28278 + Interview Questions in Maths in Class 12

1.	Ifalpha, beta , gammain[0,pi] andifalpha , beta, gammaarein A.Pthen( sinalpha- singamma)/( cos gamma-cosalpha) is equalto
Answer» `sin BETA ` `cosbeta ` `cot beta ` `2 COS beta ` ANSWER :C

Discussion

2.	Statement-1: Each point on the line 7x-y=0 is equidistant from the lines 4x+3y-1=0" and "3x-4y+1=0 Statement-2: The locus of point which is equidistant from 2 given lines L_(1)-=a_(1)x+b_(1)y+c_(1)=0 and L_(2)-=a_(2)x+b_(2)y+c_(2)=0 need not always be the angle bisector of 2 given lines.
Answer» Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1 . Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. Statement-1is true, statement-2 is false. Statement-1 is false, statement-2 is true. Solution :`(4x+3y-1)/(5) = +- ((3x-4y+1)/(5))` The 2 angle BISECTORS are : `x+7y-2 =0` `7x-y = 0` Statement-2 is correct as the lines can be PARALLEL ALSO.

Discussion

3.	What is the least value of 25 "cosec"^(2)x+36sec^(2)x?
Answer» 1 11 120 121 Answer :D

Discussion

4.	int_(-1)^(1) (sqrt(1+x+x^2)-sqrt(1-x+x^2))/(sqrt(1+x+x^2)+sqrt(1-x+x^2)) dx=
Answer» `(3pi)/(2)` `(pi)/(2)` 0 `-1` ANSWER :C

Discussion

5.	If m is mean of distribution, then sum(x_(i) - m) is equal to
Answer» MEAN deviation standard deviation 0 `-2` ANSWER :C

Discussion

6.	If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?
Answer» ANSWER :`1xx24,2xx12,3xx8,4xx6,6xx4,8xx3,12xx2,24xx1; 1xx13, 13xx1`

Discussion

7.	Differentiate tan^(-1)(( sqrt(1+x^(2))-1)/(x))
Answer» ANSWER :`(1)/(2(1+x^(2)))`

Discussion

8.	Point P lie on hypertola 2xy=1. Atriangle is constucted by P, S and S' (where S and S' are focl). Find the locus of excentre opposite S (S and P lie in first quadrant).
Answer» ANSWER :`(x+y)^(2) = (SQRT2 -1) ^(2) (x-y)^(2) +4`

Discussion

9.	A book of 500 pages has 50 misprints. Find the probability that three are not less than 3 misprints on a given page.
Answer» ANSWER :`1508 XX 10^(-7)`

Discussion

10.	\|{:(sin40^@,-cos40^@),(sin50^@,cos50^@):}\|=.......
Answer» 0 1 `-1` not EXIST ANSWER :B

Discussion

11.	arg z=0 if and only if z is a
Answer» PURELY IMAGINARY number positive integer positive REAL number non NEGATIVE real number Answer :C

Discussion

12.	The equation of the circles which touch the x-axis at the origin and the line 4x-3y+24=0
Answer» `X^(2)+y^(2)+6y=0, x^(2)+y^(2)-24y=0` `x^(2)+y^(2)+2y=0, x^(2)+y^(2)-18y=0` `x^(2)+y^(2)+18x=0, x^(2)+y^(2)-8x=0` `x^(2)+y^(2)+4x=0,x^(2)+y^(2)-16x=0` ANSWER :A

Discussion

13.	If ""^(2)C_(r)=495, find the possible values of (r ).
Answer» ANSWER :4,8

Discussion

14.	Match the following lists:
Answer» Solution :`a to R,s, b to p,q,r,s, c to p , q, r, s, d top.` a. P(SUCCESS) = 1/2, P(failure)=1/2 Suppose 'n' bombs are to dropped. Let E be the event that the bridge is destroyed. Then, P(E) = 1 - P(0or 1 success) `=1-(((1)/(2))^(n)+""^(n)C_(1)1/2((1)/(2))^(n-1))` `=1-1/10ge(n+1)/(2^(n))or (2^(n))/(10(n+1))ge1` b. The bag contains 2 red 3 white and 5 black balls. Hence `P(S)=1//5,P(F)=4//5,LetE` be the event of getting a red ball. `P(E) =P(S or FSorFFS or ...]ge1/2` The value of n consistent is 4. c. Let there be x red socks and y blue socks and `x gt y.` Then `(""^(x)C_(2)+""^(y)C_(2))/(""^(x+y)C_(2))=1/2` `or (x(x-1)+y(y-1))/((x-y)(x+y-1))=1/2` Multiplying both sides by `2(x+y)(x+y-1)` and EXPANDING, we get `2x^(2)-2x+2y^(2)-2y=x^(2)+2xy+y^(2)-x-y` REARRANGING, we have `x^(2)-2xy+y^(2)=x+y` or `(x-y)^(2) =x+y` or ` \|x-y\|=x+y` `Now, x+y le17` `x-y lesqrt17` As x- y must be an integer, so `x-y=4` `therefore x+y=16` Adding both together and dividing by 2 yields `x GE 10.` d. Let the number of green socks be `x gt 0.` Let E: be the event that two socks drawn are of the same colour. `P(E)=P(R R or BB or WW or GG)` `=(3)/(""^(6+x)C_(2))+(""^(x)C_(2))/(""^(6+x)C_(2))` `=(6)/((x+6)(x+5))+(x(x-1))/((x+6)(x+5))=1/5` `implies5(x^(x)-x+6)=x^(2)+11x+30` `or 4x^(2)-16x=0` `x=4`

Discussion

15.	Select the INCORRECT order of EN of following species :
Answer» S lt Si lt O<BR>`Fe^(2+) lt Fe^(3+)` Al lt Si lt Cl I lt Br lt F

Discussion

16.	Evaluate int_(2)^(3)1/xdx
Answer» ANSWER :`log3//2`

Discussion

17.	Evaluate : lim_(x rarr 0)""(sin x^(@))/(x)
Answer» 1 0 `(PI)/(180)` `(180)/(pi)` ANSWER :C

Discussion

18.	The perpendicular distance from the point (3,1,1) on the plane passing through the point (1,2,3) and containing the line r=i+j+lambda(2i+j+4k) is
Answer» `(3)/(sqrt(11))` `(1)/(sqrt(11))` `(4)/(sqrt(41))` 0 Answer :D

Discussion

19.	Two sides of a rhombus ABCD are parallel to the lines x-y=5 and 6x-y=3. If the diagonals of the rhombus intersects at the point (2,1), find the equation of the diagonals. Further, find the possible coordinates of the vertex A if it lies on the x-axis.
Answer» ANSWER :`3x-y=3, x+2y=4; ((3)/(2)0) and (4,0)`

Discussion

20.	Considering the implicit functionax^(2) + by^(2) + 2hxy + 2gx + 2fy + c=0, " find " (dy)/ (dx)
Answer» Solution :GIVEN `ax^(2) + by^(2) + 2HXY + 2gx + 2fy + c=0` Differentiating both sides w.r.t x, we get `a d/(DX)x^(2) + 2hd/(dx) (xy) +bd/(dx)y^(2) + 2g d/(dx) (x) +2F d/(dx) (y) + 0=0` ` 2ax + 2h (x(dy)/(dx) + y.1) + 2by (dy)/(dx) + 2g + 2f (dy)/(dx) =0` ` (2ax +2hy +2g) + (dy)/(dx) (2hx +2by +2f) =0` ` (dy)/(dx) = - (ax +hy+g)/(hx +by +f)`

Discussion

21.	to removethe2^(nd)termof the equationx^4 -10 x^3 +35 x^2 -50 x^2 - 50 x+ 24=0, diminishthe rootsby
Answer» `2/5` `-2/5` `5/2` `-5/2` ANSWER :C

Discussion

22.	underset(x to 5+)"Lt" {x-[x]}=
Answer» 0 `1//2` `-1//2` does not exist Answer :A

Discussion

23.	Let S = sum_(i=1)^(n) a_(j) and sum_(l=1)^(n) s/(s-a_(j)) gt (n^(2))/(n-1)assumbing not all a_(i)s are equal
Answer» ANSWER :` RARR sum_(i=1)^(n) s/(s-a_(1)) gt (n^(2))/((n-1))`

Discussion

24.	An equation of a common tangent to the circle x ^(2) + y ^(2) + 14 x - 4y + 28 =0 and x ^(2) + y ^(2) - 14 x + 4y - 28 =0 is
Answer» `x-7=0` `y + 7=0` `28X + 45 y + 371=0` NONE of these ANSWER :C

Discussion

25.	Find the area enclosed between the curves y^(2)=2x+6 and y=x-1
Answer» ANSWER :18

Discussion

26.	Equation of the bisector of the acute angle between lines 3x+4y+5=0 and 12x -5y-7=0 is
Answer» 21x + 77y + 100=0 99x -27y +30=0 99x +27y +30=0 21x-77y -100=0 Solution :Given lines are 3x + 4y + 5=0 and12 x-5y -7=0 Here ` a_(1) = 3, b_(1) = 4, a_(2) =12 and b_(2) = -5 ` `a_(1)a_(2) +b_(1)b_(2) = 3xx 12 + 4 xx (-5) = 16 lt 0` For acute ANGLE bisector ` (3x + 4y+5)/(sqrt(9+16)) = ((12x-5y-7))/(sqrt(12^(2)+(-5)^(2))` ` (3x+4y+5)/5 = ((12x-5y-7))/13` ` Rightarrow 39X + 52y + 65 =- 60 x + 25 y + 35` ` Rightarrow 99 x + 27 y + 30 =0`

Discussion

27.	Find the ratio in which (i) the X -axis.
Answer» ANSWER :A::B

Discussion

28.	Let A be a squarematrix of order n. l= maximum number of different entries if A is a upper triangular matrix. m= minimum number of zeros if A is a triangular matrix. p = minimum number of zeros if A is a diagonal matrix. If l+2m=2p+1, then n=
Answer» 1 2 3 4 Answer :C

Discussion

29.	Find the parametric equations of the circles x^(2) + y^(2) - 4x + 6y -12=0
Answer» Answer :` X= 2+ 5 cos THETA , y =-3 + 5 SIN theta) `

Discussion

30.	Which of the following ratios is closest to the ratio carrot sales to potato sales at Produce Stand P in the month of April?
Answer» `1:4` `2:9` `1:5` `1:6` ANSWER :A

Discussion

31.	The ordinate of any point P on the hyperbola 25x^(2)-16y^(2)=400 is produced to cut the asymptoles in the points Q and R. Find the value of QP. PR
Answer» ANSWER :25

Discussion

32.	If =intlog(x+sqrt(1+x^(2)))/(sqrt(1+x^(2)))dx=g o f (x) xConst. then
Answer» `F(x)=LOG(x+sqrt(x^(2)+1))` `f(x)=log(x+sqrt(x^(2)+1))andg(x)=x^(2)` `f(x)=log(x+sqrt(x^(2)+1))andg(x)=x^(2)//2` `f(x)=x^(2)and G(x)=log(x+sqrt(x^(2)+1))` Answer :C

Discussion

33.	A: length of the intercept made by the circle x^(2)+y^(2)-12+14y+11=0 on x-axis is 10. R: The length of the intercept made by the circle S=0 on y-axis is root2(f^(2)-c).
Answer» Both A and R are true and R is the correct EXPLANATION of A Both A and R are true and R is not the correct explanation of A A is true but R is false A is false but R is false Answer :B

Discussion

34.	Find (dy)/(dx), if y= 12(1- cos t), x= 10 (t- sin t), -(pi)/(2) lt t lt (pi)/(2)
Answer» ANSWER :`(6)/(5) COT ((t)/(2))`

Discussion

35.	A + B+ C =0అయితే , cos^(2) A + cos^(2) B +cos^(2)C = 1+2 cos A cos B cosC అని రుజువు చేయండి.
Answer» 1 2 0 3 Answer :A

Discussion

36.	A box contains 4 defective and 6 good bulbs. Two bulbs are drawn at random without replacement. Find the probability that the both the bulbs drawn are good.
Answer» ANSWER :`(1)/(3)`

Discussion

37.	A man is known to speak the truth 2 out of 3 times. If the throws a die and reports that it is six. Then the probability that it actually five. Is
Answer» `(3)/(8)` `(1)/(7)` `(2)/(7)` `(4)/(5)` ANSWER :B

Discussion

38.	Prove that "^(2n)C_0 + ^(2n)C_2 + .... + ^(2n)C_(2n) = 2^(2n-1)
Answer» Solution :`"^(2N)C_0 + ^(2n)C_2 + .... + ^(2n)C_(2n)` = 2^(2n-1)` We know that `(1+X)^(2n) = "^(2n)C_0 + ^(2n)C_1 x + ^(2n)C_2 x^2 + ... ^(2n)C_(2n) x^n` ... (1) Putting x = 1 we get putting x = 1 we get `("^(2n)C_0 + ^(2n)C_2 + ^(2n)C_4 + .... + ^(2n)C_(2n)) - (^(2n)C_1 + ^(2n)C_3 + ... + ^(2n)C_(2n-1))` = 0 therefore ^(2n)C_0 + ^(2n)C_2 + .... + ^(2n)C_(2n)` = `"^(2n)C_1 + ^(2n)C_3 + .... + ^(2n)C_(2n-1)` = `2^(2n)/2` = `2^(2n-1)`

Discussion

39.	If f(a)=f'(a)=g(a)=-g'(a)=- then lim_(xtoa)(g(x)f(a)-g(a)f(x))/(x-a)
Answer» `-5` `3` `-3` `5` ANSWER :C

Discussion

40.	The transformed equation of x^(4) + 8x^(3) + x - 5 = 0 by eliminating second term is
Answer» `x^4 -24x^2 +65X -55=0` `x^4 +24 x^2+65 x+55=0` `x^4 -24x^2 -65x+55=0` `x^4+24x^2 +65x-55=0` ANSWER :A

Discussion

41.	Find values of a and b if A =B whereA=[{:(a+4,3b),(8,-6):}],B=[{:(2a+2,b^(2)+2),(8,b^(2)-5b):}] Hints for solution : In given two square matrix if corresponding elements of each raw and column are equal then both matrix are said to be equal matrix.
Answer» ANSWER :`=2`

Discussion

42.	For continuous functions f and g on R, let f(a)=4, f'(a)=6, g(a)=2, g'(a)=1 . Then the value of lim_(x to a)(sqrt(f(x)g(a))-sqrt(g(x)f(a)))/((x-a)(sqrt(f(x)g(a))+sqrt(g(x)f(a))))
Answer» 0 3 `1//4` `2//3` ANSWER :C

Discussion

43.	Integrate the following rational functions : int(x^(2))/((x^(2)+2)(x^(2)+3))dx
Answer» ANSWER :`-sqrt2tan^(-1)""(x)/(sqrt2)+sqrt3tan^(-1)""(x)/(SQRT3)+C`

Discussion

44.	Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If BC = 6, AC = 8, then the length of side AB is equal to
Answer» `(1)/(2)` `(2)/(SQRT3)` `5sqrt2` none of these Solution : `FG xx FC = FA^(2)` `RARR (1)/(3) (FC^(2)) = FA^(2)` `rArr (2a^(2) + 2b^(2) -C^(2))/(3 xx4) = (c^(2))/(4)` (Using Apollonious theorem) `rArr 2C^(2) = a^(2) + b^(2)`

Discussion

45.	Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If angleGAC = (pi)/(3) and a = 3b, then sin C is equal to
Answer» `(3)/(4)` `(1)/(2)` `(2)/(sqrt3)` NONE of these Solution :In `DeltaADC`, we have, `(a//2)/(sin (pi//3)) = (AD)/(sin C) RARR sin C = (sqrt3)/(2a) sqrt(2B^(2) + 2c^(2) -a^(2))` `=(sqrt3)/(2a) sqrt(3B^(2)) = (3)/(2) (b)/(a) = (1)/(2)`

Discussion

46.	Find x if A = [[2,3,-1],[x,-5,0],[-1,0,7]] is symmetric matrix
Answer» `-3` `3` `2` `-2` ANSWER :B

Discussion

47.	Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If AC = 1, then the length of the median of triangle ABC through the vertex A is equal to
Answer» `(SQRT3)/(2)` `(1)/(2)` `(2)/(sqrt3)` `(5)/(sqrt2)` SOLUTION :We have `AD = sqrt((2B^(2) + 2c^(2) -a^(2))/(4)) = (sqrt3b)/(2)` If `b = 1 " then " AD = (sqrt3)/(2)`

Discussion

48.	Consider f as a twice differentiable function such that f(x)+f^('')(x)=-xg(x)f^(')(x)AAxge0 where,g(x)ge0AA x ge0, then (AAxge0)
Answer» `(f(x)^(2))+(f^(')(x)^(2))` is a non increasing FUNCTION `(f(x))(2)LT3(f(0))^(2)+(2f^(')(0))^(2)` `\|f(x))ge alpha, alpha` is a fixed real constant `lim_(xto oo) f(x).sin(1/x)` exist Solution :`d/(DX)((f(x))^(2))=2f^(')(x).f(x)+2f^(')(x).f^(")(x)=-2xg(x)(f^(')(x))^(2)le0`

Discussion

49.	If onerootofx^3 -6x^2+3x +10 =0is2 thenthe remainingtworoots are
Answer» `2,-5/2` `5,-1` `-5,1` `2,5/2` ANSWER :B

Discussion

50.	Observe the following statements: I) In DeltaABC,bcos^2""C/2+c cos^2""B/2=sII. In Delta ABC,cot""A/2=(b+c)/2impliesB=90^@ Which of the following correct?
Answer» Both I and II are TRUE I is true, II is false I is false, II is true Both I and II are false Answer :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Ifalpha, beta , gammain[0,pi] andifalpha , beta, gammaarein A.Pthen( sinalpha- singamma)/( cos gamma-cosalpha) is equalto

Statement-1: Each point on the line 7x-y=0 is equidistant from the lines 4x+3y-1=0" and "3x-4y+1=0 Statement-2: The locus of point which is equidistant from 2 given lines L_(1)-=a_(1)x+b_(1)y+c_(1)=0 and L_(2)-=a_(2)x+b_(2)y+c_(2)=0 need not always be the angle bisector of 2 given lines.

What is the least value of 25 "cosec"^(2)x+36sec^(2)x?

int_(-1)^(1) (sqrt(1+x+x^2)-sqrt(1-x+x^2))/(sqrt(1+x+x^2)+sqrt(1-x+x^2)) dx=

If m is mean of distribution, then sum(x_(i) - m) is equal to

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

Differentiate tan^(-1)(( sqrt(1+x^(2))-1)/(x))

Point P lie on hypertola 2xy=1. Atriangle is constucted by P, S and S' (where S and S' are focl). Find the locus of excentre opposite S (S and P lie in first quadrant).

A book of 500 pages has 50 misprints. Find the probability that three are not less than 3 misprints on a given page.

|{:(sin40^@,-cos40^@),(sin50^@,cos50^@):}|=.......

arg z=0 if and only if z is a

The equation of the circles which touch the x-axis at the origin and the line 4x-3y+24=0

If ""^(2)C_(r)=495, find the possible values of (r ).

Match the following lists:

Select the INCORRECT order of EN of following species :

Evaluate int_(2)^(3)1/xdx

Evaluate : lim_(x rarr 0)""(sin x^(@))/(x)

The perpendicular distance from the point (3,1,1) on the plane passing through the point (1,2,3) and containing the line r=i+j+lambda(2i+j+4k) is

Two sides of a rhombus ABCD are parallel to the lines x-y=5 and 6x-y=3. If the diagonals of the rhombus intersects at the point (2,1), find the equation of the diagonals. Further, find the possible coordinates of the vertex A if it lies on the x-axis.

Considering the implicit functionax^(2) + by^(2) + 2hxy + 2gx + 2fy + c=0, " find " (dy)/ (dx)

to removethe2^(nd)termof the equationx^4 -10 x^3 +35 x^2 -50 x^2 - 50 x+ 24=0, diminishthe rootsby

underset(x to 5+)"Lt" {x-[x]}=

Let S = sum_(i=1)^(n) a_(j) and sum_(l=1)^(n) s/(s-a_(j)) gt (n^(2))/(n-1)assumbing not all a_(i)s are equal

An equation of a common tangent to the circle x ^(2) + y ^(2) + 14 x - 4y + 28 =0 and x ^(2) + y ^(2) - 14 x + 4y - 28 =0 is

Find the area enclosed between the curves y^(2)=2x+6 and y=x-1

Equation of the bisector of the acute angle between lines 3x+4y+5=0 and 12x -5y-7=0 is

Find the ratio in which (i) the X -axis.

Let A be a squarematrix of order n. l= maximum number of different entries if A is a upper triangular matrix. m= minimum number of zeros if A is a triangular matrix. p = minimum number of zeros if A is a diagonal matrix. If l+2m=2p+1, then n=

Find the parametric equations of the circles x^(2) + y^(2) - 4x + 6y -12=0

Which of the following ratios is closest to the ratio carrot sales to potato sales at Produce Stand P in the month of April?

The ordinate of any point P on the hyperbola 25x^(2)-16y^(2)=400 is produced to cut the asymptoles in the points Q and R. Find the value of QP. PR

If =intlog(x+sqrt(1+x^(2)))/(sqrt(1+x^(2)))dx=g o f (x) xConst. then

A: length of the intercept made by the circle x^(2)+y^(2)-12+14y+11=0 on x-axis is 10. R: The length of the intercept made by the circle S=0 on y-axis is root2(f^(2)-c).

Find (dy)/(dx), if y= 12(1- cos t), x= 10 (t- sin t), -(pi)/(2) lt t lt (pi)/(2)

A + B+ C =0అయితే , cos^(2) A + cos^(2) B +cos^(2)C = 1+2 cos A cos B cosC అని రుజువు చేయండి.

A box contains 4 defective and 6 good bulbs. Two bulbs are drawn at random without replacement. Find the probability that the both the bulbs drawn are good.

A man is known to speak the truth 2 out of 3 times. If the throws a die and reports that it is six. Then the probability that it actually five. Is

Prove that "^(2n)C_0 + ^(2n)C_2 + .... + ^(2n)C_(2n) = 2^(2n-1)

If f(a)=f'(a)=g(a)=-g'(a)=- then lim_(xtoa)(g(x)f(a)-g(a)f(x))/(x-a)

The transformed equation of x^(4) + 8x^(3) + x - 5 = 0 by eliminating second term is

Find values of a and b if A =B whereA=[{:(a+4,3b),(8,-6):}],B=[{:(2a+2,b^(2)+2),(8,b^(2)-5b):}] Hints for solution : In given two square matrix if corresponding elements of each raw and column are equal then both matrix are said to be equal matrix.

For continuous functions f and g on R, let f(a)=4, f'(a)=6, g(a)=2, g'(a)=1 . Then the value of lim_(x to a)(sqrt(f(x)g(a))-sqrt(g(x)f(a)))/((x-a)(sqrt(f(x)g(a))+sqrt(g(x)f(a))))

Integrate the following rational functions : int(x^(2))/((x^(2)+2)(x^(2)+3))dx

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If BC = 6, AC = 8, then the length of side AB is equal to

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If angleGAC = (pi)/(3) and a = 3b, then sin C is equal to

Find x if A = [[2,3,-1],[x,-5,0],[-1,0,7]] is symmetric matrix

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If AC = 1, then the length of the median of triangle ABC through the vertex A is equal to

Consider f as a twice differentiable function such that f(x)+f^('')(x)=-xg(x)f^(')(x)AAxge0 where,g(x)ge0AA x ge0, then (AAxge0)

If onerootofx^3 -6x^2+3x +10 =0is2 thenthe remainingtworoots are

Observe the following statements: I) In DeltaABC,bcos^2""C/2+c cos^2""B/2=sII. In Delta ABC,cot""A/2=(b+c)/2impliesB=90^@ Which of the following correct?