14949 + Interview Questions in Maths in Class 11

1.	Express the following in the form a+bi (sqrt3 + 5i) (sqrt3 -5i)^(2) + (-4+ 5i)^(2)
Answer» ANSWER :`(28sqrt3-9)-180i`

Discussion

2.	Ifsin 2 theta + cos theta = 0"then " theta =
Answer» `2 N pi - (pi)/(6), n in Z` `2 n pi + (pi)/(3), n in Z` `(2 n pi)/(3)- (pi)/(6) , n in Z` `(2 n pi)/(3)+ (pi)/(4) , n in Z` ANSWER :C

Discussion

3.	The value of tan^(-1)((x cos theta)/(1-x sin theta))-cot^(-1)((cos theta)/(x-sin theta)) is
Answer» `2 THETA` `theta` `theta//2` INDEPENDENT of `theta` ANSWER :B

Discussion

4.	d/(dx)(a^(log_asqrtx))=1/(2sqrtx) where a gt 1 inR^+
Answer» ANSWER :TRUE STATEMENT

Discussion

5.	The orthocentre of triangle formed by lines xy+3x+3y+9 = 0 and the line 3x+4y-5=0 is
Answer» (3,3) (-3,3) (3,-3) (-3,-3) ANSWER :D

Discussion

6.	If Lt_(xto0)(1+ax+bx^(2))^(2//x)=e^(3), find a and b.
Answer» ANSWER :`a=3/2,binR`

Discussion

7.	Evaluate lim_(xrarrinfty)[(x^2 -3x -4 )/(x^2 +3x+2)]^x
Answer» ANSWER :`1/(e^6)`

Discussion

8.	cos^(-1)("cos"(7pi)/6) is equal to
Answer» `(7pi)/6` `(5PI)/3` `(5pi)/6` `(13pi)/6` ANSWER :C

Discussion

9.	Find the number of terms in the expansion of the following : (x+2a)^(10)+(x-2a)^(10)
Answer» ANSWER :6

Discussion

10.	Differentiate x^(a) with respect to a^(x).
Answer» ANSWER :`X^(a-1)/(LOG a^(x-1))`

Discussion

11.	Match the following
Answer» a,C,d,b b,a,d,c a,b,c,d d,c,b,a Answer :D

Discussion

12.	Using binomial theorem, evaluate (101)^4
Answer» ANSWER :` 104060401`

Discussion

13.	If (d)/(dx)((1+x^(4)+x^8)/(1+x^(2)+x^(4)))=ax^(3)+bx then …………….
Answer» a=4,B=2 a=4,b=-2 a=-2,b=4 None of these Answer :B

Discussion

14.	A coin is tossed four times write the elements of sample space.
Answer» Answer :`={HHHH,HHTH,HTHH,THHH,T T TH,T THH,THTH,HT TH,HHHT,HHT T,HTHT,THHT,T T T T,T THT,THT T,HT T T}`

Discussion

15.	If y= Tan^(-1)""(sqrt(1+x^2) -1)/x then (dy)/(dx)=
Answer» `1/(1+x^2)` `(-1)/(1+x^2)` `1/(2(1+x^2))` `2/((1+x^2))` ANSWER :C

Discussion

16.	If x^(p) occurs in the expansion of (x^(2)+1/x)^(2n) then prove that its coefficient is (2n!)/((((4n-p)!)/(3!))(((2n+p)!)/(3!)))
Answer» ANSWER :`=((2N)!)/(((2n+p)!)/(3!)XX((4n-p)!)/(3!))`

Discussion

17.	If f_(n)(x)=(sinx)/(cos3x)+(sin3^2x)/(cos3^2x)+(sin3^2x)/(cos3^(3)x)+....+(sin3^(n-1)x)/(cos3^(n)x) Then f_(2)(pi//4)+f_3(pi//4)=
Answer» 0 1 `-1` 2 Answer :C

Discussion

18.	If bar(AB)=2bara+barb and bar(AD) = bara-2barb " where " absbara=1, absbarb =1, (bara,barb) = 60^(@) are the adjacent sides of a parallelogram, then the length of the diagonal "bar(BD) is
Answer» `SQRT13` `SQRT7` `sqrt12` `SQRT10` ANSWER :A

Discussion

19.	If the lengths of the sides of triangle are 3, 5, and 7, then the largest angle of the triangle is
Answer» `pi/2` `(5pi)/6` `(2PI)/3` `(3PI)/4` ANSWER :C

Discussion

20.	Find the equation of parabolawith itsaxis parallelto x - axisand passing through the points (-2,1) ,(1,2) and (-1,3) .
Answer» ANSWER :`y^(2)-y + 2X + 4 = 0 `

Discussion

21.	Evaluate the following limits in lim_(xrarr1)(ax^(2)+bx+c)/(cx^(2)+bx+a), a+b+c ne0
Answer» ANSWER :1

Discussion

22.	Differentiateby 1^(st) principalf(x) = tan (1-2x)
Answer» ANSWER :`-2 SEC^(2) (1-2x)`

Discussion

23.	d/(dx)(sinh^(-1)(sqrtx)) =
Answer» `1/(SQRT(1+x)).1/sqrtx` `1/(sqrt(1+x)).1/(2sqrtx)` `-1/(sqrt(1+x)).1/(2sqrtx)` `-1/(sqrt(1+x)).1/sqrtx` ANSWER :B

Discussion

24.	Find Lt_(xtoa)(log(x-a))/(log(e^(x)-e^(a)))
Answer» ANSWER :1

Discussion

25.	The point on the parabola y =x^(2) + 7x + 2 which is elosest to the line y = 3x - 3 is
Answer» ANSWER :(2, -8)

Discussion

26.	The locus of the point x=a+lamda^(2),y=b-lamda where lamda is a parameter is
Answer» `(x-a)^(2)=b-y` `x-a=(b-y)^(2)` `x+a=y^(2)` `x-a=y^(2)` ANSWER :2

Discussion

27.	How many strings of length 6 can be formedusing the letter of the word FRIEND if (i) either starts with F or ends with D (ii) neither starts with F nor ends with D.
Answer» ANSWER :504

Discussion

28.	If X={(1,2,3,4,5} and Y={1,3,5,7,9}, then find which of the following sets are functions from X to Y? (i) R_(1)={(x,y):y=x+2, x in X, y in Y} (ii) R_(2) ={(1,2),(2,1),(3,3),(4,3), (5,3)} (iii)R_(3)={(1,1),(1,3),(3,5),(3,7),(5,7)} (iv) R_(4)={(1,3),(2,5),(4,7),(5,9),(3,1)}
Answer» ANSWER :`R_(2) and R_(4)` are FUNCTIONS

Discussion

29.	If z = x + yi, omega = (2-iz)/(2z-i) and \|omega\|=1, find the locus of z in the complex plane
Answer» ANSWER :`3X^(2) + 3y^(2)- 8y-3= 0`. This is a circle WHOSE centre is `(0, (4)/(3))` and radius is `(5)/(3)`

Discussion

30.	sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi)/(8)+sin^(2)(7pi)/(8)=?
Answer» `-1` 1 `-2` 2 Solution :N//A

Discussion

31.	If f: R rarr R, f(x)= x-2, g: R rarr R, g(x)= x + 2 then (f+ g) (x)= ……..
Answer» X `x^(2)-4` 2x 4 Answer :C

Discussion

32.	If f and g are differentiable functions in [0,1] satifying f(0)=2=g(1),g(0)=0 and f(1) =6 , then for some c in (0,1)
Answer» G'(C ) `-g'(c )` `2G'(c )` `3G'(c )` ANSWER :C

Discussion

33.	If xgt0 then the interval of monotonically increasing of f(x)=2x^(2)-logx is
Answer» `(-OO,(-1)/(2))` `((-1)/(2),0)` `(0,(1)/(2))` `((1)/(2),oo)` ANSWER :D

Discussion

34.	The mean deviation about mean of the observation 3, 10, 10, 4, 7, 10, 5 is
Answer» 2 2.57 3 3.75 Answer :B

Discussion

35.	Let barr be a vector perpendicular to bara + barb + barc . If barr=l(barbxxbarc)+m(barcxxbara)+n(baraxxbarb) then l+m+n is
Answer» 0 1 2 `3SQRT3` ANSWER :A

Discussion

36.	The side of triangle ABC satisfy the relation a + b - c = 2 " and " 2ab - c^(2) = 4, then square of the area of triangle is :
Answer» 3 `SQRT3` 9 81 Answer :A

Discussion

37.	log ( x )^(n) = n .log x is true for n.
Answer» `AA N in N` `AA n in Z` `n` is POSITIVE odd integer `n` is positive EVEN integer Answer :C

Discussion

38.	A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes at points P and Q. Then the absolute minimum value of OP+OQ as L varies, [where O is the origin ] is 6n, then n=
Answer» ANSWER :3

Discussion

39.	If f: R to [0, infty) defined by f(x) = 10^(x) then f^(-1)(x)=
Answer» `log_(X)10` `x^(10)` `log_(10)x` `10^(x)` ANSWER :C

Discussion

40.	Lt_(ntooo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)
Answer» ANSWER :1

Discussion

41.	If ""^(n)C_(9)=""^(n)C_(8), find ""^(n)C_(17).
Answer» ANSWER :1

Discussion

42.	If sin((picottheta)/(4))=cos((pitantheta)/(4)) and theta is in the first quadrant, then theta =
Answer» `pi//3` `pi//2` `pi//4` `pi//6` ANSWER :C

Discussion

43.	If (sqrt(8)+i)^(50)=3^(49)(a+ib) then a^(2)+b^(2)=....
Answer» 3 8 9 `SQRT(8)` ANSWER :C

Discussion

44.	Evaluate C(31,26)-C(30,26)
Answer» ANSWER :` 142506`

Discussion

45.	If the vectors 2bar(i) + lambda bar(j) - bar(k) and 4bar(i)-2bar(j)+2bar(k) are perpendicular to each other than find lambda.
Answer» ANSWER :3

Discussion

46.	If the equation of the pair of straight lines passing through the point (1,1) one making an angle theta with the positive dirction of the x-axis and the other making the same angle with the positive direction of the y-axis is x^2-(a+2)xyy^2+a(x+y-1)=0, ane-2 then the value of sin2theta is
Answer» a-2 a+b `2//(a+2)` `2//a` ANSWER :C

Discussion

47.	Let A = { a, e, i, o, u } and B = { a, i, u }. Show that A ∪ B= A
Answer» ANSWER :`B SUB A," then "A CUP B = A`

Discussion

48.	f:R rarr R, function f(x) is defined as f(x)= 2x +\|x\| then f(2x)+f(-x)-f(x) = ...........
Answer» ANSWER :`2\|x\|`

Discussion

49.	Prove thatsum (r+r_1)tan ((B-C)/( 2))=0
Answer» ` ( ABC)/( Delta ^(3)) ` `0` ` 4Rr^(2) ` ` (1)/ ( r ) ` Answer :B

Discussion

50.	A(-1,1)B(5,3) are the opposite vertices of a square. Perpendicular distance from (1,2) to the other diagonal (which is not passing through A,B) of the square is
Answer» `1/(SQRT(10))` `2/(sqrt(10))` `3/(sqrt(10))` `4/(sqrt(10))` Answer :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Express the following in the form a+bi (sqrt3 + 5i) (sqrt3 -5i)^(2) + (-4+ 5i)^(2)

Ifsin 2 theta + cos theta = 0"then " theta =

The value of tan^(-1)((x cos theta)/(1-x sin theta))-cot^(-1)((cos theta)/(x-sin theta)) is

d/(dx)(a^(log_asqrtx))=1/(2sqrtx) where a gt 1 inR^+

The orthocentre of triangle formed by lines xy+3x+3y+9 = 0 and the line 3x+4y-5=0 is

If Lt_(xto0)(1+ax+bx^(2))^(2//x)=e^(3), find a and b.

Evaluate lim_(xrarrinfty)[(x^2 -3x -4 )/(x^2 +3x+2)]^x

cos^(-1)("cos"(7pi)/6) is equal to

Find the number of terms in the expansion of the following : (x+2a)^(10)+(x-2a)^(10)

Differentiate x^(a) with respect to a^(x).

Match the following

Using binomial theorem, evaluate (101)^4

If (d)/(dx)((1+x^(4)+x^8)/(1+x^(2)+x^(4)))=ax^(3)+bx then …………….

A coin is tossed four times write the elements of sample space.

If y= Tan^(-1)""(sqrt(1+x^2) -1)/x then (dy)/(dx)=

If x^(p) occurs in the expansion of (x^(2)+1/x)^(2n) then prove that its coefficient is (2n!)/((((4n-p)!)/(3!))(((2n+p)!)/(3!)))

If f_(n)(x)=(sinx)/(cos3x)+(sin3^2x)/(cos3^2x)+(sin3^2x)/(cos3^(3)x)+....+(sin3^(n-1)x)/(cos3^(n)x) Then f_(2)(pi//4)+f_3(pi//4)=

If bar(AB)=2bara+barb and bar(AD) = bara-2barb " where " absbara=1, absbarb =1, (bara,barb) = 60^(@) are the adjacent sides of a parallelogram, then the length of the diagonal "bar(BD) is

If the lengths of the sides of triangle are 3, 5, and 7, then the largest angle of the triangle is

Find the equation of parabolawith itsaxis parallelto x - axisand passing through the points (-2,1) ,(1,2) and (-1,3) .

Evaluate the following limits in lim_(xrarr1)(ax^(2)+bx+c)/(cx^(2)+bx+a), a+b+c ne0

Differentiateby 1^(st) principalf(x) = tan (1-2x)

d/(dx)(sinh^(-1)(sqrtx)) =

Find Lt_(xtoa)(log(x-a))/(log(e^(x)-e^(a)))

The point on the parabola y =x^(2) + 7x + 2 which is elosest to the line y = 3x - 3 is

The locus of the point x=a+lamda^(2),y=b-lamda where lamda is a parameter is

How many strings of length 6 can be formedusing the letter of the word FRIEND if (i) either starts with F or ends with D (ii) neither starts with F nor ends with D.

If X={(1,2,3,4,5} and Y={1,3,5,7,9}, then find which of the following sets are functions from X to Y? (i) R_(1)={(x,y):y=x+2, x in X, y in Y} (ii) R_(2) ={(1,2),(2,1),(3,3),(4,3), (5,3)} (iii)R_(3)={(1,1),(1,3),(3,5),(3,7),(5,7)} (iv) R_(4)={(1,3),(2,5),(4,7),(5,9),(3,1)}

If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1, find the locus of z in the complex plane

sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi)/(8)+sin^(2)(7pi)/(8)=?

If f: R rarr R, f(x)= x-2, g: R rarr R, g(x)= x + 2 then (f+ g) (x)= ……..

If f and g are differentiable functions in [0,1] satifying f(0)=2=g(1),g(0)=0 and f(1) =6 , then for some c in (0,1)

If xgt0 then the interval of monotonically increasing of f(x)=2x^(2)-logx is

The mean deviation about mean of the observation 3, 10, 10, 4, 7, 10, 5 is

Let barr be a vector perpendicular to bara + barb + barc . If barr=l(barbxxbarc)+m(barcxxbara)+n(baraxxbarb) then l+m+n is

The side of triangle ABC satisfy the relation a + b - c = 2 " and " 2ab - c^(2) = 4, then square of the area of triangle is :

log ( x )^(n) = n .log x is true for n.

A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes at points P and Q. Then the absolute minimum value of OP+OQ as L varies, [where O is the origin ] is 6n, then n=

If f: R to [0, infty) defined by f(x) = 10^(x) then f^(-1)(x)=

Lt_(ntooo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

If ""^(n)C_(9)=""^(n)C_(8), find ""^(n)C_(17).

If sin((picottheta)/(4))=cos((pitantheta)/(4)) and theta is in the first quadrant, then theta =

If (sqrt(8)+i)^(50)=3^(49)(a+ib) then a^(2)+b^(2)=....

Evaluate C(31,26)-C(30,26)

If the vectors 2bar(i) + lambda bar(j) - bar(k) and 4bar(i)-2bar(j)+2bar(k) are perpendicular to each other than find lambda.

If the equation of the pair of straight lines passing through the point (1,1) one making an angle theta with the positive dirction of the x-axis and the other making the same angle with the positive direction of the y-axis is x^2-(a+2)xyy^2+a(x+y-1)=0, ane-2 then the value of sin2theta is

Let A = { a, e, i, o, u } and B = { a, i, u }. Show that A ∪ B= A

f:R rarr R, function f(x) is defined as f(x)= 2x +|x| then f(2x)+f(-x)-f(x) = ...........

Prove thatsum (r+r_1)tan ((B-C)/( 2))=0

A(-1,1)B(5,3) are the opposite vertices of a square. Perpendicular distance from (1,2) to the other diagonal (which is not passing through A,B) of the square is