43030 + Interview Questions in Mathematics Page 27 InterviewSolution

1301.	If α,β are roots of the equation 6x2+11x+3=0 then
Answer» If $α, β$ are roots of the equation $6 x^{2} + 11 x + 3 = 0$ then

Discussion

1302.	Let minimum value of f(x)=2tan2x+8cot2x,x∈(0,π2) be m. If number of integral values of N for which m+0.2≤log32N≤m+0.8 is (λ⋅241+μ), where λ and μ are co-prime numbers, then the value of (λ+μ) is
Answer» Let minimum value of $f (x) = 2 {tan}^{2} x + 8 {cot}^{2} x, x \in (0, \frac{π}{2})$ be $m .$ If number of integral values of $N$ for which $m + 0.2 \leq {log}_{32} N \leq m + 0.8$ is $(λ \cdot 2^{41} + μ),$ where $λ$ and $μ$ are co-prime numbers, then the value of $(λ + μ)$ is

Discussion

1303.	Three vertices are chosen randomly from the seven vertices of a regular 7 sided polygon. The probability that they form the vertices of an isosceles triangle is
Answer» Three vertices are chosen randomly from the seven vertices of a regular 7 sided polygon. The probability that they form the vertices of an isosceles triangle is

Discussion

1304.	If general solution of the differential equation ydx−xdy(x−y)2=2dx√1−x2 is xx−y+K(sin−1x)=C, then the value of K is (where C is the constant of integration and K∈R )
Answer» If general solution of the differential equation $\frac{y d x - x d y}{(x - y)^{2}} = \frac{2 d x}{\sqrt{1 - x^{2}}}$ is $\frac{x}{x - y} + K ({sin}^{- 1} x) = C,$ then the value of $K$ is (where $C$ is the constant of integration and $K \in R$ )

Discussion

1305.	How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
Answer» How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?

Discussion

1306.	If x=6+5, then x2+1x2-2=_________.
Answer» If $x = \sqrt{6} + \sqrt{5}, then x^{2} + \frac{1}{x^{2}} - 2 =_________.$

Discussion

1307.	Select a figure from the alternatives which when placed in the blank space of (X) would complete the pattern.
Answer» Select a figure from the alternatives which when placed in the blank space of $(X)$ would complete the pattern.

Discussion

1308.	Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+23+49+⋯
Answer» Find the sum of first $n$ terms and the sum of first $5$ terms of the geometric series $1 + \frac{2}{3} + \frac{4}{9} + \dots$

Discussion

1309.	If f : R → R be given by , then f o f ( x ) is (A) (B) x 3 (C) x (D) (3 − x 3 )
Answer» If f : R → R be given by , then f o f ( x ) is (A) (B) x 3 (C) x (D) (3 − x 3 )

Discussion

1310.	7. xy- log y +C
Answer» 7. xy- log y +C

Discussion

1311.	Applying mean value theorem on f(x)=logx ; x∈[1,e], the value of c is
Answer» Applying mean value theorem on $f (x) = log x; x \in [1, e]$ , the value of $c$ is

Discussion

1312.	If y=sin−1[2ax√1−a2x2], ax∈(−1√2,1√2), then dydx is equal to
Answer» If $y = {sin}^{- 1} [2 a x \sqrt{1 - a^{2} x^{2}}], a x \in (- \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$ , then $\frac{d y}{d x}$ is equal to

Discussion

1313.	If A,B,C are the angles of a triangle, then the value of cosA+cosB+cosC=(where r=inradius, R=circumradius)
Answer» If $A, B, C$ are the angles of a triangle, then the value of $cos A + cos B + cos C =$ (where $r =$ inradius, $R =$ circumradius)

Discussion

1314.	The graphs y−2=2x(x2−2) and y+1=x(x2+2) intersect at exactly three distinct points. If all the three points are collinear, then the slope of the line joining these points is
Answer» The graphs $y - 2 = 2 x (x^{2} - 2)$ and $y + 1 = x (x^{2} + 2)$ intersect at exactly three distinct points. If all the three points are collinear, then the slope of the line joining these points is

Discussion

1315.	In a swimming race 3 swimmers compete . The probability of A and B wining is same and twice that of C. What is the probability that B or C wins. Assuming no two finish the race at the same time.
Answer» In a swimming race 3 swimmers compete . The probability of A and B wining is same and twice that of C. What is the probability that B or C wins. Assuming no two finish the race at the same time.

Discussion

1316.	∫sin3x(cos4x+3cos2x+1)tan−1(secx+cosx)dx=
Answer» $\int \frac{{sin}^{3} x}{({cos}^{4} x + 3 {cos}^{2} x + 1) {tan}^{- 1} (sec x + cos x)} d x =$

Discussion

1317.	If \|x\|≤4,\|y\|≤3, then the maximum value of \|x+y\| is
Answer» If $\| x \| \leq 4, \| y \| \leq 3$ , then the maximum value of $\| x + y \|$ is

Discussion

1318.	What is proof of the derivative of sec inverse (x)
Answer» What is proof of the derivative of sec inverse (x)

Discussion

1319.	If π2<x<π, then 1-cos 2x1+cos 2x= ______________.
Answer» If $\frac{π}{2} < x < π,$ then $\sqrt{\frac{1 - \cos 2 x}{1 + \cos 2 x}} =$ ______________.

Discussion

1320.	How is deposit multiplier calculated?
Answer» How is deposit multiplier calculated?

Discussion

1321.	If a2+122a-i=x+iy, find the value of x2+y2.
Answer» If $\frac{{(a^{2} + 1)}^{2}}{2 a - i} = x + i y$ , find the value of $x^{2} + y^{2}$ .

Discussion

1322.	8.What is the current drawn from the battery of 6V
Answer» 8.What is the current drawn from the battery of 6V

Discussion

1323.	Let P=(1xp,p),Q=(1xq,q) and R=(1xr,r), where xk≠0 denotes the kthterm of an H.P. for k∈N. If the area formed by the points P,Q and R is λpqr sq. units, then the value of λ is
Answer» Let $P = (\frac{1}{x_{p}}, p), Q = (\frac{1}{x_{q}}, q)$ and $R = (\frac{1}{x_{r}}, r)$ , where $x_{k} \neq 0$ denotes the $k^{t h}$ term of an H.P. for $k \in N$ . If the area formed by the points $P, Q$ and $R$ is $λ p q r$ sq. units, then the value of $λ$ is

Discussion

1324.	Prove the following trigonometric identities.tan θ+1cos θ2+tan θ-1cos θ2=21+sin2 θ1-sin2 θ
Answer» Prove the following trigonometric identities. ${(\tan θ + \frac{1}{\cos θ})}^{2} + {(\tan θ - \frac{1}{\cos θ})}^{2} = 2 (\frac{1 + \sin^{2} θ}{1 - \sin^{2} θ})$

Discussion

1325.	Find the equation of the curve passing through the point (0,π3) and satisfying the differential equation sinxcosy dx+cosxsiny dy=0, wherex,y∈(0,π2)
Answer» Find the equation of the curve passing through the point $(0, \frac{π}{3})$ and satisfying the differential equation $sin x cos y d x + cos x sin y d y = 0,$ where $x, y \in (0, \frac{π}{2})$

Discussion

1326.	If the line xcosα+ysinα=P touches the curve (xa)m+(yb)m=1, then (acosα)mm−1+(bsinα)mm−1=
Answer» If the line $x cos α + y sin α = P$ touches the curve ${(\frac{x}{a})}^{m} + {(\frac{y}{b})}^{m} = 1,$ then $(a cos α)^{\frac{m}{m - 1}} + (b sin α)^{\frac{m}{m - 1}} =$

Discussion

1327.	The largest interval in which f(x) = x1/x is strictly increasing is ______________.
Answer» The largest interval in which f(x) = x^1/x is strictly increasing is ______________.

Discussion

1328.	5x−6x+6<1
Answer» $\frac{5 x - 6}{x + 6} < 1$

Discussion

1329.	The shortest distance between the curves y2=x3 and 9x2+9y2−30y+16=0 is
Answer» The shortest distance between the curves $y^{2} = x^{3}$ and $9 x^{2} + 9 y^{2} - 30 y + 16 = 0$ is

Discussion

1330.	Find the union of each of the following pairs of sets: (i) X = {1, 3, 5} Y = {1, 2, 3} (ii) A = { a , e , i , o , u } B = { a , b , c } (iii) A = { x : x is a natural number and multiple of 3} B = { x : x is a natural number less than 6} (iv) A = { x : x is a natural number and 1 < x ≤ 6} B = { x : x is a natural number and 6 < x < 10} (v) A = {1, 2, 3}, B = Φ
Answer» Find the union of each of the following pairs of sets: (i) X = {1, 3, 5} Y = {1, 2, 3} (ii) A = { a , e , i , o , u } B = { a , b , c } (iii) A = { x : x is a natural number and multiple of 3} B = { x : x is a natural number less than 6} (iv) A = { x : x is a natural number and 1 < x ≤ 6} B = { x : x is a natural number and 6 < x < 10} (v) A = {1, 2, 3}, B = Φ

Discussion

1331.	Show that the vectors are collinear.
Answer» Show that the vectors are collinear.

Discussion

1332.	The cartesian form of the given plane →r=2^i−^k+t(3^i−^j)+s(2^j+3^k) is
Answer» The cartesian form of the given plane $\to r = 2^i -^k + t (3^i -^j) + s (2^j + 3^k)$ is

Discussion

1333.	\xrightarrow[{A }]{},\xrightarrow[B]{},\xrightarrow[{C }]{} are vectors each having a unit magnitude .if \xrightarrow[A]{}+\xrightarrow[B]{}+\xrightarrow[C]{}=0, then \xrightarrow[A]{}.\xrightarrow[B]{}+\xrightarrow[B]{}.\xrightarrow[C]{}+\xrightarrow[C]{}.\xrightarrow[A]{} will b
Answer» \xrightarrow[{A }]{},\xrightarrow[B]{},\xrightarrow[{C }]{} are vectors each having a unit magnitude .if \xrightarrow[A]{}+\xrightarrow[B]{}+\xrightarrow[C]{}=0, then \xrightarrow[A]{}.\xrightarrow[B]{}+\xrightarrow[B]{}.\xrightarrow[C]{}+\xrightarrow[C]{}.\xrightarrow[A]{} will b

Discussion

1334.	Using elementary transformations, find the inverse of the followng matrix. [2−3−12]
Answer» Using elementary transformations, find the inverse of the followng matrix. $[\begin{matrix} 2 & - 3 - 1 & 2 \end{matrix}]$

Discussion

1335.	Which one of the following is a polynomial?(a) x22-2x2(b) 2x-1(c) x2+3x3/2x(4) x-1x+1
Answer» Which one of the following is a polynomial? (a) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$ (b) $\sqrt{2 x} - 1$ (c) $x^{2} + \frac{3 x^{3 / 2}}{\sqrt{x}}$ (4) $\frac{x - 1}{x + 1}$

Discussion

1336.	If x = 1 + a + a2 .......... to ∞ (\|a\|<1), y = 1 + b + b2 ......... to ∞ (\|b\| < 1), then Z = 1 + ab + a2 b2 + a3 b3..... to ∞ is
Answer» If x = 1 + a + $a^{2}$ .......... to $\infty$ (\|a\|<1), y = 1 + b + $b^{2}$ ......... to $\infty$ (\|b\| < 1), then Z = 1 + ab + $a^{2}$ $b^{2}$ + $a^{3}$ $b^{3}$ ..... to ∞ is

Discussion

1337.	Expandusing Binomial Theorem.
Answer» Expand using Binomial Theorem.

Discussion

1338.	If z1 and z2 are conjugate to each other, and arg(−z1z2)=kπ, then k=
Answer» If $z_{1}$ and $z_{2}$ are conjugate to each other, and $arg (- z_{1} z_{2}) = k π$ , then $k =$

Discussion

1339.	If k∑r=1r=12(n2+11n+30) is true for n∈N, then k= (use principle of mathematical induction)
Answer» If $k \sum r = 1 r = \frac{1}{2} (n^{2} + 11 n + 30)$ is true for $n \in N,$ then $k =$ (use principle of mathematical induction)

Discussion

1340.	If ∫cos5x dx=psinxcosmx+qsin3x+rcosx+C, then the value of 1p+1q+3r−m is equal to (where C is integration constant)
Answer» If $\int {cos}^{5} x d x = p sin x {cos}^{m} x + q sin 3 x + r cos x + C,$ then the value of $\frac{1}{p} + \frac{1}{q} + \frac{3}{r} - m$ is equal to $($ where $C$ is integration constant $)$

Discussion

1341.	Find the domain of the each of the following functions: f(x)=sin−1x+sin−12x
Answer» Find the domain of the each of the following functions: $f (x) = s i n^{- 1} x + s i n^{- 1} 2 x$

Discussion

1342.	139.When a + b + c = x/2, then the value of (x/3 - 2a) + (x/3 - 2b) + (x/3 - 2c) - 3(x/3 - 2a) (x/3 - 2b) (x/3 - 2c) is (1) 0 (2) 1 (3) 3x (4) 6x
Answer» 139.When a + b + c = x/2, then the value of (x/3 - 2a) + (x/3 - 2b) + (x/3 - 2c) - 3(x/3 - 2a) (x/3 - 2b) (x/3 - 2c) is (1) 0 (2) 1 (3) 3x (4) 6x

Discussion

1343.	Find the derivative of the following functions from first principle:(i) −x(ii) (−x)−1(iii) sin(x+1)(iv) cos(x−π8)
Answer» Find the derivative of the following functions from first principle: $(i)$ $- x$ $(i i)$ $(- x)^{- 1}$ $(i i i)$ $sin (x + 1)$ $(i v)$ $cos (x - \frac{π}{8})$

Discussion

1344.	Which of the following functions in the interval's mentioned are one-one functions.
Answer» Which of the following functions in the interval's mentioned are one-one functions.

Discussion

1345.	show that the equation 1/(x-a) +1/(x-b) +1/(x-c)=0can have a pair of equal roots if a=b=
Answer» show that the equation 1/(x-a) +1/(x-b) +1/(x-c)=0can have a pair of equal roots if a=b=

Discussion

1346.	Find the sum of the vectors .
Answer» Find the sum of the vectors .

Discussion

1347.	Solve 2cos2θ+cosθ−1=0
Answer» Solve $2 {cos}^{2} θ + cos θ - 1 = 0$

Discussion

1348.	Two ships leave a port at the same time. One goes 24 km/hr in the direction N 38∘ E and other travels 32 km/hr in the direction S 52∘ E. Find the distance between the ships at fine end of 3 hrs.
Answer» Two ships leave a port at the same time. One goes 24 $k m / h r$ in the direction N $38^{\circ}$ E and other travels 32 $k m / h r$ in the direction S $52^{\circ}$ E. Find the distance between the ships at fine end of 3 hrs.

Discussion

1349.	The Boolean expression (p⇒q)∧(q⇒∼p) is equivalent to
Answer» The Boolean expression $(p \Rightarrow q) \land (q \Rightarrow\sim p)$ is equivalent to

Discussion

1350.	What are the differences between internal and external sources of recruitment?
Answer» What are the differences between internal and external sources of recruitment?

Discussion

Explore topic-wise InterviewSolutions in .

If α,β are roots of the equation 6x2+11x+3=0 then

Let minimum value of f(x)=2tan2x+8cot2x,x∈(0,π2) be m. If number of integral values of N for which m+0.2≤log32N≤m+0.8 is (λ⋅241+μ), where λ and μ are co-prime numbers, then the value of (λ+μ) is

Three vertices are chosen randomly from the seven vertices of a regular 7 sided polygon. The probability that they form the vertices of an isosceles triangle is

If general solution of the differential equation ydx−xdy(x−y)2=2dx√1−x2 is xx−y+K(sin−1x)=C, then the value of K is (where C is the constant of integration and K∈R )

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?

If x=6+5, then x2+1x2-2=_________.

Select a figure from the alternatives which when placed in the blank space of (X) would complete the pattern.

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+23+49+⋯

If f : R → R be given by , then f o f ( x ) is (A) (B) x 3 (C) x (D) (3 − x 3 )

7. xy- log y +C

Applying mean value theorem on f(x)=logx ; x∈[1,e], the value of c is

If y=sin−1[2ax√1−a2x2], ax∈(−1√2,1√2), then dydx is equal to

If A,B,C are the angles of a triangle, then the value of cosA+cosB+cosC=(where r=inradius, R=circumradius)

The graphs y−2=2x(x2−2) and y+1=x(x2+2) intersect at exactly three distinct points. If all the three points are collinear, then the slope of the line joining these points is

In a swimming race 3 swimmers compete . The probability of A and B wining is same and twice that of C. What is the probability that B or C wins. Assuming no two finish the race at the same time.

∫sin3x(cos4x+3cos2x+1)tan−1(secx+cosx)dx=

If |x|≤4,|y|≤3, then the maximum value of |x+y| is

What is proof of the derivative of sec inverse (x)

If π2&lt;x&lt;π, then 1-cos 2x1+cos 2x= ______________.

How is deposit multiplier calculated?

If a2+122a-i=x+iy, find the value of x2+y2.

8.What is the current drawn from the battery of 6V

Let P=(1xp,p),Q=(1xq,q) and R=(1xr,r), where xk≠0 denotes the kthterm of an H.P. for k∈N. If the area formed by the points P,Q and R is λpqr sq. units, then the value of λ is

Prove the following trigonometric identities.tan θ+1cos θ2+tan θ-1cos θ2=21+sin2 θ1-sin2 θ

Find the equation of the curve passing through the point (0,π3) and satisfying the differential equation sinxcosy dx+cosxsiny dy=0, wherex,y∈(0,π2)

If the line xcosα+ysinα=P touches the curve (xa)m+(yb)m=1, then (acosα)mm−1+(bsinα)mm−1=

The largest interval in which f(x) = x1/x is strictly increasing is ______________.

5x−6x+6&lt;1

The shortest distance between the curves y2=x3 and 9x2+9y2−30y+16=0 is

Show that the vectors are collinear.

The cartesian form of the given plane →r=2^i−^k+t(3^i−^j)+s(2^j+3^k) is

\xrightarrow[{A }]{},\xrightarrow[B]{},\xrightarrow[{C }]{} are vectors each having a unit magnitude .if \xrightarrow[A]{}+\xrightarrow[B]{}+\xrightarrow[C]{}=0, then \xrightarrow[A]{}.\xrightarrow[B]{}+\xrightarrow[B]{}.\xrightarrow[C]{}+\xrightarrow[C]{}.\xrightarrow[A]{} will b

Using elementary transformations, find the inverse of the followng matrix. [2−3−12]

Which one of the following is a polynomial?(a) x22-2x2(b) 2x-1(c) x2+3x3/2x(4) x-1x+1

If x = 1 + a + a2 .......... to ∞ (|a|&lt;1), y = 1 + b + b2 ......... to ∞ (|b| &lt; 1), then Z = 1 + ab + a2 b2 + a3 b3..... to ∞ is

Expandusing Binomial Theorem.

If z1 and z2 are conjugate to each other, and arg(−z1z2)=kπ, then k=

If k∑r=1r=12(n2+11n+30) is true for n∈N, then k= (use principle of mathematical induction)

If ∫cos5x dx=psinxcosmx+qsin3x+rcosx+C, then the value of 1p+1q+3r−m is equal to (where C is integration constant)

Find the domain of the each of the following functions: f(x)=sin−1x+sin−12x

139.When a + b + c = x/2, then the value of (x/3 - 2a) + (x/3 - 2b) + (x/3 - 2c) - 3(x/3 - 2a) (x/3 - 2b) (x/3 - 2c) is (1) 0 (2) 1 (3) 3x (4) 6x

Find the derivative of the following functions from first principle:(i) −x(ii) (−x)−1(iii) sin(x+1)(iv) cos(x−π8)

Which of the following functions in the interval's mentioned are one-one functions.

show that the equation 1/(x-a) +1/(x-b) +1/(x-c)=0can have a pair of equal roots if a=b=

Find the sum of the vectors .

Solve 2cos2θ+cosθ−1=0

Two ships leave a port at the same time. One goes 24 km/hr in the direction N 38∘ E and other travels 32 km/hr in the direction S 52∘ E. Find the distance between the ships at fine end of 3 hrs.

The Boolean expression (p⇒q)∧(q⇒∼p) is equivalent to

What are the differences between internal and external sources of recruitment?

If π2<x<π, then 1-cos 2x1+cos 2x= ______________.

5x−6x+6<1

If x = 1 + a + a2 .......... to ∞ (|a|<1), y = 1 + b + b2 ......... to ∞ (|b| < 1), then Z = 1 + ab + a2 b2 + a3 b3..... to ∞ is