28278 + Interview Questions in Maths in Class 12

1.	Find the Principle values of the following : sec^(-1)(2/(sqrt(3)))
Answer» ANSWER :`(PI)/6`

Discussion

2.	[hati hatk hatj]+[hatk hatj hati]+[hatj hatk hati] is equal to
Answer» 1 3 `-3` `-1` SOLUTION :`[HAT(i)hat(k)hat(J)]+[hat(k)hat(j)hat(i)]+[hat(j)hat(k)hat(i)]=[hat(i)hat(k)hat(j)]+[hat(i)hat(k)hat(j)]-[hat(i)hat(k)hat(j)]=[hat(i)hat(k)hat(j)]=hat(i).(hat(k)xxhat(j))=hat(i).(-hat(i))=-1`

Discussion

3.	Find the equation of the circle passing through (0,0) and Making intercept 4 units on Y- axis.
Answer» ANSWER :`x^(2) +y^(2) + 6X + 4y =0`

Discussion

4.	a.a' + b.b' + c.c' =
Answer» 0 1 2 3 Answer :D

Discussion

5.	Prove that the function f given by f(x) = x ^(2) – x + 1 is neither strictly increasing nor decreasing on (– 1, 1).
Answer» ANSWER :`((1)/(2),1)`

Discussion

6.	A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be (i) red (ii) yellow (iii) blue (iv) not blue
Answer» SOLUTION :(i) `4/9` (II) `2/9` (III) `1/3` (IV) `2/3`

Discussion

7.	The shortest distance from (1,1,1) to the line of intersection of the pair of planes xy+yz+zx+y^(2)=0 is
Answer» `sqrt(8/3)` `2/sqrt(3)` `1/sqrt(3)` `2/3` Solution :`xy+yz+y^(2)=0` `RARR y(x+y)+z(x+y)=0` `rArr` Line of intersection is `x=-y=z`. Distance of OP on line having direction RATIOS 1,-1 is `1/sqrt(3)`. Then required shortest distance `=sqrt(3-1/3)=sqrt(8/3)`.

Discussion

8.	If the matrix A=[(1,-1),(-1,1)] then A^(n+1)=
Answer» `[(1,-1),(-1,1)]` `N[(1,-1),(-1,1)]` `2^(n)[(1,-1),(-1,1)]` `2^(n+1)[(1,-1),(-1,1)]` ANSWER :C

Discussion

9.	PSQ is a focal chord of a parabola whose focus is S and vertex A . PA and QA are produced to meet the directrix in R and T respectively . Then angleRST =
Answer» `90^(@)` `60^(@)` `45^(@)` `30^(@)` ANSWER :A

Discussion

10.	The set S={1,2,3….12} is to be partitioned into three sets A,BC of equal size Thus A cup B cup C =S ,A cap B =B capC=A cap C=varphi the number of ways to partitions S is
Answer» `(12!)/((4!)^(3))` `(12!)/(3!(3!)4)` `(12!)/((4!)^(3)3!)` `(12!)/((3!)^(4))` ANSWER :A

Discussion

11.	x = 1+(3 ) /(1 ! )xx (1 )/(6) +( 3 xx 7 ) /(2 ! )( (1 )/(6) ) ^ 2+ (3 xx 7 xx 11 ) /(3 ! )((1 )/(6))^ 3+… rArrx ^4 =
Answer» `81 ` `54 ` `27` `8` Solution : ` x = 1+(3 ) /(1! )XX(1 )/(6)+(3 xx 7 ) /(2 ! )((1 )/(6))^ 2+(3 xx 7 xx 11 ) /(3 ! )((1 )/(6))^(3)+…` `x= (1 - y ) ^(-p//q ) ` `p =3,p + q= 7,(y ) /(q)= (1 )/(6) ` `q =4 ` ` (y) /(4)=(1 )/(6)` `rArry =(4 ) /(6)` ` thereforey=(2 ) /(3)` ` x = (1 -(2 ) /(3) ) ^(-3//4)` ` RARRX =((1)/(3)) ^( -3/4)` `rArrx=3^(3//4)` ` rArr x = 4 sqrt(27)` `thereforex ^ 4 =27 `

Discussion

12.	If x is real , then least value of the expression (ax^(2) + bx + c), a lt 0is :
Answer» `- (b)/(2a)` `b^(2) - 4 AC ` `(4 ac - b^(2))/(4A) ` `(4 ac - b^(2))/(4a^(2)) ` ANSWER :C

Discussion

13.	If a = Sigma_(n=1)^(oo) (2n)/(2n-1!),b=Sigma__(n=1)^(oo) (2n)/(2n+1!) then ab equals
Answer» 1 `E^(2)` `(e-1)/(e+1)` `(e+1)/(e-1)` ANSWER :a

Discussion

14.	4a-b=-2.25, a+b4.25 If (a, b) satisfies the system of equations above, what is the valeu of a?
Answer» ANSWER :`0.4 OR (2)/(5)`

Discussion

15.	The compound statement p rarr (~p vv q) is false. Then the truth values of p and q are respectively
Answer» F, F T,T T,F F,T Answer :C

Discussion

16.	Let the cubic equation x^(3)-ax^(2)+bx-1=0 has only one real root alpha(a lt b) Statemennt -1 alpha lis between 0 and 1 because Statement 2: The value of 2cot^(-1)(coseca)-cot^(-1)(cosec a cos^(2)a)/(2) is pi if a lt 0
Answer» `5/3` `3/5` `5/8` NONE of these ANSWER :B

Discussion

17.	If r_1=2r_2=3r_3, then
Answer» `(a)/(B)=(4)/(5)` `(a)/(b)=(5)/(4)` `(a)/(C )=(3)/(5)` `(a)/(c )=(5)/(3)` Answer :B::D

Discussion

18.	Considera parabola y=(x^(2))/4 and the point F(0,1). Let A_(1)(x_(1),y_(1)),A_(2)(x_(2),y_(2)),A_(3)(x_(3),y_(3)),.,A_(n)(x_(n),y_(n)) are n points on the parabola such that x_(k)gt0 and /_OFA_(k)=(kpi)/(2n)(k=1,2,……n) If the value of lim_(xto oo)(1/n). sum_(k=1)^(n)FA_(k)=m/(pi) then m is .........
Answer» ANSWER :4

Discussion

19.	(d)/(dx )( e^( tan^(-1)x+ cot^(-1) x)) =…….: (xinR)
Answer» 0 1 E `e^(pi/2)` ANSWER :A

Discussion

20.	Consider the equation (x^(2) +x+1) ^(2) - (m-3)(x^(2) +x+1) +m=0, where m is a real parameter. The number of positive integeral values of m for which equation has two distinct real roots, is:
Answer» ANSWER :1

Discussion

21.	Integrate the rational functions x/((x-1)(x-2)(x-3))
Answer» ANSWER :`(1)/(2)log\|x-1\|-2log\|x-2\|+(3)/(2)log\|x-3\|+c`

Discussion

22.	The solution of x^(3)(dy)/(dx)+4x^(2)tan y=e^(x)sec y satisfying y(1) = 0, is
Answer» `TAN y = e^(x)(x-2)lnx` `SINY=e^(x)(x-1)x^(-4)` `tany=e^(x)(x-1)x^(-3)` `siny=e^(x)(x-1)x^(-3)` SOLUTION :`x^(3)(dy)/(dx)+4x^(2)tany=e^(x)secyimpliesx^(3)cosy(dy)/(dx)+4x^(2)siny =e^(x)` `implies x^(3).(dt)/(dx)+4x^(2).t=e^(x), ""("where " t=siny)` `impliesx^(4)(dt)/(dx)+4x^(3)t=XE^(x)implies(d)/(dx)(x^(4).t)=xe^(x)impliesx^(4)t=(x-1)e^(x)+c` `impliesx^(4)siny=(x-1)e^(x)+c` `becausey(1)=0impliesc=0impliessiny=(e^(x)(x-1))/(x^(4))`

Discussion

23.	Three vertices of a parallelogram ABCD are A(3,-1,2),B(1,2,-4) and C(-1,1,2). The corrdinates of the fourth vertex is
Answer» ANSWER :`(1,-2,8)`

Discussion

24.	The phenomenon of interference demonstrates the fact that :
Answer» LIGHT possesses transvers WAVE NATURE light possesses LONGITUDINAL wave nature light possesses particle nature light possesses wave nature ANSWER :D

Discussion

25.	Differentiate the functions given in Exercises 1 to 11 w.r.t. x. sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5))).
Answer» ANSWER :`(1)/(2)SQRT(((x-1)(x-2))/((x-3)(x-4)(x-5)))[(1)/(x-1)+(1)/(x-2)-(1)/(x-3)-(1)/(x-4)-(1)/(x-5)]`

Discussion

26.	A car starts from rest and travels 50 m with uniform acceleration in 5 sec, then acceleration of car is :
Answer» `4 m//s^2` `2 m//s^2` `1 m//s^2` `3 m//s^2`

Discussion

27.	Which of the following is endothermic process ?
Answer» `S to S^-` `As^(+) to As^(THETA)` `N^(o+) to N^(3-)` `C^(+2) to C^+`

Discussion

28.	IFthereare mcopiesof eachof then differerntbooks s thennumberof differentordersinwhichtheycan bearrangedon ashelfis
Answer» `((MN)!)/(m!)` `(m!)^N` `(mn)!` `((mn)!)/((m!)^n )` ANSWER :D

Discussion

29.	If int (dx)/(cos^(3) x sqrt(2 sin 2x)) = (tan x)^(A) + C(tan x)^(B) + k ,where K is a costant of integration , then A+B + C equls :
Answer» `(16)/(5)` `(27)/(10)` `(7)/(10)` `(21)/(5)` Answer :A

Discussion

30.	Find the value of x, y,z and w from the equation. [{:(x,3x-y),(2x+z,3y-w):}]=[{:(3,2),(4,7):}]
Answer» ANSWER :`x=3,y=7,z=-2,w=14`

Discussion

31.	Find the maximum and minimum values, if any, of thefunctions given by f(x) = – \| x + 1\| + 3
Answer» ANSWER :MAXIMUM VALUE = 3; No MINIMUM value

Discussion

32.	Evaluation of definite integrals by subsitiution and properties of its : If int(1)/(e^(x)+1)dx=px-qlog\|1+e^(x)\|+C then p+q=………….
Answer» 0 2 `-2` 1 Answer :B

Discussion

33.	How many integers between 1 and 10^6 have the sum of digits equal to 18.
Answer» ANSWER :`""^(23)C_5-6xx^(13)C_5`

Discussion

34.	int_(0)^(pi//4)[sqrt(tanx)+sqrt(cotx)]dx=
Answer» `(PI)/(SQRT(2))` `(pi)/(2)` `(3PI)/(sqrt(2))` `pi` ANSWER :A

Discussion

35.	int2xcos3xcos2xdx
Answer» Solution :`INT2XCOS3XCOS2XDX` =`INTX[cos5x+cosx]dx` =`intx.cos5xdx+intx.cosxdx` =`X.(sin5x)/5-int1.(sin5x)/5dx+x.sinx-int1.sinxdx` 1/5.xsin5x+1/25cos5x+xsinx+cosx+C

Discussion

36.	Equation 3sqrt(-2(x+3))-1=\|x+3\|+a has exactly two real roots , then the maximum possiblevalue of \|[a]\| is _________. { where [.] denotes the greatestinteger function } .
Answer» ANSWER :1

Discussion

37.	Evaluate int e^(x + (1)/(x)) ( 1 - (1)/(x^(2)) )dx
Answer» ANSWER :`E^(X + (1)/(x)) `+ C

Discussion

38.	int_0^picos^3xdx
Answer» SOLUTION :`int_0^picos^3xdx=int_0^pi(cos3x+3cosx)/4dx` =`1/4[int_0^picos3xdx+3int_0^picosxdx]` =`1/4{[1/3sin3x]_0^pi+3[SINX]_0^pi}` =`1/12(sin3pi-sin0)+3/4(sinpi-sin0)=0`

Discussion

39.	Area bounded between two latus-rectum of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1, a gt b is ______. (where, e is eccentricity of the ellipse)
Answer» `2b(be+asin^(-1)E)` `8b(be+asin^(-1)e)` `B(be+asin^(-1)e)` `4B(be+asin^(-1)e)` Answer :A

Discussion

40.	A tangent drawn to the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 at P(a "sec" pi/6, b tan pi/6) form a triangle of area 3a^2 sq. units with the coordinate axes. The eccentricity of the conjugatehyperbola of (x^2)/(a^2) - (y^2)/(b^2) = 1 is
Answer» `SQRT(17)` `(SQRT17)/(4)` `(sqrt17)/(2)` `8/(sqrt17)` ANSWER :B

Discussion

41.	Using Mathematical Induction, the number a_(n)'s are defined by a_(0)=1,a_(n+1)=3n^(2)+n+a_(n)(nle0)" then "a_(n)=
Answer» `n^(3)+n^(2)+1` `n^(3)-n^(2)+1` `n^(3)-n^(2)` `n^(3)+n^(2)` Answer :B

Discussion

42.	Prove that the locus of centre of the circle which toches two given disjoint circles externally is hyperbola.
Answer» Solution :As SHOWN in the figure, variable circle S with centre C and RADIUS r touches two GIVEN disjoint CIRCLES `S_(1)` and `S_(2)` having centres `C_(1)` and `C_(2)` and radii `r_(1)` and `r_(2)`, respectively. Clearly, `"CC"_(1)=r+r_(1) and "CC"_(2)=r+r_(2)` `therefore"CC"_(1)-"CC"_(2)=r_(1)-r_(2)(="constant")` Thus, LOCUS of centre C is hyperbola having foci `C_(1) and C_(2)`.

Discussion

43.	Integrate the function 1/((x-a)(x-b)))
Answer»

Discussion

44.	If a,b in R and a ltb, then prove that there exists at least one real number c in(a,b)"such that"(b^(2)+a^(2))/(4c^(2))=(c)/(a+b).
Answer»

Discussion

45.	A coin is tossed 'n' times. Find the probability of getting head an odd number of times.
Answer» ANSWER :`(1)/(2)`

Discussion

46.	If there is an error 0f 0.02 cm in the measurement of the side as 10 cm of a cube, then error in the surface area is
Answer» 1.2 sq.cm 1.4 sq.cm 2.4 sq.cm 3.6 sq.cm Answer :C

Discussion

47.	Evaluate int e^(x) sin 3x cos 3x dx
Answer» Answer :`(E^(X))/(74) ` [ sin 6X -6 cos 6 x ] C

Discussion

48.	Find the area enclosed between the curves y=x^(2)+1,y=2x-2 and the ordinates x=-1 and x = 2
Answer» ANSWER :9

Discussion

49.	-5^(2)
Answer» ANSWER :25

Discussion

50.	If x sqrt(1 + y) + ysqrt(1 + x)= 0, for -1 lt x lt 1, prove that (dy)/(dx) = - (-1)/((1 + x)^(2))
Answer» ANSWER :`(-1)/((1+ X)^(2))`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the Principle values of the following : sec^(-1)(2/(sqrt(3)))

[hati hatk hatj]+[hatk hatj hati]+[hatj hatk hati] is equal to

Find the equation of the circle passing through (0,0) and Making intercept 4 units on Y- axis.

a.a' + b.b' + c.c' =

Prove that the function f given by f(x) = x ^(2) – x + 1 is neither strictly increasing nor decreasing on (– 1, 1).

A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be (i) red (ii) yellow (iii) blue (iv) not blue

The shortest distance from (1,1,1) to the line of intersection of the pair of planes xy+yz+zx+y^(2)=0 is

If the matrix A=[(1,-1),(-1,1)] then A^(n+1)=

PSQ is a focal chord of a parabola whose focus is S and vertex A . PA and QA are produced to meet the directrix in R and T respectively . Then angleRST =

The set S={1,2,3….12} is to be partitioned into three sets A,BC of equal size Thus A cup B cup C =S ,A cap B =B capC=A cap C=varphi the number of ways to partitions S is

x = 1+(3 ) /(1 ! )xx (1 )/(6) +( 3 xx 7 ) /(2 ! )( (1 )/(6) ) ^ 2+ (3 xx 7 xx 11 ) /(3 ! )((1 )/(6))^ 3+… rArrx ^4 =

If x is real , then least value of the expression (ax^(2) + bx + c), a lt 0is :

If a = Sigma_(n=1)^(oo) (2n)/(2n-1!),b=Sigma__(n=1)^(oo) (2n)/(2n+1!) then ab equals

4a-b=-2.25, a+b4.25 If (a, b) satisfies the system of equations above, what is the valeu of a?

The compound statement p rarr (~p vv q) is false. Then the truth values of p and q are respectively

Let the cubic equation x^(3)-ax^(2)+bx-1=0 has only one real root alpha(a lt b) Statemennt -1 alpha lis between 0 and 1 because Statement 2: The value of 2cot^(-1)(coseca)-cot^(-1)(cosec a cos^(2)a)/(2) is pi if a lt 0

If r_1=2r_2=3r_3, then

(d)/(dx )( e^( tan^(-1)x+ cot^(-1) x)) =…….: (xinR)

Consider the equation (x^(2) +x+1) ^(2) - (m-3)(x^(2) +x+1) +m=0, where m is a real parameter. The number of positive integeral values of m for which equation has two distinct real roots, is:

Integrate the rational functions x/((x-1)(x-2)(x-3))

The solution of x^(3)(dy)/(dx)+4x^(2)tan y=e^(x)sec y satisfying y(1) = 0, is

Three vertices of a parallelogram ABCD are A(3,-1,2),B(1,2,-4) and C(-1,1,2). The corrdinates of the fourth vertex is

The phenomenon of interference demonstrates the fact that :

Differentiate the functions given in Exercises 1 to 11 w.r.t. x. sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5))).

A car starts from rest and travels 50 m with uniform acceleration in 5 sec, then acceleration of car is :

Which of the following is endothermic process ?

IFthereare mcopiesof eachof then differerntbooks s thennumberof differentordersinwhichtheycan bearrangedon ashelfis

If int (dx)/(cos^(3) x sqrt(2 sin 2x)) = (tan x)^(A) + C(tan x)^(B) + k ,where K is a costant of integration , then A+B + C equls :

Find the value of x, y,z and w from the equation. [{:(x,3x-y),(2x+z,3y-w):}]=[{:(3,2),(4,7):}]

Find the maximum and minimum values, if any, of thefunctions given by f(x) = – | x + 1| + 3

Evaluation of definite integrals by subsitiution and properties of its : If int(1)/(e^(x)+1)dx=px-qlog|1+e^(x)|+C then p+q=………….

How many integers between 1 and 10^6 have the sum of digits equal to 18.

int_(0)^(pi//4)[sqrt(tanx)+sqrt(cotx)]dx=

int2xcos3xcos2xdx

Equation 3sqrt(-2(x+3))-1=|x+3|+a has exactly two real roots , then the maximum possiblevalue of |[a]| is _________. { where [.] denotes the greatestinteger function } .

Evaluate int e^(x + (1)/(x)) ( 1 - (1)/(x^(2)) )dx

int_0^picos^3xdx

Area bounded between two latus-rectum of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1, a gt b is ______. (where, e is eccentricity of the ellipse)

A tangent drawn to the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 at P(a "sec" pi/6, b tan pi/6) form a triangle of area 3a^2 sq. units with the coordinate axes. The eccentricity of the conjugatehyperbola of (x^2)/(a^2) - (y^2)/(b^2) = 1 is

Using Mathematical Induction, the number a_(n)'s are defined by a_(0)=1,a_(n+1)=3n^(2)+n+a_(n)(nle0)" then "a_(n)=

Prove that the locus of centre of the circle which toches two given disjoint circles externally is hyperbola.

Integrate the function 1/((x-a)(x-b)))

If a,b in R and a ltb, then prove that there exists at least one real number c in(a,b)"such that"(b^(2)+a^(2))/(4c^(2))=(c)/(a+b).

A coin is tossed 'n' times. Find the probability of getting head an odd number of times.

If there is an error 0f 0.02 cm in the measurement of the side as 10 cm of a cube, then error in the surface area is

Evaluate int e^(x) sin 3x cos 3x dx

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

-5^(2)

If x sqrt(1 + y) + ysqrt(1 + x)= 0, for -1 lt x lt 1, prove that (dy)/(dx) = - (-1)/((1 + x)^(2))