43030 + Interview Questions in Mathematics Page 28 InterviewSolution

1351.	3.Compute the indicated products,()212 3 4()21 -211 2 3]3 2 3 111) D2 1(v) 3 22 3 413 54 5 6 3 0 53-1 3(iv) 3 4 50 2 41V(vi)-1 0 2-」131
Answer» 3.Compute the indicated products,()212 3 4()21 -211 2 3]3 2 3 111) D2 1(v) 3 22 3 413 54 5 6 3 0 53-1 3(iv) 3 4 50 2 41V(vi)-1 0 2-」131

Discussion

1352.	56. tan 4theta tan 2theta = 1 then tan 3theta=? 1) 1 2)0 3)1/root3 4) root3
Answer» 56. tan 4theta tan 2theta = 1 then tan 3theta=? 1) 1 2)0 3)1/root3 4) root3

Discussion

1353.	The number of integer(s) in the range of f(x)=sin2x+sin2(x+π3)+cosxcos(x+π3) is
Answer» The number of integer(s) in the range of $f (x) = {sin}^{2} x + {sin}^{2} (x + \frac{π}{3}) + cos x cos (x + \frac{π}{3})$ is

Discussion

1354.	Using properties of determinants prove the following questions. ∣∣∣∣∣αα2β+γββ2γ+αγγ2α+β∣∣∣∣∣=(β−γ)(γ−α)(α−β)(α+β+γ)
Answer» Using properties of determinants prove the following questions. $∣ ∣∣∣ ∣ \begin{matrix} α & α^{2} & β + γ β & β^{2} & γ + α γ & γ^{2} & α + β \end{matrix} ∣ ∣∣∣ ∣ = (β - γ) (γ - α) (α - β) (α + β + γ)$

1354.

Using properties of determinants prove the following questions. ∣∣∣∣∣αα2β+γββ2γ+αγγ2α+β∣∣∣∣∣=(β−γ)(γ−α)(α−β)(α+β+γ)

Answer»

Using properties of determinants prove the following questions.

$∣ ∣∣∣ ∣ \begin{matrix} α & α^{2} & β + γ β & β^{2} & γ + α γ & γ^{2} & α + β \end{matrix} ∣ ∣∣∣ ∣ = (β - γ) (γ - α) (α - β) (α + β + γ)$

Discussion

1355.	let relation R' on the set R of all real numbers be defined as (a, b) R' =1 +ab> 0 for all a, b R. (a) (a, a)R' aR (b) (a, b) R' = (b,a) R' a, b R.
Answer» let relation R' on the set R of all real numbers be defined as (a, b) R' =1 +ab> 0 for all a, b R. (a) (a, a)R' aR (b) (a, b) R' = (b,a) R' a, b R.

Discussion

1356.	The complex number 2n(1+i)2n+(1+i)2n2n, n∈I is equal to
Answer» The complex number $\frac{2^{n}}{(1 + i)^{2 n}} + \frac{(1 + i)^{2 n}}{2^{n}}, n \in I$ is equal to

Discussion

1357.	Find theabsolute maximum and minimum values of the function f given by
Answer» Find the absolute maximum and minimum values of the function f given by

1357.

Find theabsolute maximum and minimum values of the function f given by

Answer»

Find the
absolute maximum and minimum values of the function f given by

Discussion

1358.	If cos−1x>sin−1x then
Answer» If $c o s^{- 1} x > s i n^{- 1} x$ then

Discussion

1359.	If each term of an infinite G.P. is thrice the sum of the terms following it, then the common ratio of the G.P. is .
Answer» If each term of an infinite G.P. is thrice the sum of the terms following it, then the common ratio of the G.P. is .

Discussion

1360.	The product of infinite terms in x12.x14.x18...........∞ is
Answer» The product of infinite terms in $x^{\frac{1}{2}} . x^{\frac{1}{4}} . x^{\frac{1}{8}} . . . . . . . . . . . \infty$ is

Discussion

1361.	The equation ax2+bx+c=0 will be an identity iff
Answer» The equation $a x^{2} + b x + c = 0$ will be an identity iff

Discussion

1362.	If AB is a double ordinate of the hyperbola x2a2−y2b2=1 such that △ABC is equilateral, C being centre of hyperbola, then eccentricity e of hyperbola satisfies
Answer» If $A B$ is a double ordinate of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ such that $△ A B C$ is equilateral, $C$ being centre of hyperbola, then eccentricity $e$ of hyperbola satisfies

Discussion

1363.	Volume of parallelopiped whose coterminous edges are given by →u=^i+^j+λ^k,→v=^i+^j+3^k and →w=2^i+^j+^k is 1 cu. unit. If θ be the angle between the edges →u and →w, then cosθ can be:
Answer» Volume of parallelopiped whose coterminous edges are given by $\to u =^i +^j + λ^k, \to v =^i +^j + 3^k$ and $\to w = 2^i +^j +^k$ is $1$ cu. unit. If $θ$ be the angle between the edges $\to u$ and $\to w$ , then $cos θ$ can be:

Discussion

1364.	Let Sn=n∑k=1k(k−1)4/3+(k2−1)2/3+(k+1)4/3 and limn→∞Snn2/3=1p. Then the value of p is
Answer» Let $S_{n} = n \sum k = 1 \frac{k}{(k - 1)^{4 / 3} + (k^{2} - 1)^{2 / 3} + (k + 1)^{4 / 3}}$ and $lim n \to \infty \frac{S_{n}}{n^{2 / 3}} = \frac{1}{p} .$ Then the value of $p$ is

Discussion

1365.	The total number of straight lines equally inclined with the coordinate axis is ____________.
Answer» The total number of straight lines equally inclined with the coordinate axis is ____________.

Discussion

1366.	I did a question that asked how many 3digit even numbers can be made using the digits 1,2,3,4,5,6,7 if no digit is repeated? then the answer when I checked was fpc=3X5X4=60 But for an even number if only the last digit is even then the number will be even as it is So why it can't be fpc=7X6X3. ?
Answer» I did a question that asked how many 3digit even numbers can be made using the digits 1,2,3,4,5,6,7 if no digit is repeated? then the answer when I checked was fpc=3X5X4=60 But for an even number if only the last digit is even then the number will be even as it is So why it can't be fpc=7X6X3. ?

Discussion

1367.	Find ∫2xx2+1x2+22dx
Answer» Find $\int \frac{2 x}{(x^{2} + 1) {(x^{2} + 2)}^{2}} d x$

Discussion

1368.	Tan 9- tan 27-tan 63+ tan 81
Answer» Tan 9- tan 27-tan 63+ tan 81

Discussion

1369.	Let z1 and z2 be two distinct complex numbers and let z=(1–t)z1+tz2 for some real number t with 0<t<1. If Arg(w) denotes the principal argument of a non-zero complex number w, then
Answer» Let $z_{1}$ and $z_{2}$ be two distinct complex numbers and let $z = (1 - t) z_{1} + t z_{2}$ for some real number $t$ with $0 < t < 1$ . If $Arg (w)$ denotes the principal argument of a non-zero complex number $w$ , then

Discussion

1370.	Find limx→1f(x), if f(x)={x2−1,x≤1−x2−1,x>1
Answer» Find ${lim}_{x \to 1} f (x)$ , if $f (x) = {\begin{matrix} x^{2} - 1, x \leq 1 - x^{2} - 1, x > 1 \end{matrix}$

Discussion

1371.	The number of integral roots of the equation x4+√x4+20=22 is
Answer» The number of integral roots of the equation $x^{4} + \sqrt{x^{4} + 20} = 22$ is

Discussion

1372.	The annual requirement of rivets at a ship manufacturing company is 2000 units. The rivets are supplied in units of 1 kg costing Rs. 25 each. If it costs Rs. 100 to place an order and the annual cost of carrying one unit is 9% of its purchase cost, the cycle length of the order (in days) will be .76.948
Answer» The annual requirement of rivets at a ship manufacturing company is 2000 units. The rivets are supplied in units of 1 kg costing Rs. 25 each. If it costs Rs. 100 to place an order and the annual cost of carrying one unit is 9% of its purchase cost, the cycle length of the order (in days) will be . 76.948

Discussion

1373.	4. Range of sin3x/sinx
Answer» 4. Range of sin3x/sinx

Discussion

1374.	Find thegeneral solution of the equation
Answer» Find the general solution of the equation

Discussion

1375.	If cos−1x>sin−1x then
Answer» If ${cos}^{- 1} x > {sin}^{- 1} x$ then

Discussion

1376.	37. What is meant by rational number and rationalisation Real numbers
Answer» 37. What is meant by rational number and rationalisation Real numbers

Discussion

1377.	Choose the correct answer in the following question: If A is square matrix such that A2=A,then(I+A)3−7A is equal to (a)A (b)I - A (c) I (d)3A
Answer» Choose the correct answer in the following question: If A is square matrix such that $A^{2} = A, t h e n (I + A)^{3} - 7 A$ is equal to (a)A (b)I - A (c) I (d)3A

Discussion

1378.	Direction ratios of two lines are a, b, c and 1bc,1ca,1ab.The lines are
Answer» Direction ratios of two lines are a, b, c and $\frac{1}{b c}, \frac{1}{c a}, \frac{1}{a b}$ .The lines are

Discussion

1379.	The sum of n terms of the series whose nth term is n(n+1) is equal to
Answer» The sum of n terms of the series whose $n^{t h}$ term is n(n+1) is equal to

Discussion

1380.	Let f(x)={x+e2x−1, x<0x2+2λx, x≥0. If f(x) is differentiable at x=0, then the value of 2λ is
Answer» Let $f (x) = {\begin{matrix} x + e^{2 x} - 1, & x < 0 x^{2} + 2 λ x, & x \geq 0 \end{matrix} .$ If $f (x)$ is differentiable at $x = 0,$ then the value of $2 λ$ is

Discussion

1381.	Whar are leptons and mesons?
Answer» Whar are leptons and mesons?

Discussion

1382.	The least positive value of t, so that the lines x=t+α,y+16=0 and y=αx are concurrent, is:
Answer» The least positive value of $t,$ so that the lines $x = t + α, y + 16 = 0$ and $y = α x$ are concurrent, is:

Discussion

1383.	A dice is thrown. What is the probability of getting a composite number ?
Answer» A dice is thrown. What is the probability of getting a composite number ?

Discussion

1384.	The coefficient of x10 in the expansion of [1+x2(1−x)]8 is
Answer» The coefficient of $x^{10}$ in the expansion of $[1 + x^{2} (1 - x)]^{8}$ is

Discussion

1385.	If 9-14-213=A+12-1049, then find matrix A.
Answer» If $[\begin{matrix} 9 & - 1 & 4 \\ - 2 & 1 & 3 \end{matrix}] = A + [\begin{matrix} 1 & 2 & - 1 \\ 0 & 4 & 9 \end{matrix}]$ , then find matrix A.

Discussion

1386.	number of solutions for Mod 2 raised to the power x - 1 + Mod 24 - 2 raise to the power x is smaller than 3 are
Answer» number of solutions for Mod 2 raised to the power x - 1 + Mod 24 - 2 raise to the power x is smaller than 3 are

Discussion

1387.	Let A=Q×Q, where Q is the set of all rational numbers, and ∗ is a binary operation on A defined by (a,b)∗(c,d)=(ac,b+ad) for (a,b),(c,d)∈A. Then find (i) The identity element of ∗ in A. (ii) Invertible elements of A, and hence write the inverse of elements (5,3) and (12,4).
Answer» Let $A = Q \times Q$ , where $Q$ is the set of all rational numbers, and $$ is a binary operation on $A$ defined by $(a, b) (c, d) = (a c, b + a d)$ for $(a, b), (c, d) \in A$ . Then find (i) The identity element of $*$ in $A .$ (ii) Invertible elements of $A,$ and hence write the inverse of elements $(5, 3)$ and $(\frac{1}{2}, 4)$ .

Discussion

1388.	For two independent events A and B, if P(A) = 0.5 and P(B) = 0.3 , then the value of100P(A∪B) = ___
Answer» For two independent events A and B, if P(A) = 0.5 and P(B) = 0.3 , then the value of $100 P (A \cup B)$ = ___

Discussion

1389.	Triangle ABC is isosceles with AC=BC and ∠ACB=106∘. Point M is in the interior of the triangle so that ∠MAC=7∘ and ∠MCA=23∘. Find the number of degrees in ∠CMB. (correct answer + 5, wrong answer 0)
Answer» Triangle $A B C$ is isosceles with $A C = B C$ and $∠ A C B = 106^{\circ} .$ Point $M$ is in the interior of the triangle so that $∠ M A C = 7^{\circ}$ and $∠ M C A = 23^{\circ} .$ Find the number of degrees in $∠ C M B .$ (correct answer + 5, wrong answer 0)

Discussion

1390.	What is the angle between the tangents to the curve y=x2−5x+6 at the points (2, 0) and (3, 0)
Answer» What is the angle between the tangents to the curve $y = x^{2} - 5 x + 6$ at the points (2, 0) and (3, 0)

Discussion

1391.	Prove that: cos2π15 cos4π15 cos 8π15 cos 16π15 =116
Answer» Prove that: $\cos \frac{2 π}{15} \cos \frac{4 π}{15} \cos \frac{8 π}{15} \cos \frac{16 π}{15} = \frac{1}{16}$

Discussion

1392.	If the points (a cosα, a sinα) and (a cosβ, a sinβ) are at a distance k sinα-β2 apart, then k = __________.
Answer» If the points (a cosα, a sinα) and (a cosβ, a sinβ) are at a distance k $\sin (\frac{α - β}{2})$ apart, then k = __________.

Discussion

1393.	A particle moves on a line according to the law s=at2+bt+c. If the displacement after one second is 16 cm, the velocity after 2 seconds is 24 cm/sec and the acceleration is 8 cm/sec2, then (a,b,c)
Answer» A particle moves on a line according to the law $s = a t^{2} + b t + c .$ If the displacement after one second is $16$ cm, the velocity after $2$ seconds is $24$ cm/sec and the acceleration is $8$ cm/sec $^{2},$ then $(a, b, c)$

Discussion

1394.	Prove that summation(0 to infinity) n^2/n!=2e
Answer» Prove that summation(0 to infinity) n^2/n!=2e

Discussion

1395.	The number of solution(s) of log10x=−x is
Answer» The number of solution(s) of ${log}_{10} x = - x$ is

Discussion

1396.	Form the differential equation of the family of circles touching the y -axis at the origin.
Answer» Form the differential equation of the family of circles touching the y -axis at the origin.

Discussion

1397.	If the points (–1, 3, 2), (–4, 2, –2) and (5, 5, λ ) are collinear, then λ =
Answer» If the points (–1, 3, 2), (–4, 2, –2) and (5, 5, $λ$ ) are collinear, then $λ$ =

Discussion

1398.	Findequation of the line perpendicular to the line x – 7y+ 5 = 0 and having x intercept 3.
Answer» Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.

Discussion

1399.	Third term of a GP is 4. What is the product of first 5 terms? a) 1024 b) 2048 c) 1536 d) 4096
Answer» Third term of a GP is 4. What is the product of first 5 terms? a) 1024 b) 2048 c) 1536 d) 4096

1399.

Third term of a GP is 4. What is the product of first 5 terms? a) 1024 b) 2048 c) 1536 d) 4096

Answer»

Third term of a GP is 4. What is the product of first 5 terms?

a) 1024

b) 2048

c) 1536

d) 4096

Discussion

1400.	If A and B are two finite sets such that n(A) > n(B) and the difference of the number of elements of the power sets of A and B is 96, then n(A) – n(B) = ____________.
Answer» If A and B are two finite sets such that n(A) > n(B) and the difference of the number of elements of the power sets of A and B is 96, then n(A) – n(B) = ____________.

Discussion

Explore topic-wise InterviewSolutions in .

3.Compute the indicated products,()212 3 4()21 -211 2 3]3 2 3 111) D2 1(v) 3 22 3 413 54 5 6 3 0 53-1 3(iv) 3 4 50 2 41V(vi)-1 0 2-」131

56. tan 4theta tan 2theta = 1 then tan 3theta=? 1) 1 2)0 3)1/root3 4) root3

The number of integer(s) in the range of f(x)=sin2x+sin2(x+π3)+cosxcos(x+π3) is

Using properties of determinants prove the following questions. ∣∣∣∣∣αα2β+γββ2γ+αγγ2α+β∣∣∣∣∣=(β−γ)(γ−α)(α−β)(α+β+γ)

let relation R' on the set R of all real numbers be defined as (a, b) R' =1 +ab> 0 for all a, b R. (a) (a, a)R' aR (b) (a, b) R' = (b,a) R' a, b R.

The complex number 2n(1+i)2n+(1+i)2n2n, n∈I is equal to

Find theabsolute maximum and minimum values of the function f given by

If cos−1x&gt;sin−1x then

If each term of an infinite G.P. is thrice the sum of the terms following it, then the common ratio of the G.P. is .

The product of infinite terms in x12.x14.x18...........∞ is

The equation ax2+bx+c=0 will be an identity iff

If AB is a double ordinate of the hyperbola x2a2−y2b2=1 such that △ABC is equilateral, C being centre of hyperbola, then eccentricity e of hyperbola satisfies

Volume of parallelopiped whose coterminous edges are given by →u=^i+^j+λ^k,→v=^i+^j+3^k and →w=2^i+^j+^k is 1 cu. unit. If θ be the angle between the edges →u and →w, then cosθ can be:

Let Sn=n∑k=1k(k−1)4/3+(k2−1)2/3+(k+1)4/3 and limn→∞Snn2/3=1p. Then the value of p is

The total number of straight lines equally inclined with the coordinate axis is ____________.

I did a question that asked how many 3digit even numbers can be made using the digits 1,2,3,4,5,6,7 if no digit is repeated? then the answer when I checked was fpc=3X5X4=60 But for an even number if only the last digit is even then the number will be even as it is So why it can't be fpc=7X6X3. ?

Find ∫2xx2+1x2+22dx

Tan 9- tan 27-tan 63+ tan 81

Let z1 and z2 be two distinct complex numbers and let z=(1–t)z1+tz2 for some real number t with 0&lt;t&lt;1. If Arg(w) denotes the principal argument of a non-zero complex number w, then

Find limx→1f(x), if f(x)={x2−1,x≤1−x2−1,x&gt;1

The number of integral roots of the equation x4+√x4+20=22 is

4. Range of sin3x/sinx

Find thegeneral solution of the equation

If cos−1x&gt;sin−1x then

37. What is meant by rational number and rationalisation Real numbers

Choose the correct answer in the following question: If A is square matrix such that A2=A,then(I+A)3−7A is equal to (a)A (b)I - A (c) I (d)3A

Direction ratios of two lines are a, b, c and 1bc,1ca,1ab.The lines are

The sum of n terms of the series whose nth term is n(n+1) is equal to

Let f(x)={x+e2x−1, x&lt;0x2+2λx, x≥0. If f(x) is differentiable at x=0, then the value of 2λ is

Whar are leptons and mesons?

The least positive value of t, so that the lines x=t+α,y+16=0 and y=αx are concurrent, is:

A dice is thrown. What is the probability of getting a composite number ?

The coefficient of x10 in the expansion of [1+x2(1−x)]8 is

If 9-14-213=A+12-1049, then find matrix A.

number of solutions for Mod 2 raised to the power x - 1 + Mod 24 - 2 raise to the power x is smaller than 3 are

Let A=Q×Q, where Q is the set of all rational numbers, and ∗ is a binary operation on A defined by (a,b)∗(c,d)=(ac,b+ad) for (a,b),(c,d)∈A. Then find (i) The identity element of ∗ in A. (ii) Invertible elements of A, and hence write the inverse of elements (5,3) and (12,4).

For two independent events A and B, if P(A) = 0.5 and P(B) = 0.3 , then the value of100P(A∪B) = ___

Triangle ABC is isosceles with AC=BC and ∠ACB=106∘. Point M is in the interior of the triangle so that ∠MAC=7∘ and ∠MCA=23∘. Find the number of degrees in ∠CMB. (correct answer + 5, wrong answer 0)

What is the angle between the tangents to the curve y=x2−5x+6 at the points (2, 0) and (3, 0)

Prove that: cos2π15 cos4π15 cos 8π15 cos 16π15 =116

If the points (a cosα, a sinα) and (a cosβ, a sinβ) are at a distance k sinα-β2 apart, then k = __________.

A particle moves on a line according to the law s=at2+bt+c. If the displacement after one second is 16 cm, the velocity after 2 seconds is 24 cm/sec and the acceleration is 8 cm/sec2, then (a,b,c)

Prove that summation(0 to infinity) n^2/n!=2e

The number of solution(s) of log10x=−x is

Form the differential equation of the family of circles touching the y -axis at the origin.

If the points (–1, 3, 2), (–4, 2, –2) and (5, 5, λ ) are collinear, then λ =

Findequation of the line perpendicular to the line x – 7y+ 5 = 0 and having x intercept 3.

Third term of a GP is 4. What is the product of first 5 terms? a) 1024 b) 2048 c) 1536 d) 4096

If A and B are two finite sets such that n(A) > n(B) and the difference of the number of elements of the power sets of A and B is 96, then n(A) – n(B) = ____________.

If cos−1x>sin−1x then

Let z1 and z2 be two distinct complex numbers and let z=(1–t)z1+tz2 for some real number t with 0<t<1. If Arg(w) denotes the principal argument of a non-zero complex number w, then

Find limx→1f(x), if f(x)={x2−1,x≤1−x2−1,x>1

If cos−1x>sin−1x then

Let f(x)={x+e2x−1, x<0x2+2λx, x≥0. If f(x) is differentiable at x=0, then the value of 2λ is