28278 + Interview Questions in Maths in Class 12

1.	int_(-(pi)/(2))^((pi)/(2))x sinxdxis :
Answer» `-1` `-2` `1` `2` ANSWER :D

Discussion

2.	Fill in the blanks in each of the following, using the answers given against each of them : The lines 3x + ky - 4 = 0 and k - 4y - 3x = 0 are coincident if k = _____ .
Answer» 1 `-4` 4 `-1` ANSWER :C

Discussion

3.	Let be the binary opertion on N given by a b=L.C.M. of a and b. Find (i) 5 7, 20 16 (ii) Is commutative ? (iii) Is associative ? (iv) Find the identity of ? (v) Which elements of N are invertible for the opertion ?
Answer» Answer :(i) `5 7 =35,20 16 =80 ` (II) Yes (III) Yes (IV) 1 (v) 1

Discussion

4.	If A=[(alpha, beta),(gamma, -alpha)] is such that A^(2)=I, then
Answer» `I+alpha^(2)+BETA gamma=0` `I-alpha^(2)+beta gamma=0` `I-alpha^(2)-beta gamma=0` `I+alpha^(2)-beta gamma=0` ANSWER :C

Discussion

5.	Derive the equation of a plane in normal form both in the vector and Cartesian form .
Answer» ANSWER :`lx+my+nz=d`

Discussion

6.	If veca. hati+veca. (2hati+hatj)=veca. (hati+hatj+3hatk)=1 then veca is equal to
Answer» `hati-hatk` `(3hati+3hatj+hatk)//3` `(hati+hatj+hatk)//3` `(3hati-3hatj+hatk)//3` ANSWER :D

Discussion

7.	Evaluate the integrals :I = int_(0)^(1) (x^(3) dx)/(1 + x^(3)) ,
Answer» ANSWER :`(PI)/(16)`

Discussion

8.	Evaluate : (i) int_(-1)^(1)e^(x)dx , (ii) int_(-pi//4)^(pi//4)\|sinx\|dx , (iii) int_(-pi//4)^(pi//4)(x+pi//4)/(2-cos2x)dx (iv) int_(-1)^(1)sin^(5)xcos^(4)x dx, (v) int_(-pi//2)^(pi//2)(g(x)-g(-x))/(f(-x)+f(x))
Answer» SOLUTION :N//A

Discussion

9.	\|(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0)\|=
Answer» `B^(2)-AC` `(b^(2)-ac)(AX^(2)+2bxy+cy^(2))` `ac-b^(2)` `(ac-b^(2))(ax^(2)+2bxy+cy^(2))` ANSWER :B

Discussion

10.	In triangle ABC , prove that sin .(A)/(2)+ sin. (B)/(2) -sin. (C)/(2)=-1+4 cos.(pi-A)/(4)cos. (pi-B)/(4)sin. (pi-C)/(4)
Answer» ANSWER :RHS

Discussion

11.	Assertion (A) : The unknown coefficient of the equation x^(2)+bx+3=0 is determined by throwing an ordinary six faced die. Then the prob. That the equation has real roots is 1//2 Reason (R ) : For the quadratic equation ax^(2)+bx+c=0, condition for real roots is b^(2)-4ac ge 0. Then the correct answer is
Answer» Both A and R are true, R is the correct EXPLANATION of A Both A and R are true, R is not the correct explanation of A A is true but R is FALSE A is false R is true Answer :A

Discussion

12.	Using the I'Hopital Rule prove that, underset(xrarr0^(+))lim(1+x)^((1)/(x))=e
Answer» ANSWER :`E=(1)/(2LOG X)`

Discussion

13.	Given three idential boxes I, II and IIl each containing two coins. In box I, both coins are gold coins, in box II, both are silver coins and in box III, there is one gold coin and one silver coin. A person chooses a box at random and takes out a coin. If the coin is gold, what is the probability that the other coin in the box is also gold.
Answer» ANSWER :`(2)/(3)`

Discussion

14.	show that if. y =sin 3x : then(d^(2)y)/(dx^(2)) + 9y= 0
Answer»

Discussion

15.	As system of line is given as y = mx + c, where m, can take any vlaue out of 1, -1 and when m, is positive this c _(1) can be 1 or -1 when m_(1) equal 0, c_(1)can be 0 or 1 and when m_(1) equals-1 c_(1) can take 0 or 2. Then the area enclosed by all these straight line is
Answer» `(3)/(sqrt2) (sqrt2 -1)` `(3)/(sqrt2)` `3//2` NONE of these Answer :C

Discussion

16.	If A and B are two independent events such that P(A cap B)= (3)/(25)and P(A' cap B)= (8)/(25) , then P(B)= ……….
Answer» `(11)/(25)` `(7)/(25)` `(3)/(11)` `(9)/(11)` Answer :A

Discussion

17.	If a and b are the position vectors of A and B respectively and C is a point on AB producted such that AC = 3 AB, then the position vector of C is
Answer» 3 a -2b 3b -2a 3b +2a 2a - 3b Solution :Let the POSITION vector for C be c. Clearly , B divides AC internally in the ratio 1:2 ` thereforeb=(2a +1.c ) /(2+1)IMPLIES c=3b-2a`

Discussion

18.	If \|z-i\| lt 1, then the value of \|z + 12-6i\| is less than
Answer» 14 2 28 None of these Answer :A

Discussion

19.	Consider f(x) =x^(2)+ax+3 and g(x)=x+bandF(x) =lim_( n to oo)(f(x)+x^(2n)g(x))/(1+x^(2n)) if F(x)is continuousat x=1 , then
Answer» b=a+3 b=a-1 a=b-2 noneof these Answer :A

Discussion

20.	Calculate the greatest and least values of the functionf(x)=(x^4)/(x^8+2x^6-4x^4+8x^2+16)
Answer» Solution :`(1)/(f(x)) = (x^(4) + (16)/(x^(4))) + 2 (x^(2) + (4)/(x^(2))) - 4` Now, `A.M ge G.M` `IMPLIES x^(4) + (16)/(x^(4)) ge 8` and `x^(2) + (4)/(x^(2)) ge 4` `implies (1)/(f(x)) ge 12 implies f(x) le (1)/(12)` Again using `A.M ge G.M` we have `(2x^(6) + 8 x^(2))/(2) ge 4x^(4)` or `2 x^(6) + 8 x^(2) - 4 x^(4) ge 4 x^(4) ge 0` or `x^(8) + 2x^(6) - 4x^(4) + 8x^(2) + 16 lt 0` ALSO, `x^(4) ge 0` `implies (x^(4))/(x^(8) + 2x^(6) - 4x^(8) + 8x^(2) + 16) ge 0` `implies f(x) ge 0` HENCE, the greatest value is 1/12 and the least value is 0

Discussion

21.	Integrate the function in Exercise. x tan^(-1)x
Answer» ANSWER :`(X^(2))/(2)*TAN^(-1)x(x)/(2)+(1)/(2)tan^(-1)x+c`

Discussion

22.	A circle C_1 is drawn having any point P on x-axis as its centre and passingthrough the centre of the circle (C )x^2+y^2=1 . A commontangent to C_1 to C intersects the circle at Q and R respectively. Then Q(x,y) always satisfies
Answer» `x^2-1=0` `x^2+y^2=1` `y^2-1=0` NONE of these ANSWER :A

Discussion

23.	Find the area of the region bounded by y=3^(x) and the lines y = 3 and x = 0.
Answer» ANSWER :`3-((2)/(LN 3))`

Discussion

24.	Find the graph of linear inequation in xy plane y+2 le 0
Answer»

Discussion

25.	Choose the correct answer in the example no . (18) so that statement becomes true .Matrices A and B will be inverse of each other only if ……..
Answer» AB=BA AB =BA =O AB =Q,BA=I AB=BA=I Answer :(D)

Discussion

26.	Find the graph of linear inequation in xy plane x-2 le 0
Answer»

Discussion

27.	The roots of the equation (a+c-b) x^(2)-2cx+(b+c-a)=0 are
Answer» `1, (2C)/(a+c-B)` `1, (b+c-a)/(a+c-b)` `1, (b+c-a)/(2c)` `1, (a+c-b)/(b+c-a)` ANSWER :b

Discussion

28.	Find the graph of linear inequation in xy plane x+4 gt 0
Answer»

Discussion

29.	The value of int(e^(6logx)-e^(5logx))/(e^(4logx)-e^(3logx))dx is equal to
Answer» 1)0 2)`(X^(3))/(3)` 3)`(3)/(x^(3))` 4)`(1)/(x)` Answer :B

Discussion

30.	Find the graph of linear inequation in xy plane 2x-1 ge 0
Answer»

Discussion

31.	If one root ofsqrt(a-x) + sqrt(b+x) = sqrt(a) + sqrt(b)is 2012, then a possible value of (a, b) is:
Answer» ANSWER :`(4024, 2012)`

Discussion

32.	If Q denotes the set of all rational numbers and f(p/q) = sqrt(p^(2) -q^(2)) for any (p)/(q) in Q then observe the following Statements Statement-I : f ((p)/(q)) is real for each (p)/(q) in Q Statement -II : f ((p)/(q)) is a complex number for each (p)/(q) in Q
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 :C

Discussion

33.	If A = [(a,0,0),(0,a,0),(0,0,a)], then det (Adj A) is :
Answer» `a^(27)` `a^(5)` `a^(6)` `a^(2)` ANSWER :C

Discussion

34.	IfD_(30) is the set of all divisors of 30 , x,y in D_(30), we definex+y=LCM(x,y),xy=GCD(x,y), x'=(30)/(x) and f(x,y,z)=(x+y)(y'+z), then f(2,5,15) is equal to
Answer» 2 5 10 15 Solution :`D_(30)={1,2,3,5,6,10,15,30}` `F(2,5,5_=2+5)(5'+15)` `10((30)/(5)+15)` `=10(6+15)` `10*30` `=10`

Discussion

35.	Match the following. {:("I. The coefficient of" x^(-4) "in" (2x-3//x)^8 "is", "a)" ^17 C_10 5^7),( "II. The coefficient of" x^7 "in" (3x^2 //7 + 4//5x^3)^11 "is", "b)"^11 C_3 (3//7)^5 (4//5)^3),( "III. The coefficient of" x "in" (5x^3 - 1 //x^2 )^17 "is", "c)"^8 C_6 2^2 3^6):}
Answer» a, B, c b, c, a c, a, b c, b, a Answer :D

Discussion

36.	If alpha" and "beta, alpha" and "gamma" and "alpha" and "delta are the roots of the equations ax^(2)+2bx+c=0, 2bx^(2)+cx+a=0" and "cx^(2)+ax+2b=0 respectively, where a,b and c are positive real numbers, thenalpha+alpha^(2)=
Answer» `-1` `0` `1` `ABC` ANSWER :A

Discussion

37.	Find the area of the region in the first quadrant enclosed by X-axis and x=sqrt(3)y and the circle x^2+y^2=4.
Answer» ANSWER :`pi/3`

Discussion

38.	Find (dy)/( dx), if y=log( log x)
Answer» ANSWER :`(DY)/( dx) = (1) /( log7) ( 1)/( LOG X) (1)/(x)`

Discussion

39.	Let f:RtoR be a function such that f(x)=x^(3)+x^(2)f'(1)+xf"(2)+f"(3),xinR. Then f(2) equals:
Answer» 30 8 2 `-4` SOLUTION :`f(x)=x^(3)+x^(2)f'(1)+XF"(2)+f"'(3)` f"(3)=6 `f'(x)=3x^(2)+2xf'(1)+f"(2)` `f'(1)=3+2f'(1)+f"(2)` `f'(1)+f"(2)+3=0` …(i) `f"(x)=6x+2f'(1)` f"(2)=12+2f'(1) …(ii) Substitute in (i) `f'(1)+12+2f'(1)+3=0` `rArrf'(1)=-5F"(2)=2` `f(x)=x^(3)-5X^(2)+2x+6` f(2)=2

Discussion

40.	Integrate the functions (3x+7)^3
Answer»

Discussion

41.	Are difference and symmetric difference commutative ? Give reason.
Answer» Solution :An examination was conducted in physics, CHEMISTRY and mathematics. If P.C.M. denote RESPECTIVELY the sets of students who passed in Physics, in Chemistry and in Mathematics, EXPRESS the SET of candidates who passed in all the three subjects USING union , intersection and different symbols.

Discussion

42.	f(x)= {(-4 sin x + cos x",",x le - (pi)/(2)),(a sin x + b",",-(pi)/(2) lt x lt (pi)/(2)),(cos x + 2",",(pi)/(2) le x):}. If f(x) is continuous for x in R, then find the value of a and b.
Answer» ANSWER :`a= -1, B= 3`

Discussion

43.	Write the principal value of [tan^(-1)(-sqrt3)+tan^(-1)(1)].
Answer» ANSWER :`-(PI)/(12)`

Discussion

44.	If \|{:(a,b,a),(b,c,1),(c,a,1):}\|=2010 and if \|{:(c-a,c-b,ab),(a-b,a-c,bc),(b-c,b-a,ca):}\|-\|{:(c-a,c-b,c^(2)),(a-b,a-c,a^(2)),(b-c,b-a,b^(2)):}\|=p , then the number of positive divisors of p is
Answer» <P>`36` `49` `64` `81` Solution :`(d)` `\|{:(C-a,c-b,ab-c^(2)),(a-b,a-c,bc-a^(2)),(b-c,b-a,ca-b^(2)):}\|=\|{:(a,b,1),(b,c,1),(c,a,1):}\|^(2)=(2010)^(2)` `=(2xx3xx6xx67)^(2)=2^(2)3^(2)5^(2)(67)^(2)` No. of divisors of `P=(2+1)(2+1)(2+1)(2+1)=81`

Discussion

45.	Evaluate inte^(3logx)(x^(4)+1)^(-1)dx
Answer» ANSWER :`1/4logabs(X^(4)+1)+C`

Discussion

46.	If a, b, c, d satisfy the equation a + 7b + 3c + 5d = 0, 8a + 4b + 6c + 2d = - 16, 2a + 6b + 4c + 8d =16 5a + 3b + 7c + d = -16 then the value of (a + d) (b + c) =______
Answer» ANSWER :`-16`

Discussion

47.	Using the method of integration find the area of the region bounded by lines : 2x + y = 4, 3x - 2y = 6 and x - 3y + 5 = 0
Answer» ANSWER :`7/2`

Discussion

48.	Evaluate the following:lim_(ntoinfty)(n!)/((n+1)!-n!
Answer» SOLUTION :`lim_(ntoinfty)(N!)/((n+1)!-n!)` `lim_(ntoinfty)(n!)/((n+1)!-n!)` `=lim_(ntoinfty)(n!)/(n!(n+1-1))` `lim_(ntoinfty)1/n=0[THEREFORE(n+1)! =(n+1)! CDOT n!]`

Discussion

49.	((cosA+cos B)/(sinA-sinB))^(2013)+((sin A+sin B)/( cos A-cos B))^(2013)=
Answer» `1` `-1 `0` `2` ANSWER :C

Discussion

50.	Using properties of determinants in Exercise 11 to 15 prove that \|{:(alpha,alpha^2,beta+gamma),(beta,beta^2,gamma+alpha),(gamma,gamma^2,alpha+beta):}\|=(beta-gamma)(gamma-alpha)(alpha+beta+gamma)(alpha-beta)
Answer» ANSWER :`(beta-gamma)(gamma-alpha)(alpha+beta+gamma)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

int_(-(pi)/(2))^((pi)/(2))x sinxdxis :

Fill in the blanks in each of the following, using the answers given against each of them : The lines 3x + ky - 4 = 0 and k - 4y - 3x = 0 are coincident if k = _____ .

Let ** be the binary opertion on N given by a **b=L.C.M. of a and b. Find (i) 5 **7, 20 **16 (ii) Is ** commutative ? (iii) Is ** associative ? (iv) Find the identity of ** ? (v) Which elements of N are invertible for the opertion ** ?

If A=[(alpha, beta),(gamma, -alpha)] is such that A^(2)=I, then

Derive the equation of a plane in normal form both in the vector and Cartesian form .

If veca. hati+veca. (2hati+hatj)=veca. (hati+hatj+3hatk)=1 then veca is equal to

Evaluate the integrals :I = int_(0)^(1) (x^(3) dx)/(1 + x^(3)) ,

Evaluate : (i) int_(-1)^(1)e^(x)dx , (ii) int_(-pi//4)^(pi//4)|sinx|dx , (iii) int_(-pi//4)^(pi//4)(x+pi//4)/(2-cos2x)dx (iv) int_(-1)^(1)sin^(5)xcos^(4)x dx, (v) int_(-pi//2)^(pi//2)(g(x)-g(-x))/(f(-x)+f(x))

|(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0)|=

In triangle ABC , prove that sin .(A)/(2)+ sin. (B)/(2) -sin. (C)/(2)=-1+4 cos.(pi-A)/(4)cos. (pi-B)/(4)sin. (pi-C)/(4)

Using the I'Hopital Rule prove that, underset(xrarr0^(+))lim(1+x)^((1)/(x))=e

show that if. y =sin 3x : then(d^(2)y)/(dx^(2)) + 9y= 0

As system of line is given as y = mx + c, where m, can take any vlaue out of 1, -1 and when m, is positive this c _(1) can be 1 or -1 when m_(1) equal 0, c_(1)can be 0 or 1 and when m_(1) equals-1 c_(1) can take 0 or 2. Then the area enclosed by all these straight line is

If A and B are two independent events such that P(A cap B)= (3)/(25)and P(A' cap B)= (8)/(25) , then P(B)= ……….

If a and b are the position vectors of A and B respectively and C is a point on AB producted such that AC = 3 AB, then the position vector of C is

If |z-i| lt 1, then the value of |z + 12-6i| is less than

Consider f(x) =x^(2)+ax+3 and g(x)=x+bandF(x) =lim_( n to oo)(f(x)+x^(2n)g(x))/(1+x^(2n)) if F(x)is continuousat x=1 , then

Calculate the greatest and least values of the functionf(x)=(x^4)/(x^8+2x^6-4x^4+8x^2+16)

Integrate the function in Exercise. x tan^(-1)x

A circle C_1 is drawn having any point P on x-axis as its centre and passingthrough the centre of the circle (C )x^2+y^2=1 . A commontangent to C_1 to C intersects the circle at Q and R respectively. Then Q(x,y) always satisfies

Find the area of the region bounded by y=3^(x) and the lines y = 3 and x = 0.

Find the graph of linear inequation in xy plane y+2 le 0

Choose the correct answer in the example no . (18) so that statement becomes true .Matrices A and B will be inverse of each other only if ……..

Find the graph of linear inequation in xy plane x-2 le 0

The roots of the equation (a+c-b) x^(2)-2cx+(b+c-a)=0 are

Find the graph of linear inequation in xy plane x+4 gt 0

The value of int(e^(6logx)-e^(5logx))/(e^(4logx)-e^(3logx))dx is equal to

Find the graph of linear inequation in xy plane 2x-1 ge 0

If one root ofsqrt(a-x) + sqrt(b+x) = sqrt(a) + sqrt(b)is 2012, then a possible value of (a, b) is:

If Q denotes the set of all rational numbers and f(p/q) = sqrt(p^(2) -q^(2)) for any (p)/(q) in Q then observe the following Statements Statement-I : f ((p)/(q)) is real for each (p)/(q) in Q Statement -II : f ((p)/(q)) is a complex number for each (p)/(q) in Q

If A = [(a,0,0),(0,a,0),(0,0,a)], then det (Adj A) is :

IfD_(30) is the set of all divisors of 30 , x,y in D_(30), we definex+y=LCM(x,y),x*y=GCD(x,y), x'=(30)/(x) and f(x,y,z)=(x+y)*(y'+z), then f(2,5,15) is equal to

Match the following. {:("I. The coefficient of" x^(-4) "in" (2x-3//x)^8 "is", "a)" ^17 C_10 5^7),( "II. The coefficient of" x^7 "in" (3x^2 //7 + 4//5x^3)^11 "is", "b)"^11 C_3 (3//7)^5 (4//5)^3),( "III. The coefficient of" x "in" (5x^3 - 1 //x^2 )^17 "is", "c)"^8 C_6 2^2 3^6):}

If alpha" and "beta, alpha" and "gamma" and "alpha" and "delta are the roots of the equations ax^(2)+2bx+c=0, 2bx^(2)+cx+a=0" and "cx^(2)+ax+2b=0 respectively, where a,b and c are positive real numbers, thenalpha+alpha^(2)=

Find the area of the region in the first quadrant enclosed by X-axis and x=sqrt(3)y and the circle x^2+y^2=4.

Find (dy)/( dx), if y=log( log x)

Let f:RtoR be a function such that f(x)=x^(3)+x^(2)f'(1)+xf"(2)+f"(3),xinR. Then f(2) equals:

Integrate the functions (3x+7)^3

Are difference and symmetric difference commutative ? Give reason.

f(x)= {(-4 sin x + cos x",",x le - (pi)/(2)),(a sin x + b",",-(pi)/(2) lt x lt (pi)/(2)),(cos x + 2",",(pi)/(2) le x):}. If f(x) is continuous for x in R, then find the value of a and b.

Write the principal value of [tan^(-1)(-sqrt3)+tan^(-1)(1)].

If |{:(a,b,a),(b,c,1),(c,a,1):}|=2010 and if |{:(c-a,c-b,ab),(a-b,a-c,bc),(b-c,b-a,ca):}|-|{:(c-a,c-b,c^(2)),(a-b,a-c,a^(2)),(b-c,b-a,b^(2)):}|=p , then the number of positive divisors of p is

Evaluate inte^(3logx)(x^(4)+1)^(-1)dx

If a, b, c, d satisfy the equation a + 7b + 3c + 5d = 0, 8a + 4b + 6c + 2d = - 16, 2a + 6b + 4c + 8d =16 5a + 3b + 7c + d = -16 then the value of (a + d) (b + c) =______

Using the method of integration find the area of the region bounded by lines : 2x + y = 4, 3x - 2y = 6 and x - 3y + 5 = 0

Evaluate the following:lim_(ntoinfty)(n!)/((n+1)!-n!

((cosA+cos B)/(sinA-sinB))^(2013)+((sin A+sin B)/( cos A-cos B))^(2013)=

Using properties of determinants in Exercise 11 to 15 prove that |{:(alpha,alpha^2,beta+gamma),(beta,beta^2,gamma+alpha),(gamma,gamma^2,alpha+beta):}|=(beta-gamma)(gamma-alpha)(alpha+beta+gamma)(alpha-beta)

Let be the binary opertion on N given by a b=L.C.M. of a and b. Find (i) 5 7, 20 16 (ii) Is commutative ? (iii) Is associative ? (iv) Find the identity of ? (v) Which elements of N are invertible for the opertion ?

IfD_(30) is the set of all divisors of 30 , x,y in D_(30), we definex+y=LCM(x,y),xy=GCD(x,y), x'=(30)/(x) and f(x,y,z)=(x+y)(y'+z), then f(2,5,15) is equal to