14949 + Interview Questions in Maths in Class 11 Page 156 InterviewSolution

7751.	The rainfall and the output of wheat per acre for a firm are as follows: Find the correlation coefficient between rainfall and wheat production.
Answer» ANSWER :`-0.17`

Discussion

7752.	If vec(a)= 4vec(i) + 5vec(j)- vec(k), vec(b)= vec(i)- 4vec(j) + 5vec(k) and vec(c )= 3vec(i) + vec(j)- vec(k), the find vector vec(alpha) which is perpendicular to both vec(a), vec(b) and vec(alpha).vec(c )= 21
Answer» ANSWER :`7vec(i)-7vec(J)-7vec(K)`

Discussion

7753.	Which of the following sentences are statements? Give reasons for your answer The sides of a quadrilateral have equal length.
Answer» Answer :This SENTENCE is sometimes true and sometimes false. For example, SQUARES and rhombus have EQUAL LENGTH whereas rectangles and trapezium have unequal length. Therefore, it is not a statement.

Discussion

7754.	Sketch the region represented by y ge1
Answer» ANSWER :`y=1`

Discussion

7755.	The minimum value of 4e^(x)+9e^(-x) is
Answer» 5 25 12 13 Answer :C

Discussion

7756.	Simplify: (1- 3omega + omega^(2)) (1 + omega- 3omega^(2))
Answer» ANSWER :16

Discussion

7757.	Let A (2,3,5), B(-1,5,-1) and C(4,-3,2) be the vertices of a DeltaABC Find the sides AB,BC and AC
Answer» SOLUTION :`7,sqrt98,7`

Discussion

7758.	The new equation of the curve 4(x-2y+1)^(2)+9(2x+y+2)^(2)=25, if the lines 2x+y+2=0 and x-2y+1=0 are taken as the new x and y axes respectively is
Answer» `9X^(2)+4y^(2)=5` `4x^(2)+9y^(2)=25` `9x^(2)+4y^(2)=7` `4x^(2)+9y^(2)=49` Answer :A

Discussion

7759.	If it is known that the third term of the binomial expanison (x+x ^(log 10 x))^5 "is " 10 ^6 then x is equal to
Answer» 10 `10^(-5//2)` 100 5 Answer :A::B

Discussion

7760.	Find the ratio in which the xZ-plane divides the line joining(-3,4,-8) and(5,-6,4) and write the co-ordinate of the point of division.
Answer» ANSWER :`2:1,((7)/(3),(8)/(3),0)`

Discussion

7761.	A quadratic ax^(2) + bx + c = 0distinctcoefficientis formed. If a , b, carechosenform thenumber 2,3,5them theprobabilitythat theequationhasreal roots is
Answer» `(1)/(2)` `(2)/(5)` `(1)/(4)` `(1)/(5)` ANSWER :A

Discussion

7762.	If theta in [0, 5 pi] and r in Rsuch that 2 sin theta = r^(4) - 2 r^(2) + 3 then the maximum number of values of the pair (r, theta) is
Answer» 8 10 6 4 Answer :C

Discussion

7763.	Show that Tan9-Tan27-Tan63+Tan81=4
Answer» ANSWER :` = 2 [1+1] =2(4) = 4 = RHS`

Discussion

7764.	Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students from Class XI who are in the school football team. Find X ∪ Y and interpret the set.
Answer» Answer :{RAM, Geeta, AKBAR, David, ASHOK}

Discussion

7765.	A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. A cup B cup C
Answer» ANSWER :`= {4, 5}`

Discussion

7766.	The value of (sin50^(@))/(sin130^(@)) is …………
Answer» ANSWER :1

Discussion

7767.	A and B are mutually exclusive events. P(A)=0.38, then P(AcapB')=…….
Answer» 0.38 1 0.12 0.62 Answer :A

Discussion

7768.	In [0,1], Lagrange's mean value theorem is not applicable to
Answer» `F(X) = {:{((1)/(2) -x,x lt (1)/(2)),(((1)/(2)-x)^(2),xge(1)/(2)):}` `f(x) ={:{((SINX )/(x),","x cancel(=)0),(1,","0):}` `f(x) = x\|x\|` `f(x) = \|x\|` Answer :A

Discussion

7769.	construct truthtable for(p ^^q) v (~p ^^ q)
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E04_024_A01##)`

Discussion

7770.	f(x) is differentiable function sattisfying the relationship f^2(x) + f^2 (y) + 2(xy - 1) = f^(2) (x + y) AA x, y in R . Also f(x)gt 0 A x in R, and f(sqrt2) = 2 . Then which of the following statements is//are correct about f(x)?
Answer» `[f(3) = 3([.] "is GIF")` `f(SQRT(7)) = 3` `f(X)` is even `f'(0) = 0` ANSWER :A::B::C::D

Discussion

7771.	If x in (-1,1) prove that 2Tan^(-1)x="Tan"^(-1)(2x)/(1-x^(2))
Answer» ANSWER :`2TAN^(-1)X`

Discussion

7772.	Find foot of perpendicular from point (2,3) on the line x+y+1=0.
Answer» ANSWER :`(5,6)`

Discussion

7773.	ABC is a triangle, P is a point on AB and Q is a point on AC such that angle AQP = angle ABC. Complete the "Area of " Delta APQ (.... relation ("Area of " Delta APQ)/("Area of " Delta ABC) = (…)/(AC^(2)).
Answer» `AP^(2)` `AB^(2)` `AQ^(2)` NONE Answer :A

Discussion

7774.	The period of tan theta+ tan (theta+(pi)/(3)) +tan (theta+(2pi)/(3)) is
Answer» `(PI)/(2)` `pi` `2PI` `(pi)/(3)` ANSWER :D

Discussion

7775.	If in a triangle ABC, in the usual notation, 2a cos ((B-C)/(2))=b+c and Be neC. Then the measure of the angle A is
Answer» `(pi)/(3)` `(pi)/(4)` `(pi)/(6)` `(pi)/(2)` Answer :A

Discussion

7776.	A rod of length / slides with its ends on two perpendicular lines. Find the locus of its mid-point.
Answer» ANSWER : `4X^(2)+4Y^(2)=L^(2)`

Discussion

7777.	7 le ((3x+11))/(2) le 11.
Answer» ANSWER :`[1, (11)/(3)]`

Discussion

7778.	The value of sum_(n=1)^(oo)(tan""((theta)/(2^n)))/(2^(n-1)cos""(theta)/(2^n-1)) is
Answer» `2/(SIN2THETA)-1/theta` `2/(sin2theta)+1/theta` `1/(sin2theta)-1/theta` `1/(SINTHETA)-1/theta` ANSWER :A

Discussion

7779.	Show that the following statement is true by the method of contrapositive.P: If x is an integer andx^(2) is even, then x is also even.
Answer» Answer :The STATEMENT is of the form "If p, then q'. Let q be false, i.e.,let X be not even => x=2n+1, Where n is an INTEGER . => `x^(2)=(2n -: 1)2=4n^(2) -:4n+1=4(n^(2)+n)+1=1` more then an even number =>`x^(2)` is odd i.e., If q is not true, then p is not true is proved. Hence, the GIVEN statement is true.

Discussion

7780.	Express the following in the form a+ib. (i) (5+sqrt(2)i)/(1-sqrt(2)i), (ii) i^(-35)
Answer» ANSWER :`1+2 SQRT(2) (II) i`

Discussion

7781.	If the angle subtended at the centre of a circle of diameter 50 cm by an arc of length 11 cm is theta radians.Find the angle subtended above in degree (use pi=22/7)
Answer» SOLUTION :`25^@12.`

Discussion

7782.	Find the derivative of the following functions: secx
Answer» ANSWER :`SECXTANX`

Discussion

7783.	If \|y\| = sin (x) and y = cos x are two given equations, then the number of solutions is (where [*] denotesthe greatest integer function )
Answer» 2 3 4 infinitely MANY solutions Answer :D

Discussion

7784.	For interval (-1, 1) which of the following statements is true?
Answer» `-1 in (-1, 1)` `0 in (-1, 1)` `(-1, 1)= (-1, 1)` `(-1, 1)= {PHI}` ANSWER :B

Discussion

7785.	Assertion (A) : If a line make angles 45^(@), 45^(@) with the x and y axis repectively then it makes angle 60^(@) with z - axis Reason (R ) : If alpha,beta,lambda are the angle made by a line with the coordinate axes then cos^(2) alpha + cos^(2)beta + cos^(2) lambda = 1
Answer» Both A and R are ture and R is the CORRECT explanation of A Both A and R are true but R is the correct explanation of A A is true but R is FALSE A is false but R is true Answer :D

Discussion

7786.	(d)/(dx)(x+\|x\|)\|x\|=……..(xlt0)
Answer» 1 0 2 4 Answer :B

Discussion

7787.	There are 5 gentleman and 4 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are together?
Answer» ANSWER :` 2880 `

Discussion

7788.	Find the value of k if the lines (3x+4y+5)-k(x+y+3)=0 is (i) parallel to y-axis (ii) parallel to x-axis.
Answer» ANSWER :(i) k=4 (II) k=3

Discussion

7789.	sin{2(sin^(-1)""sqrt(5)/3-cos^(-1)""sqrt(5)/3)} is equal to (ksqrt(5))/81 then k =
Answer» ANSWER :8

Discussion

7790.	Two ships leave a port at the same time . One goes 24km per hour in the directionN45^(@)E and other travels 32km per hour in the directionS 75 ^(@) E.Find the distance between the ships at the end of 3 hours
Answer» ANSWER :` 86. 4 ` KM ( APPROX)

Discussion

7791.	Evaluate : lim_(xto 0) (e^(sinx)-1)/x
Answer» ANSWER :1

Discussion

7792.	If A and B are symmetric matrices of order n,where(A ne B),then:
Answer» A+B is SKEW -SYMMETRIC A+B is symmetric A+B is symmetric A+B is a ZERO matrix ANSWER :A::B::C

Discussion

7793.	The vectors equation of the plane which is per-pendicular to 2bari -3barj+bark and at a distance of 5 units from the origin is
Answer» `BARR.(2bari-3barj+bark)=5` `barrxx(2bari-3barj+bark)=5` `barr.(2bari-3barj+bark)/(SQRT(14))=5` none Answer :C

Discussion

7794.	sin[cot^(-1){cos(tan^(-1)x)}]=
Answer» `SQRT((X^(2)+2)/(x^(2)+1))` `sqrt((x^(2)+1)/(x^(2)+2))` `x/(sqrt(x^(2)+2))` `1/(sqrt(x^(2)+2))` Answer :B

Discussion

7795.	If a finite set S contains n elements, then the number of non empty proper subsets of S is
Answer» `2.2^(N-1)` `2(2^(n)-1)` `2^(n-1)-1)` `2(2^(n-1)-1)` ANSWER :D

Discussion

7796.	If (1+x-2x^2)^(6) = 1 + a_(1) x + a_(2) x^(2) + ... + a_(12) x^(12), then finda_2+ a_4 + ... + a_12
Answer» ANSWER :31

Discussion

7797.	If z=3-2i then show that z^(2)-6z+13=0 Hence find the value of z^(4)-4z^(3)+6z^(2)-4z+17
Answer» ANSWER :-48

Discussion

7798.	Find the sum: 5+ 13+ 21+ …..+ 181
Answer» ANSWER :2139

Discussion

7799.	(sin (n +1) A +2sin n A + sin ( n -1) A )/( cos (n +1) A - cos ( n -1) A )=
Answer» `TAN A//2` `COT A//2` `tan A ` `cot A` ANSWER :B

Discussion

7800.	Which of the following are sets? Justify your answer : The collection of best cricketer of India.
Answer» ANSWER :it is not a SET

Discussion

Explore topic-wise InterviewSolutions in .

The rainfall and the output of wheat per acre for a firm are as follows: Find the correlation coefficient between rainfall and wheat production.

If vec(a)= 4vec(i) + 5vec(j)- vec(k), vec(b)= vec(i)- 4vec(j) + 5vec(k) and vec(c )= 3vec(i) + vec(j)- vec(k), the find vector vec(alpha) which is perpendicular to both vec(a), vec(b) and vec(alpha).vec(c )= 21

Which of the following sentences are statements? Give reasons for your answer The sides of a quadrilateral have equal length.

Sketch the region represented by y ge1

The minimum value of 4e^(x)+9e^(-x) is

Simplify: (1- 3omega + omega^(2)) (1 + omega- 3omega^(2))

Let A (2,3,5), B(-1,5,-1) and C(4,-3,2) be the vertices of a DeltaABC Find the sides AB,BC and AC

The new equation of the curve 4(x-2y+1)^(2)+9(2x+y+2)^(2)=25, if the lines 2x+y+2=0 and x-2y+1=0 are taken as the new x and y axes respectively is

If it is known that the third term of the binomial expanison (x+x ^(log 10 x))^5 "is " 10 ^6 then x is equal to

Find the ratio in which the xZ-plane divides the line joining(-3,4,-8) and(5,-6,4) and write the co-ordinate of the point of division.

A quadratic ax^(2) + bx + c = 0distinctcoefficientis formed. If a , b, carechosenform thenumber 2,3,5them theprobabilitythat theequationhasreal roots is

If theta in [0, 5 pi] and r in Rsuch that 2 sin theta = r^(4) - 2 r^(2) + 3 then the maximum number of values of the pair (r, theta) is

Show that Tan9-Tan27-Tan63+Tan81=4

Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students from Class XI who are in the school football team. Find X ∪ Y and interpret the set.

A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. A cup B cup C

The value of (sin50^(@))/(sin130^(@)) is …………

A and B are mutually exclusive events. P(A)=0.38, then P(AcapB')=…….

In [0,1], Lagrange's mean value theorem is not applicable to

construct truthtable for(p ^^q) v (~p ^^ q)

f(x) is differentiable function sattisfying the relationship f^2(x) + f^2 (y) + 2(xy - 1) = f^(2) (x + y) AA x, y in R . Also f(x)gt 0 A x in R, and f(sqrt2) = 2 . Then which of the following statements is//are correct about f(x)?

If x in (-1,1) prove that 2Tan^(-1)x="Tan"^(-1)(2x)/(1-x^(2))

Find foot of perpendicular from point (2,3) on the line x+y+1=0.

ABC is a triangle, P is a point on AB and Q is a point on AC such that angle AQP = angle ABC. Complete the "Area of " Delta APQ (.... relation ("Area of " Delta APQ)/("Area of " Delta ABC) = (…)/(AC^(2)).

The period of tan theta+ tan (theta+(pi)/(3)) +tan (theta+(2pi)/(3)) is

If in a triangle ABC, in the usual notation, 2a cos ((B-C)/(2))=b+c and Be neC. Then the measure of the angle A is

A rod of length / slides with its ends on two perpendicular lines. Find the locus of its mid-point.

7 le ((3x+11))/(2) le 11.

The value of sum_(n=1)^(oo)(tan""((theta)/(2^n)))/(2^(n-1)cos""(theta)/(2^n-1)) is

Show that the following statement is true by the method of contrapositive.P: If x is an integer andx^(2) is even, then x is also even.

Express the following in the form a+ib. (i) (5+sqrt(2)i)/(1-sqrt(2)i), (ii) i^(-35)

If the angle subtended at the centre of a circle of diameter 50 cm by an arc of length 11 cm is theta radians.Find the angle subtended above in degree (use pi=22/7)

Find the derivative of the following functions: secx

If |y| = sin (x) and y = cos x are two given equations, then the number of solutions is (where [*] denotesthe greatest integer function )

For interval (-1, 1) which of the following statements is true?

Assertion (A) : If a line make angles 45^(@), 45^(@) with the x and y axis repectively then it makes angle 60^(@) with z - axis Reason (R ) : If alpha,beta,lambda are the angle made by a line with the coordinate axes then cos^(2) alpha + cos^(2)beta + cos^(2) lambda = 1

(d)/(dx)(x+|x|)|x|=……..(xlt0)

There are 5 gentleman and 4 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are together?

Find the value of k if the lines (3x+4y+5)-k(x+y+3)=0 is (i) parallel to y-axis (ii) parallel to x-axis.

sin{2(sin^(-1)""sqrt(5)/3-cos^(-1)""sqrt(5)/3)} is equal to (ksqrt(5))/81 then k =

Two ships leave a port at the same time . One goes 24km per hour in the directionN45^(@)E and other travels 32km per hour in the directionS 75 ^(@) E.Find the distance between the ships at the end of 3 hours

Evaluate : lim_(xto 0) (e^(sinx)-1)/x

If A and B are symmetric matrices of order n,where(A ne B),then:

The vectors equation of the plane which is per-pendicular to 2bari -3barj+bark and at a distance of 5 units from the origin is

sin[cot^(-1){cos(tan^(-1)x)}]=

If a finite set S contains n elements, then the number of non empty proper subsets of S is

If (1+x-2x^2)^(6) = 1 + a_(1) x + a_(2) x^(2) + ... + a_(12) x^(12), then finda_2+ a_4 + ... + a_12

If z=3-2i then show that z^(2)-6z+13=0 Hence find the value of z^(4)-4z^(3)+6z^(2)-4z+17

Find the sum: 5+ 13+ 21+ …..+ 181

(sin (n +1) A +2sin n A + sin ( n -1) A )/( cos (n +1) A - cos ( n -1) A )=

Which of the following are sets? Justify your answer : The collection of best cricketer of India.