `(n^2 + 1)/(6)` `(n^2 + 1)/(12)` ANSWER :A

Discussion

16.	The value of tan""(pi)/16+2tan""(pi)/8+4 is equal to
Answer» `COT""(PI)/2` `cot""(pi)/16` `cot""(pi)/16-4` 0 Answer :B

Discussion

17.	Which of the following sentences are statements? Give reasons for your answer The sum of 5 and 7 is greater than 10.
Answer» Answer :This SENTENCE is ALWAYS true because the sum is 12 and it is GREATER than 10. Therefore, it is a statement.

Discussion

18.	(x^(2)cos(pi)/(4))/(sinx)
Answer» Answer :`(xcos (pi)/(4)[2sinx-xcosx])/(sin^(2)x)(because (1)/(sqrt(2))=COS (pi)/(4))`

Discussion

19.	If Tan22^(@) + Tan38^(@) - sqrt(3) = k Tan22^(@) Tan38^(@) then k =
Answer» -1 `-SQRT(3)` 0 1 Answer :B

Discussion

20.	List all the elements of the following sets : A= {x : x^(2) lt 10, x in Z}
Answer» ANSWER :`A= {-3, -2, -1, 0, 1, 2, 3}`

Discussion

21.	P=(0,1,0),Q=(0,0,1) then projection of bar(PQ) on the plane x+y+z=3 is
Answer» 2 `SQRT2` `3` `SQRT3` ANSWER :B

Discussion

22.	Given Delta^("le")ABC with AB=20,AC=22(1)/(2),BC=27, Points x and y are taken on AB and AC respectively so thatAX = AY. If Area of Delta^("le") AXY=(1)/(2) area of Delta^("le")ABC find AX.
Answer» 15 16 17 14 Answer :A

Discussion

23.	A(3, 1, 5), B(-1, -1, 9) and C(0, -5, 1) are the vertices of a triangle. Then find the position vector of the centroid of DeltaABC.
Answer» ANSWER :(25,8,5) , (-11,20,23)

Discussion

24.	Find the derivative of e ^(- ax ^(2)) .sin (x log x )w.r.t.x
Answer» ANSWER :`e ^(-ax ^(2)) [-2ax SIN(X LOGX)+cos(x logx)(logx + 1)]`

Discussion

25.	Assertion (A) : sin^(-1)(sin3)=3 Reason (R) : For principal values sin^(-1)(Sinx)=x
Answer» Both A and R are TRUE and R is correct EXPLANATION of A Both A and R are true but R is not the correct explanation of A A is false, R is true A is true, R is false Answer :D

Discussion

26.	Express (8 cos^2 x + 11 sin x)/(cos x) as the sum of function and hence differentiate it w.r.t.x
Answer» SOLUTION :-8 SIN X +`11 sec^2 x`

Discussion

27.	Evaluate Lt_(xto0)(3sinx^(0)-sin3x^(0))/x^(3)
Answer» ANSWER :`4(pi/180)^(3)`

Discussion

28.	The sum and sum of square corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below: sum_(i=1)^(50)x_(i)=212, sum_(i=1)^(50)x_(i)^(2)=902.8, sum_(i=1)^(50)y_(i)=261 sum_(i=1)^(50)y_(i)^(2)=1457.6 Which is more varying , the length or weight?
Answer» SOLUTION :For length, `sumx_(i)=212, sumx_(i)^(2)=902.8,N=50` `:.` MEAN `barx=(sumx_(i))/N=212/50=4.24cm` Variance `=(sumx_(i)^(2))/N-((sumx_(i))/N)^(2)=902.8/50-(212/50)^(2)` `=(45140-44944)/(50^(2))=196/2500` `implies` Standard deviation `SIGMA=14/50=0.28cm` Coefficient of variation of length `=(sigma)/x XX 100` `=0.28/4.24xx 100=6.6` For weight, `sumy_(i)=261,sumy_(i)^(2)=1457.6, N=50` `:.` Mean `=(sumy_(i))/N=261/N=5.22` Variance `sigma^(2)=(sumy_(i)^(2))/N-((sumy_(i))/N)^(2)=1457.6/50-(261/60)^(2)` `=(72880-68121)/((50)^(2))=4759/25500` `implies` Standard deviation `sigma=sqrt(4759/2500)=68.98/50=1.38` Now coefficient of variation of weight `=(sigma)/x xx100=1.38/5.22xx 100=26.43` Therefore, the weight of products are more varying.

Discussion

29.	Fill in the blanks to make each of the following a true statement : φ′ ∩ A = . . .
Answer» ANSWER :A

Discussion

30.	For the function f(x) = \|x^2 - 5x +6\| , the right hand derivation f'(2+) is equal to
Answer» ANSWER :A

Discussion

31.	Find the derivative of the w.r.t.x (4 + x ^(2)) e ^(2x)
Answer» ANSWER :`E ^(2X)`

Discussion

32.	Find the derivative of 3x-1
Answer» ANSWER :`-(X(3x-2))/((3x-1)^(2))`

Discussion

33.	If P(-2,4,-5) and Q(1,2,3) are two points. Find the direction cosines of bar(PQ)
Answer» ANSWER :`((3)/(77),(-2)/(77),(8)/(77))`

Discussion

34.	Let theta, phi in [0,2pi] be such that 2cos theta(1-sin phi)=sin^(2)theta("tan"(theta)/2+"cot"(theta)/2)cos phi-1, tan (2pi-theta)gt0 and -1lt sin theta lt -(sqrt(3))/2. Then phi can not saitsfy
Answer» `0 lt philt(PI)/2` `(pi)/2 lt PHI lt (4pi)/3` `(4pi)/3lt phi lt (3pi)/2` `(3pi)/2lt phi lt 2pi` Answer :A::C::D

Discussion

35.	If sin h^(-1) 2 alpha= 2 coh h^(-1) beta then
Answer» `ALPHA^(2)+beta^(2)=alpha^(4)` `alpha^(2)+beta^(2)=4` `alpha^(2)+beta^(2)=beta^(4)` `alpha^(2)=beta^(2)` Answer :C

Discussion

36.	sin((7pi)/(12))cos(pi/4)-cos((7pi)/(12))sin(pi/4)=...........
Answer» ANSWER :`sqrt3/2`

Discussion

37.	If 0lexlt2pi then the number of real values of x, which satisy the equation
Answer» 5 7 9 3 Answer :B

Discussion

38.	Let A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}. Find
Answer» ANSWER :TRUE STATEMENT

Discussion

39.	A point P(x, y) moves so that the sum of its distances from the points S(4, 2) and S^(') (-2, 2) is 8. Find the equation of its locus and show that it is an ellipse.
Answer» ANSWER :`(x-1)^(2)/16+(y-2)^(2)/7=1`

Discussion

40.	Observe the following, choose correct answer : Assertion(A): The lines barr =(2bari + barj)+s(bari + barj -bark) and barr =(bari +bark)+t(7bari - barj +bark) are coplanar. Reason (R) : Condition for the lines barr = bara + sbarb and barr = barc + tbard to be coplanar is [bara-barc barb -bard]=0
Answer» A is TRUE, R is false A is false, R is true Both A, R are false A, RARE true and R `RARR` A Answer :D

Discussion

41.	Rolle's theorem can not applicable for
Answer» `f(X) = SIN x ` `f(x) = {:{((sinx )/(x),","x cancel(=)0),(1,","x=0):}` f(x) = COS 2x `sin^(2)x + sin x ` ANSWER :B

Discussion

42.	(5,2) and (3,4) are end points of latus rectums then its focii is .......... .
Answer» ANSWER :(4,3)

Discussion

43.	The vectors of bar(AB)=3bar(i)+4bar(k) and bar(AC)=5bar(i)-2bar(j)+4bar(k) are the sides of a triangle ABC. The length of the median through A is
Answer» `SQRT(72)` `sqrt(33)` `sqrt(288)` `sqrt(18)` ANSWER :B

Discussion

44.	Find the valuesof the trigonometric functions cosec(-1410^(@))
Answer» ANSWER :2

Discussion

45.	Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1) Calculate the modulus and argument of w and z
Answer» ANSWER :MODULUS of W is 1 and argumetn of w is `-120^(@)`. Modulus of z is 1, and argument of z is `120^(@)`

Discussion

46.	Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1) Calculate the modulus and argument of (w)/(z)
Answer» Answer :MODULUS of `(W)/(2)` is 1 and argument of `(w)/(z)` is `120^(@)`

Discussion

47.	lim_(xtoa)(f(x)-f(a))/(x^(3)-a^(3))=……………
Answer» `F'(a)(1)/(3A^(2))` `3a^(2)-(2)/(f(a))` `f'(a)3a^(2)` NONE of these Answer :A

Discussion

48.	The tangents from P to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are mutually perpendicular show that the locus of P is the circle x^(2)+y^(2)=a^(2)-b^(2)
Answer» ANSWER :`X^(2)+y^(2)+a^(2)-B^(2)`

Discussion

49.	Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting all cards of the same colour ,
Answer» ANSWER :`(2.(""^(26)C_(4)))/(""^(52)C_(4))`

Discussion

50.	If \| x - 1\| gt 5 then x in ............
Answer» ANSWER :`(-4,OO) CUP(6,oo)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the distance between each of pair of point: (0,3,0) and (6,0,2)

A real valued function f(x) satisfies the functional equation f(x-y) = f(x)f(y)-f(a - x)f(a + y) where a is a given constant and f(0)=1, f(2a-x) is equal to:

Find n in the Binomial (root3(2)+1/(root3(3)))^(n) , if the ratio of 7th term from the beginning to the 7th term from the end is 1/6.

State whether each of the following set is finite or infinite: The set of lines which are parallel to the x-axis

Find the distance from the origin to each of the point: (4, -1, 2)

Let the statement m^(2) gt 100, the statement P(k+1) will be true if

Alamp post is situated at the middle point M of the side AC of triangular plot ABC with BC = 7m , CA = 8m and AB = 9m. Lamp post subtends an angle15 ^(@)at the point. Find the height of the lamp post

For the proposition P(n), given by, 1+3+5+ldots+(2n-1)=n^(2)+2prove that P(k) is true implies P(k + 1) is true. But, P(n) is not true for all n in N

A point Q is at a distance 3 from the point P (1,1,1) lying on the line joining the points A(0,-1,3) and P, has the coordinates

Let f(x) = {{:("sin"("cos"^(-1) x) + "cos"("sin"^(-1)x),x le 0),("sin"("cos"^(-1)x) -"cos"("sin"^(-1)x),x gt 0):} and g(x) = f(|x|) + |f(x)| g'(1/2) =

What are the cartesian co-ordinates of the points1+i, 2+i, 2+3i, 1+3i?

Draw a quadrilateral in the Cartesian plane, whose vertices are (- 4, 5), (0, 7), (5, - 5) and (- 4, -2). Also, find its area.

Pis any point inside a Delta^("le")ABC. lines are drawn through P parallel to the sides and the area of new triangle formed are Delta_(1),Delta_(2),Delta_(3), then sqrt(Delta_(1))+sqrt(Delta_(2))+ sqrt(Delta_(3))=

Evaluate the following limits : Lim_(x to pi/4) (1- tan x)/(x - pi/4 )

Variance of first n natural number is…………

The value of tan""(pi)/16+2tan""(pi)/8+4 is equal to

Which of the following sentences are statements? Give reasons for your answer The sum of 5 and 7 is greater than 10.

(x^(2)cos(pi)/(4))/(sinx)

If Tan22^(@) + Tan38^(@) - sqrt(3) = k Tan22^(@) Tan38^(@) then k =

List all the elements of the following sets : A= {x : x^(2) lt 10, x in Z}

P=(0,1,0),Q=(0,0,1) then projection of bar(PQ) on the plane x+y+z=3 is

Given Delta^("le")ABC with AB=20,AC=22(1)/(2),BC=27, Points x and y are taken on AB and AC respectively so thatAX = AY. If Area of Delta^("le") AXY=(1)/(2) area of Delta^("le")ABC find AX.

A(3, 1, 5), B(-1, -1, 9) and C(0, -5, 1) are the vertices of a triangle. Then find the position vector of the centroid of DeltaABC.

Find the derivative of e ^(- ax ^(2)) .sin (x log x )w.r.t.x

Assertion (A) : sin^(-1)(sin3)=3 Reason (R) : For principal values sin^(-1)(Sinx)=x

Express (8 cos^2 x + 11 sin x)/(cos x) as the sum of function and hence differentiate it w.r.t.x

Evaluate Lt_(xto0)(3sinx^(0)-sin3x^(0))/x^(3)

The sum and sum of square corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below: sum_(i=1)^(50)x_(i)=212, sum_(i=1)^(50)x_(i)^(2)=902.8, sum_(i=1)^(50)y_(i)=261 sum_(i=1)^(50)y_(i)^(2)=1457.6 Which is more varying , the length or weight?

Fill in the blanks to make each of the following a true statement : φ′ ∩ A = . . .

For the function f(x) = |x^2 - 5x +6| , the right hand derivation f'(2+) is equal to

Find the derivative of the w.r.t.x (4 + x ^(2)) e ^(2x)

Find the derivative of 3x-1

If P(-2,4,-5) and Q(1,2,3) are two points. Find the direction cosines of bar(PQ)

Let theta, phi in [0,2pi] be such that 2cos theta(1-sin phi)=sin^(2)theta("tan"(theta)/2+"cot"(theta)/2)cos phi-1, tan (2pi-theta)gt0 and -1lt sin theta lt -(sqrt(3))/2. Then phi can not saitsfy

If sin h^(-1) 2 alpha= 2 coh h^(-1) beta then

sin((7pi)/(12))cos(pi/4)-cos((7pi)/(12))sin(pi/4)=...........

If 0lexlt2pi then the number of real values of x, which satisy the equation

Let A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}. Find

A point P(x, y) moves so that the sum of its distances from the points S(4, 2) and S^(') (-2, 2) is 8. Find the equation of its locus and show that it is an ellipse.

Observe the following, choose correct answer : Assertion(A): The lines barr =(2bari + barj)+s(bari + barj -bark) and barr =(bari +bark)+t(7bari - barj +bark) are coplanar. Reason (R) : Condition for the lines barr = bara + sbarb and barr = barc + tbard to be coplanar is [bara-barc barb -bard]=0

Rolle's theorem can not applicable for

(5,2) and (3,4) are end points of latus rectums then its focii is .......... .

The vectors of bar(AB)=3bar(i)+4bar(k) and bar(AC)=5bar(i)-2bar(j)+4bar(k) are the sides of a triangle ABC. The length of the median through A is

Find the valuesof the trigonometric functions cosec(-1410^(@))

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1) Calculate the modulus and argument of w and z

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1) Calculate the modulus and argument of (w)/(z)

lim_(xtoa)(f(x)-f(a))/(x^(3)-a^(3))=……………

The tangents from P to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are mutually perpendicular show that the locus of P is the circle x^(2)+y^(2)=a^(2)-b^(2)

Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting all cards of the same colour ,

If | x - 1| gt 5 then x in ............