14949 + Interview Questions in Maths in Class 11

1.	If""^(56)P_(r+6) : ""^(54)P_(r+3)= 30800,then r is
Answer» 40 51 101 410

Discussion

2.	If the pair of line ax^2+2hxy+by^2+2gx+2fy+c=0 intersect on the y-axis, then
Answer» `2fgh=bg^2+ch^2` `bg^2nech^2` `abc=2fgh` `2fgh=af+ch^2` ANSWER :A

Discussion

3.	If7 cos ^(2) x + sin x cos x - 3then x =
Answer» `X = n pi + (3 pi)/(4), n in Z` `x = K pi + TAN^(-1) ((4)/(3)), k in Z` `x = k + tan^(-1) ((4)/(3)) , k in Z` `x = n pi + (pi)/(3), n in Z` Answer :A::B

Discussion

4.	IF 13,14,15 are the sides of the triangle , then the area of the triangle in sq. unit is
Answer» ` 84 ` ` 72` ` 56` ` 68` ANSWER :A

Discussion

5.	If in a triangle ABC , a^(2) Cos^(2) A = b^(2) + c^(2) , then
Answer» `0LT A LT PI/4` `pi/4 lt A lt pi/2` `pi/2 lt A lt pi` `A = pi/2` ANSWER :C

Discussion

6.	The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
Answer» ANSWER :160

Discussion

7.	Which among the following represents the sequence whose n^th terms is n/(n+1)
Answer» 1,2,3,4,5,6 2,3,4,5,6 `2, 3/2, 4/3, 5/4, 6/5` `1/2, 2/3, 3/4, 4/5, 5/6` ANSWER :D

Discussion

8.	Lt_(x to oo)((1)/(3.5)+(1)/(5.7)+.....+(1)/((2n+1)(2n+3)))=
Answer» ANSWER :`1/6`

Discussion

9.	Two sides of a rhombus lying in the first quadrant are given by 3x-4y=0 and 12x-5y=0. The length of the longer diagonal is 12. If the equations of other two sides are 3x-4y+180/sqrta=0 and 12x-5y=468/sqrta " then " (a-40)/10=
Answer» ANSWER :9

Discussion

10.	Draw the graphs of the following : y = x^(3) if -2,2
Answer» ANSWER :`(##AKS_ELT_AI_MAT_XI_VIB_P02_C01_E01_023_A01##)`

Discussion

11.	Express the following in the form a+bi, where a and b are real numbers ((3 + sqrt5i) (3-sqrt5i))/((sqrt3+sqrt2i)- (sqrt3-sqrt2i))
Answer» ANSWER :`-(7 SQRT2)/(2)i`

Discussion

12.	For complex number z = 5 + 3i value z -barz=10.
Answer» ANSWER :FALSE STATEMENT

Discussion

13.	4 cards are drawn from a pack of 52 cards .What is the probability of obtaining 3 diamonds and a spade ?
Answer» ANSWER :`(""^(13)C_(3).""^(13)C_(1))/(""^(52)C_(4))`

Discussion

14.	Let f(x)=(2^(x)-1)(2^(x)-2)andg(x)=2sinx+cos2xin [0,pi] {:("Column -I","Column -II"),((A)"f increases on",(P)(log_(2)(3//2),oo)),((B)"f decreases on",(Q)(-oo,log_(2)(3//2))),((C)"g decreases on",(R)(0,(pi)/(6))),((D)"g increases on",(S)((5pi)/(6),pi)):}
Answer» ANSWER :A-p,;B-q;C-s;D-r

Discussion

15.	Middle term in the expansion of (a^(3)+ba)^(28) " is " ……
Answer» Answer :` :. "Middle TERM in given EXPANSION " {:((28),(14)):}a^(56) xx B^(14)`

Discussion

16.	(a)A drawer contains 50 bolts and 150 unts . Half of the bolts and half of the nuts are rusted . If one item is chosen at random , what is the probability that it is rusted or a bolt ?
Answer» ANSWER :`=(1)/(3)`

Discussion

17.	If tan""(alpha)/(2)andtan""(beta)/(2) are roots of the equation 8x^(2)-26x+15=0 then cos(alpha+beta) = …………
Answer» `-(627)/(725)` `(627)/(725)` `-1` NONE of these Answer :A

Discussion

18.	Consider the points A (1,2,3), B(2,3,1) and C(3,1,2).Find AB,BC and CA
Answer» SOLUTION :`SQRT6, sqrt6, sqrt6]`

Discussion

19.	Identify the type of ''Or'' used in the following statements and check whether the statements are true or false: To enter into a public library children need an identity card from the school or a letter from the school authorities.
Answer» ANSWER :1

Discussion

20.	Identify the type of ''Or'' used in the following statements and check whether the statements are true or false: A rectangle is a quadrilateral or a 5-sided polygon.
Answer» ANSWER :1

Discussion

21.	Identify the type of ''Or'' used in the following statements and check whether the statements are true or false: sqrt2 is a rational number or an irrational number
Answer» ANSWER :1

Discussion

22.	The mean and standard deviation of marks obtained by 50 students of a class in three subjects , mathematics, physics and chemistry are given below: Which of the three subjects shows the highest variability in marks and which shows the lowest?
Answer» ANSWER :48.9

Discussion

23.	Use the binomial theorem to find the exact value of (10.1)^(5).
Answer» ANSWER :`=105101.00501`.

Discussion

24.	For all sets A and B, (A - B) cup (A cap B)= A.
Answer» ANSWER :1

Discussion

25.	Find the derivative with respect to x of the following: (iii) 3x^(2) + (3)/( x^2)
Answer» ANSWER :`6X - (6)/( x^3)`

Discussion

26.	Consider the lines represented parametrically ass L _(1) x =1 - 2t, y = t, z =-1 + t , L _(2) x =4 + S, y = 5 + 4 S, z =-2 2-S. Let pi bet he plane containing the line L _(2) and parallel to line L _(1) The acute angle between the lines L _(1) and L _(2) is
Answer» `5x + y + 9z - 7 =0` `9x - 5y - Z - 13 =0` `2x - 3Y - 4Z - 15 =0` `5x - y + 9z + 3=0` ANSWER :A

Discussion

27.	The solution of sin^(4) x=1+cos^(6) x is x=
Answer» `2n PI+(pi)/(2), n in Z` `n pi, n in Z` `n pi+(pi)/(2), n in Z` `2n pi, n in Z` ANSWER :C

Discussion

28.	Find the angles of the triangle whose sides are x+y-4=0, 2x+y-6=0, 5x+3y-15=0
Answer» ANSWER :`(4/(SQRT(17)))`

Discussion

29.	Calculate the mean and standard deviation of first n natural numbers.
Answer» ANSWER :`(N^(2)-1)/12`

Discussion

30.	Solve the equations: x^(4)-5x^(2)+6=0.
Answer» ANSWER :`pmsqrt(3),pmsqrt(2)`.

Discussion

31.	If Sin^(2) theta + 3 Cos theta -2 =0 then Cos^(3) theta + Sec^(3) theta =
Answer» 9 16 18 1 Answer :C

Discussion

32.	Evaluate the following limits : Lim_(x to oo) ((x+6)/(x+1))^(x+4)
Answer» ANSWER :`E^(a//b)`

Discussion

33.	Write the equations for the x-and y-axes.
Answer» ANSWER :`y = 0 " and " X = 0 `

Discussion

34.	Let (c cos x)/( 2 cos 2 x - 1) = (b + sin x)/( (cos^(2) x - 3 sin^(2) x)tan x), b in R Equation has solutions if
Answer» `b in (- infty, (1)/(2))- {-1,0,(1)/(3)}` `b in (- infty, 1) - {- 1, 0, (1)/(3)}` `b in R - {-1,0,(1)/(3)}` `b in (- infty, (1)/(2))` ANSWER :A

Discussion

35.	The volume of the rectangular box whose coterminal edges along axes of magnitude 2,3, 4 is
Answer» 9 12 24 48 Answer :C

Discussion

36.	cos{(2pi)/(2^(64)-1)}cos{(2^2pi)/(2^(64)-1)}......cos{(2^(64)pi)/(2^(64)-1)}=
Answer» `1/(16^(16))` `1/8^8` `1/(32^(32))` `1/(64^(64))` ANSWER :A

Discussion

37.	If x = a cos^(3) theta sin^(2) theta,y = a sin^(3) theta cos^(2) thea and (x^(2)+y^(2))^(p)/((xy)^(q)),(p,q in N)is independent of theta then
Answer» <P>p + Q = 6 4p = 5q 4q = 5p pq = 16 Answer :B

Discussion

38.	Express the following functions as set of ordered pairs and determine their range. f: x rarr R, f(x)= x^(3) + 1, where x= {-1, 0, 3, 9, 7}
Answer» ANSWER :`f= {0, 1, 28, 730, 344}`

Discussion

39.	How many chords can be drawn through 21 points on a circle?
Answer» ANSWER :210

Discussion

40.	Let R be the set of real numbers. If f:R rarr R is a function defined by f(x)=x^(2), then f is
Answer» inective but not surjective surjective BUTNOT inective bijective neither inective nor surjective Answer :D

Discussion

41.	(i) If (n+1)!=12[(n-1)!], find n(ii)If (n+2)!=60[(n-1)!], find n(iii)If (n+2)!=(2550)(n !), find n.
Answer» ANSWER :(i) 3. (II) 3 (III)49

Discussion

42.	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, (v) either red or blue.
Answer» Answer :`(i) (4)/(9),(II) (2)/(9),(III) (1)/(3),(iv) (2)/(3),(V) (7)/(9)`

Discussion

43.	Show that the function defined by g(x) = x-[x] is a discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.
Answer» ANSWER :X

Discussion

44.	Find n if : P(n, 6 ) = 3( P(n,5)
Answer» ANSWER :` 8`

Discussion

45.	The maximum hight of the curve y=6cosx-8sinx above the x-axis
Answer» 6 8 14 10 Answer :D

Discussion

46.	Length of latus rectum of ellipse is (x^2)/b^2+y^2/a^2 = .......... 1 is (2a^2)/(\|b\|) .
Answer» ANSWER :FALSE STATEMENT

Discussion

47.	cosec ""(360^(@))/(7) + cosec "" (540^(@))/(7)=
Answer» `cosec "" (180^(@))/(7)` `cosec ""^(90^(@))/(7)` `SEC "" (180^(@))/(7)` `sec "" (90^(@))/(7)` Answer :A

Discussion

48.	In what ratio do the coordinate axes divide the line segment joing (-2,5) and (3,-4).
Answer» ANSWER :`5 : 4, 2 : 3 `

Discussion

49.	If A and B are two finite sets , then correct matchof the following is :{:(,"Column -I",,"Column -II",),((i),"(A)'",,(a)A),((ii)AuuA',,(b)U),((iii)AcapA,,(c)AcapB'),((iv)(AuuB),,(d)"phi"):}
Answer» ANSWER :a

Discussion

50.	The probability that Sunil will recelvea D in is matchematics course is 0.61and the probability that he will receive a C is 0.28. What is the probability tat Sunil will receive a C or D in mathematics ?
Answer» ANSWER :`=0.89`.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If""^(56)P_(r+6) : ""^(54)P_(r+3)= 30800,then r is

If the pair of line ax^2+2hxy+by^2+2gx+2fy+c=0 intersect on the y-axis, then

If7 cos ^(2) x + sin x cos x - 3then x =

IF 13,14,15 are the sides of the triangle , then the area of the triangle in sq. unit is

If in a triangle ABC , a^(2) Cos^(2) A = b^(2) + c^(2) , then

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

Which among the following represents the sequence whose n^th terms is n/(n+1)

Lt_(x to oo)((1)/(3.5)+(1)/(5.7)+.....+(1)/((2n+1)(2n+3)))=

Two sides of a rhombus lying in the first quadrant are given by 3x-4y=0 and 12x-5y=0. The length of the longer diagonal is 12. If the equations of other two sides are 3x-4y+180/sqrta=0 and 12x-5y=468/sqrta " then " (a-40)/10=

Draw the graphs of the following : y = x^(3) if -2,2

Express the following in the form a+bi, where a and b are real numbers ((3 + sqrt5i) (3-sqrt5i))/((sqrt3+sqrt2i)- (sqrt3-sqrt2i))

For complex number z = 5 + 3i value z -barz=10.

4 cards are drawn from a pack of 52 cards .What is the probability of obtaining 3 diamonds and a spade ?

Let f(x)=(2^(x)-1)(2^(x)-2)andg(x)=2sinx+cos2xin [0,pi] {:("Column -I","Column -II"),((A)"f increases on",(P)(log_(2)(3//2),oo)),((B)"f decreases on",(Q)(-oo,log_(2)(3//2))),((C)"g decreases on",(R)(0,(pi)/(6))),((D)"g increases on",(S)((5pi)/(6),pi)):}

Middle term in the expansion of (a^(3)+ba)^(28) " is " ……

(a)A drawer contains 50 bolts and 150 unts . Half of the bolts and half of the nuts are rusted . If one item is chosen at random , what is the probability that it is rusted or a bolt ?

If tan""(alpha)/(2)andtan""(beta)/(2) are roots of the equation 8x^(2)-26x+15=0 then cos(alpha+beta) = …………

Consider the points A (1,2,3), B(2,3,1) and C(3,1,2).Find AB,BC and CA

Identify the type of ''Or'' used in the following statements and check whether the statements are true or false: To enter into a public library children need an identity card from the school or a letter from the school authorities.

Identify the type of ''Or'' used in the following statements and check whether the statements are true or false: A rectangle is a quadrilateral or a 5-sided polygon.

Identify the type of ''Or'' used in the following statements and check whether the statements are true or false: sqrt2 is a rational number or an irrational number

The mean and standard deviation of marks obtained by 50 students of a class in three subjects , mathematics, physics and chemistry are given below: Which of the three subjects shows the highest variability in marks and which shows the lowest?

Use the binomial theorem to find the exact value of (10.1)^(5).

For all sets A and B, (A - B) cup (A cap B)= A.

Find the derivative with respect to x of the following: (iii) 3x^(2) + (3)/( x^2)

Consider the lines represented parametrically ass L _(1) x =1 - 2t, y = t, z =-1 + t , L _(2) x =4 + S, y = 5 + 4 S, z =-2 2-S. Let pi bet he plane containing the line L _(2) and parallel to line L _(1) The acute angle between the lines L _(1) and L _(2) is

The solution of sin^(4) x=1+cos^(6) x is x=

Find the angles of the triangle whose sides are x+y-4=0, 2x+y-6=0, 5x+3y-15=0

Calculate the mean and standard deviation of first n natural numbers.

Solve the equations: x^(4)-5x^(2)+6=0.

If Sin^(2) theta + 3 Cos theta -2 =0 then Cos^(3) theta + Sec^(3) theta =

Evaluate the following limits : Lim_(x to oo) ((x+6)/(x+1))^(x+4)

Write the equations for the x-and y-axes.

Let (c cos x)/( 2 cos 2 x - 1) = (b + sin x)/( (cos^(2) x - 3 sin^(2) x)tan x), b in R Equation has solutions if

The volume of the rectangular box whose coterminal edges along axes of magnitude 2,3, 4 is

cos{(2pi)/(2^(64)-1)}cos{(2^2pi)/(2^(64)-1)}......cos{(2^(64)pi)/(2^(64)-1)}=

If x = a cos^(3) theta sin^(2) theta,y = a sin^(3) theta cos^(2) thea and (x^(2)+y^(2))^(p)/((xy)^(q)),(p,q in N)is independent of theta then

Express the following functions as set of ordered pairs and determine their range. f: x rarr R, f(x)= x^(3) + 1, where x= {-1, 0, 3, 9, 7}

How many chords can be drawn through 21 points on a circle?

Let R be the set of real numbers. If f:R rarr R is a function defined by f(x)=x^(2), then f is

(i) If (n+1)!=12[(n-1)!], find n(ii)If (n+2)!=60[(n-1)!], find n(iii)If (n+2)!=(2550)(n !), find n.

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, (v) either red or blue.

Show that the function defined by g(x) = x-[x] is a discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.

Find n if : P(n, 6 ) = 3( P(n,5)

The maximum hight of the curve y=6cosx-8sinx above the x-axis

Length of latus rectum of ellipse is (x^2)/b^2+y^2/a^2 = .......... 1 is (2a^2)/(|b|) .

cosec ""(360^(@))/(7) + cosec "" (540^(@))/(7)=

In what ratio do the coordinate axes divide the line segment joing (-2,5) and (3,-4).

If A and B are two finite sets , then correct matchof the following is :{:(,"Column -I",,"Column -II",),((i),"(A)'",,(a)A),((ii)AuuA',,(b)U),((iii)AcapA,,(c)AcapB'),((iv)(AuuB),,(d)"phi"):}

The probability that Sunil will recelvea D in is matchematics course is 0.61and the probability that he will receive a C is 0.28. What is the probability tat Sunil will receive a C or D in mathematics ?