14949 + Interview Questions in Maths in Class 11 Page 42 InterviewSolution

2051.	EvaluateC(15,14)
Answer» ANSWER :` 15`

Discussion

2052.	((10),(1)) + ((10),(2))+((11),(3))+((12),(4))+((13),(5))= ........
Answer» `((14),(6))` `((14),(7))` `((13),(6))` `((14),(5))` ANSWER :D

Discussion

2053.	Let f and g be real functions defined by f(x)= 2x + 1 and g(x)= 4x- 7. For what real numbers x, f(x) lt g(x)?
Answer» ANSWER :`X GT 4`

Discussion

2054.	Number of real solutions of the equation (tanx + 1) (tan x + 3) (tan x + 5) (tan x +7)= 33
Answer» will be two in the INTERVAL `[-pi//2, pi//2]` will be FOUR in the interval `[-pi//2, pi//2]` will be three in the interval `[- pi//2, pi]` will be four in the interval `[-pi//2,pi]` ANSWER :A::D

Discussion

2055.	If m= a Cos^(3) theta + 3a Cos theta Sin^(2) theta and n=a Sin^(3) theta + 3 a Cos^(2) theta Sin thetathen (m+n)^(2//3) + (m-n)^(2//3) =
Answer» `2A^(2)` `2a^(1//3)` `2a^(2//3)` `2a^(3)` ANSWER :C

Discussion

2056.	If x= a + b, y= a omega^(2) + b omega, z= a omega + b omega^(2), then show that x^(3)+ y^(3) + z^(3)= 3(a^(3) + b^(3))
Answer» ANSWER :`3(a^(3) + B^(3))`

Discussion

2057.	Usingthe mathematicalinductionshow that for anynaturalnumbern, x^(2n)- y^(2n)is divisibleby(x +y)
Answer» ANSWER :(X +y)

Discussion

2058.	If random variable X has the following probability distribution :
Answer» `(7)/(81)` `(5)/(81)` `(2)/(81)` `(1)/(81)` Solution :`therefore sum_(r=0)^(8)P(X=r)=1` `RARR a+3a+5a+7a+9a+11a+13a+15a+17a=1` `rArr a=(1)/(81)`

Discussion

2059.	Can two different points in the complex plane represent the same complex number? Give reasons for you answer
Answer» ANSWER :No

Discussion

2060.	find the solution of sec x =2
Answer» Answer :`PI/3, (5pi)/(3), 2npi pm (pi)/(3), n in Z`

Discussion

2061.	Evaluate the following limits : Lt_(xto0)((1+x)e^(x)-1)/x
Answer» ANSWER :2

Discussion

2062.	The second, third and sixth terms of an A.P. are consecutive terms of a geometric progression. Find the common ratio of the geometric progression.
Answer» ANSWER :3

Discussion

2063.	f: R rarr R , f(x)=x^(3)-3x^(2)+6x-5 is
Answer» one-one and onto one-one and into onto but not one-one neither one-one nor onto Answer :A

Discussion

2064.	Determine whether or not the four straight lines with equations x+2y-3=0, 3x+4y-7=0, 2x+3y-4=0,4x+5y-6=0 are concurrent.
Answer» ANSWER :(5,-5)

Discussion

2065.	Find the mean deviation from the mean for the followinng data:
Answer» ANSWER :6.32

Discussion

2066.	If a, b, c are respectively the p^(th), q^(th) and r^(th) terms of a G.P., show that (q-r)log a+(r-p)log b+(p-q)log c=0.
Answer» ANSWER :`= 0 = RHS`.

Discussion

2067.	Three students A, B and C participate in the swimming competition. The probability that A and B win the game is same. The probability of B to win the game is twice the probability of C to win the game. Then the probability to win B or C is .......
Answer» `(3)/(5)` `(4)/(5)` `(1)/(5)` 1 Answer :A

Discussion

2068.	Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr1)f(x)where f(x)={(x^(2)+2,xne1),(1,x=1):}
Answer» ANSWER :3

Discussion

2069.	Evaluate Lt_(xto0)(tanx^(0))/x^(0)
Answer» ANSWER :1

Discussion

2070.	Let ABC be an acute angled triangle with orthocenter H. D, E, and F are the feet of perpendicular from A, B, and C, respectively, on opposite sides. Also, let R be the circumradius respectively, on opposite sides. Also, let R be the circumradius of DeltaABC. Given AH.BH.CH=3 and (AH)^(2)+(BH)^(2)+(CH)^(2)=7. then answer the following : Value of HD. HE. HF is
Answer» `(9)/(64R^(2))` `(9)/(8R^(3))` `(8)/(9R^(3))` `(64)/(9R^(3))` Answer :B

Discussion

2071.	Let ABC be an acute angled triangle with orthocenter H. D, E, and F are the feet of perpendicular from A, B, and C, respectively, on opposite sides. Also, let R be the circumradius respectively, on opposite sides. Also, let R be the circumradius of DeltaABC. Given AH.CH.BH=3 and (AH)^(2)+(BH)^(2)+(CH)^(2)=7. then answer the following : Value of R is
Answer» 1 `(3)/(2)` `(5)/(2)` None Answer :B

Discussion

2072.	Let ABC be an acute angled triangle with orthocenter H. D, E, and F are the feet of perpendicular from A, B, and C, respectively, on opposite sides. Also, let R be the circumradius respectively, on opposite sides. Also, let R be the circumradius of DeltABC. Given AH.CH=3 and (AH)^(2)+(BH)^(2)+(CH)^(2)=7. then answer the following : Value of (cosA. cosB cosC)/(cos^(2)A+cos^(2)B+cos^(2)C) is
Answer» `(3)/(14R)` `(3)/(7R)` `(7)/(3R)` `(14)/(3R)` ANSWER :A

Discussion

2073.	If omega is a cube root of unity, then omega^(3)= ……
Answer» ANSWER :1

Discussion

2074.	If Tantheta = (Cos29^(@)+Sin29^(@))/(Cos29^(@)-Sin29^(@))andtheta is acute then theta =
Answer» `16^(@)` `32^(@)` `44^(@)` `74^(@)` ANSWER :D

Discussion

2075.	A straight line passes through (2, 3) and the portion of the line intercepted between the axes is bisected at this point. Find its equation.
Answer» ANSWER : `3x+2y-12=0`

Discussion

2076.	The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)
Answer» are LINEARLY dependent are linearly independent form SIDES of a triangle are coplanar Answer :B

Discussion

2077.	A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there ?
Answer» ANSWER :H = HEAD and T = TAIL

Discussion

2078.	Find the mean deviation about the median for the following data:
Answer» ANSWER :10

Discussion

2079.	Evaluate : lim_(x to 0 ) (3^(x) -2^(x))/(tanx)
Answer» ANSWER :`1/e ( :' Lim_(xto0) (LOG(1+X))/x = 1)`

Discussion

2080.	Write the setA = {1, 4, 9, 16, 25, . . . }in set-builder form.
Answer» ANSWER :`A= {X : x = N^(2)," where "n in N}`

Discussion

2081.	Obtain equation of ellipse satisfying given conditions Major axis is X - axes and passes from points (4,3) and (-1, 4).
Answer» ANSWER :`3X^(2) + 7Y^(2) = 115`

Discussion

2082.	If the area of the triangle formed by the straight lines x=0, y=0 and 3x+4y=a(agt0 is 6. Find the value of a.
Answer» ANSWER :12

Discussion

2083.	Simplify the following (5i) xx 7
Answer» ANSWER :35I

Discussion

2084.	L is the foot of the perpendicular drawn from a point P(3, 4, 5) on the XY-plane. The coordinates of point L are ____ .
Answer» (3, 0, 0) (0, 4, 5) (3, 0, 5) None of these Answer :D

Discussion

2085.	Discuss the global maxima and global minima for f(x) = tan^(-1) x - log_(e)x on [(1)/(sqrt(3)), sqrt(3)]
Answer» Answer :`tan^(-1)""(1)/(sqrt(3)) - ln sqrt(3) = (pi)/(6) - ln""(1)/(sqrt(3))`

Discussion

2086.	Consider the points A (2,3) and B (6,5) Find the co-ordinates of the mid point of the segment joining A and B
Answer» SOLUTION :`(4,-1)`

Discussion

2087.	If 9 boys and 5 girls sit in a row, then probability that 4 particular persons never sit together (not even two of them ) is
Answer» `13/91` `30/91` `13/19` `14/91` ANSWER :B

Discussion

2088.	Find the roots of the equations. Q. 6x^(2)+7x-20=0.
Answer» ANSWER :`1(1)/(3),-2(1)/(2)`.

Discussion

2089.	Let P ( n) = 5^(n) - 2^(n) , P(n) is divisible by 3 lambda and n both are odd positive integers then the least value of n and lambdawill be
Answer» 13 11 1 5 Answer :C

Discussion

2090.	An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events : A : the sum is greater then 8. B : 2 occurs on either die C : the sum is at least 7 and a multiple of 3. Which pairs of these events are mutually exclusive ?
Answer» ANSWER :B and C are mutually EXCLUSIVE EVENTS.

Discussion

2091.	"Cosh"^(-1)(2)=
Answer» 2 3 `log_(E )(1+sqrt(2))` 0 Answer :D

Discussion

2092.	" Evaluate "2+(3)/(2)+1(5)/(8)+…oo.
Answer» SOLUTION :N/a

Discussion

2093.	The median AD of the triangle ABC is bisected at E. BE meets AC in F then AF : AC is
Answer» `3:4` `1:3` `1:2` `1:4` ANSWER :B

Discussion

2094.	Show that the three points (5, 1), (1, -1) and (11, 4) lie on a straight line. Further find its intercepts on the axes
Answer» ANSWER : `3, (-3)/(2)`

Discussion

2095.	If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5. Then, find each of the following f(-2) + g(-1)
Answer» ANSWER :13

Discussion

2096.	cos(n+1) alpha * cos(n-1)alpha + sin (n+1)alpha * sin (n-1) alpha =
Answer» `Cos2n ALPHA` `SIN 2N alpha` `COS 2 alpha` `Sin 2 alpha` Answer :C

Discussion

2097.	Write the negation of the following statements. (i) Both the diagonals of a rectangle have the same length.
Answer» ANSWER :Negation: LENGTH of the both the diagonal are equal is FALSE.

Discussion

2098.	A=[(-4,-1),(3,1)] then the determinant of the matrix (A^(2016)-2.A^(2-15)-A^(2014)) is
Answer» `-175` 2014 2016 `-25` ANSWER :D

Discussion

2099.	f(x) = (2x - sin^(-1))/(2x + tan^(-1) (x)) is continuous at x = 0 then f(0) =
Answer» `1/2` `-(1)/(2)` `(1)/(3)` ` - (1)/(3)` ANSWER :C

Discussion

2100.	The minimum value 4^(x) + 4^(1-x), x in R is
Answer» 2 4 1 0 Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

EvaluateC(15,14)

((10),(1)) + ((10),(2))+((11),(3))+((12),(4))+((13),(5))= ........

Let f and g be real functions defined by f(x)= 2x + 1 and g(x)= 4x- 7. For what real numbers x, f(x) lt g(x)?

Number of real solutions of the equation (tanx + 1) (tan x + 3) (tan x + 5) (tan x +7)= 33

If m= a Cos^(3) theta + 3a Cos theta Sin^(2) theta and n=a Sin^(3) theta + 3 a Cos^(2) theta Sin thetathen (m+n)^(2//3) + (m-n)^(2//3) =

If x= a + b, y= a omega^(2) + b omega, z= a omega + b omega^(2), then show that x^(3)+ y^(3) + z^(3)= 3(a^(3) + b^(3))

Usingthe mathematicalinductionshow that for anynaturalnumbern, x^(2n)- y^(2n)is divisibleby(x +y)

If random variable X has the following probability distribution :

Can two different points in the complex plane represent the same complex number? Give reasons for you answer

find the solution of sec x =2

Evaluate the following limits : Lt_(xto0)((1+x)e^(x)-1)/x

The second, third and sixth terms of an A.P. are consecutive terms of a geometric progression. Find the common ratio of the geometric progression.

f: R rarr R , f(x)=x^(3)-3x^(2)+6x-5 is

Determine whether or not the four straight lines with equations x+2y-3=0, 3x+4y-7=0, 2x+3y-4=0,4x+5y-6=0 are concurrent.

Find the mean deviation from the mean for the followinng data:

If a, b, c are respectively the p^(th), q^(th) and r^(th) terms of a G.P., show that (q-r)log a+(r-p)log b+(p-q)log c=0.

Three students A, B and C participate in the swimming competition. The probability that A and B win the game is same. The probability of B to win the game is twice the probability of C to win the game. Then the probability to win B or C is .......

Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr1)f(x)where f(x)={(x^(2)+2,xne1),(1,x=1):}

Evaluate Lt_(xto0)(tanx^(0))/x^(0)

If omega is a cube root of unity, then omega^(3)= ……

If Tantheta = (Cos29^(@)+Sin29^(@))/(Cos29^(@)-Sin29^(@))andtheta is acute then theta =

A straight line passes through (2, 3) and the portion of the line intercepted between the axes is bisected at this point. Find its equation.

The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there ?

Find the mean deviation about the median for the following data:

Evaluate : lim_(x to 0 ) (3^(x) -2^(x))/(tanx)

Write the setA = {1, 4, 9, 16, 25, . . . }in set-builder form.

Obtain equation of ellipse satisfying given conditions Major axis is X - axes and passes from points (4,3) and (-1, 4).

If the area of the triangle formed by the straight lines x=0, y=0 and 3x+4y=a(agt0 is 6. Find the value of a.

Simplify the following (5i) xx 7

L is the foot of the perpendicular drawn from a point P(3, 4, 5) on the XY-plane. The coordinates of point L are ____ .

Discuss the global maxima and global minima for f(x) = tan^(-1) x - log_(e)x on [(1)/(sqrt(3)), sqrt(3)]

Consider the points A (2,3) and B (6,5) Find the co-ordinates of the mid point of the segment joining A and B

If 9 boys and 5 girls sit in a row, then probability that 4 particular persons never sit together (not even two of them ) is

Find the roots of the equations. Q. 6x^(2)+7x-20=0.

Let P ( n) = 5^(n) - 2^(n) , P(n) is divisible by 3 lambda and n both are odd positive integers then the least value of n and lambdawill be

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events : A : the sum is greater then 8. B : 2 occurs on either die C : the sum is at least 7 and a multiple of 3. Which pairs of these events are mutually exclusive ?

"Cosh"^(-1)(2)=

" Evaluate "2+(3)/(2)+1(5)/(8)+…oo.

The median AD of the triangle ABC is bisected at E. BE meets AC in F then AF : AC is

Show that the three points (5, 1), (1, -1) and (11, 4) lie on a straight line. Further find its intercepts on the axes

If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5. Then, find each of the following f(-2) + g(-1)

cos(n+1) alpha * cos(n-1)alpha + sin (n+1)alpha * sin (n-1) alpha =

Write the negation of the following statements. (i) Both the diagonals of a rectangle have the same length.

A=[(-4,-1),(3,1)] then the determinant of the matrix (A^(2016)-2.A^(2-15)-A^(2014)) is

f(x) = (2x - sin^(-1))/(2x + tan^(-1) (x)) is continuous at x = 0 then f(0) =

The minimum value 4^(x) + 4^(1-x), x in R is