43030 + Interview Questions in Mathematics Page 116 InterviewSolution

5751.	f:R→R is a function satisfying the propertyf(2x+3)+f(2x+7)=2 ∀ x∈R, then the fundamental period of f(x) is
Answer» $f : R \to R$ is a function satisfying the property $f (2 x + 3) + f (2 x + 7) = 2 \forall x \in R,$ then the fundamental period of $f (x)$ is

Discussion

5752.	16th term in the expansion of (√x−√y)17 is
Answer» $16^{t h}$ term in the expansion of $(\sqrt{x} - \sqrt{y})^{17}$ is

Discussion

5753.	If x3+x−5=0 has atleast one real solution in (a,b); where a,b∈Z, then (a+b)=
Answer» If $x^{3} + x - 5 = 0$ has atleast one real solution in $(a, b);$ where $a, b \in Z$ , then $(a + b) =$

Discussion

5754.	Let X represents the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?
Answer» Let X represents the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?

Discussion

5755.	If f(x)=x2 and g(x)=2x+1 are two real function. Find f+g(x)
Answer» If $f (x) = x^{2}$ and $g (x) = 2 x + 1$ are two real function. Find $f + g (x)$

Discussion

5756.	How many terms of the A.P, -6, −112,−5 ........... are needed to give the sum -25 ?
Answer» How many terms of the A.P, -6, $\frac{- 11}{2}, - 5$ ........... are needed to give the sum -25 ?

Discussion

5757.	From a deck of 52 cards, four cards arc drawn simultaneously, find the chance that they will be the four honours of the same suit.
Answer» From a deck of 52 cards, four cards arc drawn simultaneously, find the chance that they will be the four honours of the same suit.

Discussion

5758.	The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is
Answer» The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is

Discussion

5759.	limx→π63sinx−√3cosx6x−π=
Answer» $lim x \to \frac{π}{6} \frac{3 sin x - \sqrt{3} cos x}{6 x - π} =$

Discussion

5760.	Integration of Sin x to the power 6 + cos x to the power 6 sin square x .Cos square x
Answer» Integration of Sin x to the power 6 + cos x to the power 6 sin square x .Cos square x

Discussion

5761.	If Na={an:n∈N} , then N3∩N4 =
Answer» If $N_{a} = {a n : n \in N}$ , then $N_{3} \cap N_{4}$ =

Discussion

5762.	The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors, →a,→b and →c respectively. Then, choose the correct relation for these vectors.
Answer» The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors, $\to a, \to b$ and $\to c$ respectively. Then, choose the correct relation for these vectors.

Discussion

5763.	If x=at2, y=2at, then d2xdy2=
Answer» If $x = a t^{2}, y = 2 a t,$ then $\frac{d^{2} x}{d y^{2}} =$

Discussion

5764.	The solutions of quadratic equation 3x2−5x+2=0 are
Answer» The solutions of quadratic equation $3 x^{2} - 5 x + 2 = 0$ are

Discussion

5765.	A straight line through A(6, 8) meets the curve 2x2+y2=2 at B and C. P is a point on BC such that AB, AP, AC are in H.P, then the minimum distance of the origin from the locus of ‘P’ is
Answer» A straight line through A(6, 8) meets the curve $2 x^{2} + y^{2} = 2$ at B and C. P is a point on BC such that AB, AP, AC are in H.P, then the minimum distance of the origin from the locus of ‘P’ is

Discussion

5766.	Let R be the set of all binary relations on the set {1,2,3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is 0.125
Answer» Let $R$ be the set of all binary relations on the set ${1, 2, 3}$ . Suppose a relation is chosen from $R$ at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is 0.125

Discussion

5767.	Apparent dips when dip circle is placed in two mutually perpendicular directions are 30^° and 45 What is actualdip at that place?
Answer» Apparent dips when dip circle is placed in two mutually perpendicular directions are 30^° and 45 What is actualdip at that place?

Discussion

5768.	If A=⎡⎢⎣0c−b−c0ab−a0⎤⎥⎦ and B=⎡⎢⎣a2abacabb2bcacbcc2⎤⎥⎦, then AB=
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & c & - b - c & 0 & a b & - a & 0 \end{matrix} ⎤ ⎥ ⎦$ and $B = ⎡ ⎢ ⎣ \begin{matrix} a^{2} & a b & a c a b & b^{2} & b c a c & b c & c^{2} \end{matrix} ⎤ ⎥ ⎦$ , then $A B =$

Discussion

5769.	plot graph of x^3 -9x^2
Answer» plot graph of x^3 -9x^2

Discussion

5770.	Prove that :((tan60+1)÷(tan60−1))2=(1+cos30)÷(1−cos30)
Answer» Prove that : $((tan 60 + 1) \div (tan 60 - 1))^{2} = (1 + cos 30) \div (1 - cos 30)$

Discussion

5771.	The maximum value of z = 4x + 2y subject to the constraints 2x+3y≤18, x+y≤10, x≥0, y≥0, is ____________.
Answer» The maximum value of z = 4x + 2y subject to the constraints $2 x + 3 y \leq 18, x + y \leq 10, x \geq 0, y \geq 0,$ is ____________.

Discussion

5772.	Find the term independent of x in the expansion of (2x2+1x)9
Answer» Find the term independent of x in the expansion of $(2 x^{2} + \frac{1}{x})^{9}$

Discussion

5773.	The number of integral solutions of the equation x+y+z+t=20, such that x≥0,y≥1,z≥2,t≥3, is
Answer» The number of integral solutions of the equation $x + y + z + t = 20,$ such that $x \geq 0, y \geq 1, z \geq 2, t \geq 3,$ is

Discussion

5774.	If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to(a) 0(b) −1(c) 1(d) None of these
Answer» If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to (a) 0 (b) −1 (c) 1 (d) None of these

Discussion

5775.	If z1 = 0, z2 = 3, z3 = 4i and z4 = 5 + 12 i then minimum value of \|z – z1\| + \|z – z2\| + \|z – z3\| + \|z – z4\| is equal to
Answer» If z1 = 0, z2 = 3, z3 = 4i and z4 = 5 + 12 i then minimum value of \|z – z1\| + \|z – z2\| + \|z – z3\| + \|z – z4\| is equal to

Discussion

5776.	If (sec A – tan A) = x then prove that 1+x21-x2= cosec A.
Answer» If (sec A – tan A) = x then prove that $\frac{1 + x^{2}}{1 - x^{2}}$ = cosec A.

Discussion

5777.	The value of 61/2×61/4×61/8×⋯∞ is
Answer» The value of $6^{1 / 2} \times 6^{1 / 4} \times 6^{1 / 8} \times \dots \infty$ is

Discussion

5778.	Pair the multiplication statements with the correct arrangement.
Answer» Pair the multiplication statements with the correct arrangement.

Discussion

5779.	Which is not the correct statement for zero order rxn ? (a)dx/dt = k[a0] (b)at=a0-Kt (c)log(a0-at)=logk+logt (d)1/(a0-at) =1/t + 1/k
Answer» Which is not the correct statement for zero order rxn ? (a)dx/dt = k[a0] (b)at=a0-Kt (c)log(a0-at)=logk+logt (d)1/(a0-at) =1/t + 1/k

Discussion

5780.	The solution of the equationdydx=3x−4y−23x−4y−3 is
Answer» The solution of the equation $\frac{d y}{d x} = \frac{3 x - 4 y - 2}{3 x - 4 y - 3}$ is

Discussion

5781.	If limx→∞(1+ax+bx2)2x=e2, then the value of a and b can be
Answer» If $lim x \to \infty {(1 + \frac{a}{x} + \frac{b}{x^{2}})}^{2 x} = e^{2},$ then the value of $a$ and $b$ can be

Discussion

5782.	Which one of following species has plane triangular shape ; NO2- , NO3- ?
Answer» Which one of following species has plane triangular shape ; NO2- , NO3- ?

Discussion

5783.	Examine the continuity of the function f(x)=2x2−1 at x = 3.
Answer» Examine the continuity of the function $f (x) = 2 x^{2} - 1$ at x = 3.

Discussion

5784.	If x + 12 = 12 + 7, then by commutativity of addition x =(a) 12 (b) 7 (c) 19 (d) 5
Answer» If x + 12 = 12 + 7, then by commutativity of addition x = (a) 12 (b) 7 (c) 19 (d) 5

Discussion

5785.	34.Y = tan\lbrack5/2Π t +Π/6\rbrack.Then dy/dt when t=0
Answer» 34.Y = tan\lbrack5/2Π t +Π/6\rbrack.Then dy/dt when t=0

Discussion

5786.	In what ratio does the point (-4, 6) internally divide the line segment joining the points A(-6, 10) and B(3, -8).
Answer» In what ratio does the point (-4, 6) internally divide the line segment joining the points A(-6, 10) and B(3, -8).

Discussion

5787.	The value(s) of k for which the quadratic equations (1−2k)x2−6kx−1=0 and kx2−x+1=0 have at least one root in common, is (are)
Answer» The value(s) of $k$ for which the quadratic equations $(1 - 2 k) x^{2} - 6 k x - 1 = 0$ and $k x^{2} - x + 1 = 0$ have at least one root in common, is (are)

Discussion

5788.	If f( n + 1) = f (n) + n for all n ≥ 0 or f (0) = 1 then f (200) equals
Answer» If f( n + 1) = f (n) + n for all n ≥ 0 or f (0) = 1 then f (200) equals

Discussion

5789.

Following are the marks obtained,out of 100 by two students Ravi and Hashina in 10 tests: Ravi: 25 50 45 30 70 42 36 48 35 60 Hashina: 10 70 50 20 95 55 42 60 48 80 Who is more intelligent and who is more consistent? [NCERT EXEMPLAR]

Answer» Following are the marks obtained,out of 100 by two students Ravi and Hashina in 10 tests:

Ravi:	25	50	45	30	70	42	36	48	35	60
Hashina:	10	70	50	20	95	55	42	60	48	80

Who is more intelligent and who is more consistent? [NCERT EXEMPLAR]

Discussion

5790.	If y=1x, then the value of dy√1+y4+dx√1+x4+1 is equal to
Answer» If $y = \frac{1}{x},$ then the value of $\frac{d y}{\sqrt{1 + y^{4}}} + \frac{d x}{\sqrt{1 + x^{4}}} + 1$ is equal to

Discussion

5791.	For what values of ?
Answer» For what values of ?

Discussion

5792.	If θ denotes the acute angle between the curves, y=10−x2 and y=2+x2 at a point of their intersection, then \|tanθ\| is equal to :
Answer» If $θ$ denotes the acute angle between the curves, $y = 10 - x^{2}$ and $y = 2 + x^{2}$ at a point of their intersection, then $\| tan θ \|$ is equal to :

Discussion

5793.	If f is a function such that f(0)=2,f(1)=3 and f(x+2)=2f(x)–f(x+1) for every real x, then f(5)–10= ___
Answer» If $f$ is a function such that $f (0) = 2, f (1) = 3$ and $f (x + 2) = 2 f (x) - f (x + 1)$ for every real $x$ , then $f (5) - 10 =$ ___

Discussion

5794.	Prove that:sec3π2-xsecx-5π2+tan5π2+xtanx-3π2=-1.
Answer» Prove that: $\sec (\frac{3 π}{2} - x) \sec (x - \frac{5 π}{2}) + \tan (\frac{5 π}{2} + x) \tan (x - \frac{3 π}{2}) = - 1 .$

Discussion

5795.	If n(∪)=700, n(A)=200, n(B)=300 and n(A∩B)=100, then n(A′∩B′)= ___.
Answer» $If n (\cup) = 700, n (A) = 200, n (B) = 300$ and $n (A \cap B) = 100,$ then $n (A^{^{'}} \cap B^{^{'}}) =$ ___.

Discussion

5796.	Number of circle(s) touching all the lines 3x+4y−1=0,4x−5y+2=0 and 6x+8y+3=0 is
Answer» Number of circle(s) touching all the lines $3 x + 4 y - 1 = 0, 4 x - 5 y + 2 = 0 and 6 x + 8 y + 3 = 0$ is

Discussion

5797.	Assume X , Y , Z , W and P are matrices of order , and respectively. If n = p , then the order of the matrix is A p × 2 B 2 × n C n × 3 D p × n
Answer» Assume X , Y , Z , W and P are matrices of order , and respectively. If n = p , then the order of the matrix is A p × 2 B 2 × n C n × 3 D p × n

Discussion

5798.	Lef f,g and h be differentiable functions. If f(0)=1, g(0)=2, h(0)=3 and the derivatives of their pairwise products at x=0 are (fg)′(0)=6, (gh)′(0)=4 and (hf)′(0)=5, then the value of (fgh)′(0) is
Answer» Lef $f, g$ and $h$ be differentiable functions. If $f (0) = 1,$ $g (0) = 2,$ $h (0) = 3$ and the derivatives of their pairwise products at $x = 0$ are $(f g)^{'} (0) = 6,$ $(g h)^{'} (0) = 4$ and $(h f)^{'} (0) = 5,$ then the value of $(f g h)^{'} (0)$ is

Discussion

5799.	Let a, b, c be the sides of the triangle. No two of them are equal and λ∈R.If the roots of the equation x2+2(a+b+c)x+3λ(ab+bc+ca)=0 are real then :
Answer» Let a, b, c be the sides of the triangle. No two of them are equal and $λ \in R$ . If the roots of the equation $x^{2} + 2 (a + b + c) x + 3 λ (a b + b c + c a) = 0$ are real then :

Discussion

5800.	If the arithmetic mean of the roots of the equation x (x – 2) + 4ax = 5 is 3, then a = ________.
Answer» If the arithmetic mean of the roots of the equation x (x – 2) + 4ax = 5 is 3, then a = ________.

Discussion

Explore topic-wise InterviewSolutions in .

f:R→R is a function satisfying the propertyf(2x+3)+f(2x+7)=2 ∀ x∈R, then the fundamental period of f(x) is

16th term in the expansion of (√x−√y)17 is

If x3+x−5=0 has atleast one real solution in (a,b); where a,b∈Z, then (a+b)=

Let X represents the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?

If f(x)=x2 and g(x)=2x+1 are two real function. Find f+g(x)

How many terms of the A.P, -6, −112,−5 ........... are needed to give the sum -25 ?

From a deck of 52 cards, four cards arc drawn simultaneously, find the chance that they will be the four honours of the same suit.

The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is

limx→π63sinx−√3cosx6x−π=

Integration of Sin x to the power 6 + cos x to the power 6 sin square x .Cos square x

If Na={an:n∈N} , then N3∩N4 =

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors, →a,→b and →c respectively. Then, choose the correct relation for these vectors.

If x=at2, y=2at, then d2xdy2=

The solutions of quadratic equation 3x2−5x+2=0 are

A straight line through A(6, 8) meets the curve 2x2+y2=2 at B and C. P is a point on BC such that AB, AP, AC are in H.P, then the minimum distance of the origin from the locus of ‘P’ is

Let R be the set of all binary relations on the set {1,2,3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is 0.125

Apparent dips when dip circle is placed in two mutually perpendicular directions are 30^° and 45 What is actualdip at that place?

If A=⎡⎢⎣0c−b−c0ab−a0⎤⎥⎦ and B=⎡⎢⎣a2abacabb2bcacbcc2⎤⎥⎦, then AB=

plot graph of x^3 -9x^2

Prove that :((tan60+1)÷(tan60−1))2=(1+cos30)÷(1−cos30)

The maximum value of z = 4x + 2y subject to the constraints 2x+3y≤18, x+y≤10, x≥0, y≥0, is ____________.

Find the term independent of x in the expansion of (2x2+1x)9

The number of integral solutions of the equation x+y+z+t=20, such that x≥0,y≥1,z≥2,t≥3, is

If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to(a) 0(b) −1(c) 1(d) None of these

If z1 = 0, z2 = 3, z3 = 4i and z4 = 5 + 12 i then minimum value of |z – z1| + |z – z2| + |z – z3| + |z – z4| is equal to

If (sec A – tan A) = x then prove that 1+x21-x2= cosec A.

The value of 61/2×61/4×61/8×⋯∞ is

Pair the multiplication statements with the correct arrangement.

Which is not the correct statement for zero order rxn ? (a)dx/dt = k[a0] (b)at=a0-Kt (c)log(a0-at)=logk+logt (d)1/(a0-at) =1/t + 1/k

The solution of the equationdydx=3x−4y−23x−4y−3 is

If limx→∞(1+ax+bx2)2x=e2, then the value of a and b can be

Which one of following species has plane triangular shape ; NO2- , NO3- ?

Examine the continuity of the function f(x)=2x2−1 at x = 3.

If x + 12 = 12 + 7, then by commutativity of addition x =(a) 12 (b) 7 (c) 19 (d) 5

34.Y = tan\lbrack5/2Π t +Π/6\rbrack.Then dy/dt when t=0

In what ratio does the point (-4, 6) internally divide the line segment joining the points A(-6, 10) and B(3, -8).

The value(s) of k for which the quadratic equations (1−2k)x2−6kx−1=0 and kx2−x+1=0 have at least one root in common, is (are)

If f( n + 1) = f (n) + n for all n ≥ 0 or f (0) = 1 then f (200) equals

Following are the marks obtained,out of 100 by two students Ravi and Hashina in 10 tests: Ravi: 25 50 45 30 70 42 36 48 35 60 Hashina: 10 70 50 20 95 55 42 60 48 80 Who is more intelligent and who is more consistent? [NCERT EXEMPLAR]

If y=1x, then the value of dy√1+y4+dx√1+x4+1 is equal to

For what values of ?

If θ denotes the acute angle between the curves, y=10−x2 and y=2+x2 at a point of their intersection, then |tanθ| is equal to :

If f is a function such that f(0)=2,f(1)=3 and f(x+2)=2f(x)–f(x+1) for every real x, then f(5)–10= ___

Prove that:sec3π2-xsecx-5π2+tan5π2+xtanx-3π2=-1.

If n(∪)=700, n(A)=200, n(B)=300 and n(A∩B)=100, then n(A′∩B′)= ___.

Number of circle(s) touching all the lines 3x+4y−1=0,4x−5y+2=0 and 6x+8y+3=0 is

Assume X , Y , Z , W and P are matrices of order , and respectively. If n = p , then the order of the matrix is A p × 2 B 2 × n C n × 3 D p × n

Lef f,g and h be differentiable functions. If f(0)=1, g(0)=2, h(0)=3 and the derivatives of their pairwise products at x=0 are (fg)′(0)=6, (gh)′(0)=4 and (hf)′(0)=5, then the value of (fgh)′(0) is

Let a, b, c be the sides of the triangle. No two of them are equal and λ∈R.If the roots of the equation x2+2(a+b+c)x+3λ(ab+bc+ca)=0 are real then :

If the arithmetic mean of the roots of the equation x (x – 2) + 4ax = 5 is 3, then a = ________.