43030 + Interview Questions in Mathematics

1.	If a+b+c=3 and a>0,b>0,c>0, then the greatest value of a2b3c2 is
Answer» If $a + b + c = 3$ and $a > 0, b > 0, c > 0$ , then the greatest value of $a^{2} b^{3} c^{2}$ is

Discussion

2.	If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability ).
Answer» If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability ).

Discussion

3.	If (1+x)n=C0+C1x+…..+Cnxn, then the value of ∑∑0≤r<s≤n(Cr+Cs) is equal to
Answer» If $(1 + x)^{n} = C_{0} + C_{1} x + \dots . . + C_{n} x^{n},$ then the value of $\sum \sum 0 \leq r < s \leq n (C_{r} + C_{s})$ is equal to

Discussion

4.	7. Range of f(x)=xsinx?
Answer» 7. Range of f(x)=xsinx?

Discussion

5.	a curve is given by y=sinx. The area enclosed bt curve and x axis between x=0 and x=pie
Answer» a curve is given by y=sinx. The area enclosed bt curve and x axis between x=0 and x=pie

Discussion

6.	102∫0[tan−1x]dx is equal to(where [⋅] denotes the greatest integer function)
Answer» $102 \int 0 [{tan}^{- 1} x] d x$ is equal to (where $[\cdot]$ denotes the greatest integer function)

Discussion

7.	The other domains of sine function on which it is one-one and onto provides_________ for arc sine function.
Answer» The other domains of sine function on which it is one-one and onto provides _________ for arc sine function.

Discussion

8.	UsingCofactors of elements of third column, evaluate
Answer» Using Cofactors of elements of third column, evaluate

Discussion

9.	If (1+i1−i)m=1, then the least positive integral value of m is
Answer» If ${(\frac{1 + i}{1 - i})}^{m} = 1,$ then the least positive integral value of $m$ is

Discussion

10.	If a→, b→ and c→ are unit vectors such that a→+b→-c→=0→, then the angle between a→ and b→ is ___________.
Answer» If $\vec{a}, \vec{b} and \vec{c}$ are unit vectors such that $\vec{a} + \vec{b} - \vec{c} = \vec{0}$ , then the angle between $\vec{a} and \vec{b}$ is ___________.

Discussion

11.	Let A={(x,y)∈R×R\|2x2+2y2−2x−2y=1},B={(x,y)∈R×R\|4x2+4y2−16y+7=0} and C={(x,y)∈R×R\|x2+y2−4x−2y+5≤r2}.Then the minimum value of \|r\| such that A∪B⊆C is equal to:
Answer» Let $A = {(x, y) \in R \times R \| 2 x^{2} + 2 y^{2} - 2 x - 2 y = 1},$ $B = {(x, y) \in R \times R \| 4 x^{2} + 4 y^{2} - 16 y + 7 = 0}$ and $C = {(x, y) \in R \times R \| x^{2} + y^{2} - 4 x - 2 y + 5 \leq r^{2}}$ . Then the minimum value of $\| r \|$ such that $A \cup B \subseteq C$ is equal to:

Discussion

12.	If S denotes the set of all real values of x such that (x2010+1)(1+x2+x4+⋯+x2008)=2010x2009, then the number of elements in set S is
Answer» If $S$ denotes the set of all real values of $x$ such that $(x^{2010} + 1) (1 + x^{2} + x^{4} + \dots + x^{2008}) = 2010 x^{2009}$ , then the number of elements in set $S$ is

Discussion

13.	Let A be a square matrix of order two such that A−AAT=I2. If trace (A)≠R and entries are complex numbers, number of such matrices possible are
Answer» Let A be a square matrix of order two such that $A - A A^{T} = I_{2}$ . If trace $(A) \neq R$ and entries are complex numbers, number of such matrices possible are

Discussion

14.	For non-zero x, let 3f(x)+4f(1x)=1x−10. If 3∫2f(x)dx=abln(ca), where a,b,c are co-prime, then the value of (a+b+c) is
Answer» For non-zero $x,$ let $3 f (x) + 4 f (\frac{1}{x}) = \frac{1}{x} - 10.$ If $3 \int 2 f (x) d x = \frac{a}{b} ln (\frac{c}{a}),$ where $a, b, c$ are co-prime, then the value of $(a + b + c)$ is

Discussion

15.	Evaluate the following integrals:∫e2x sin3x+1 dx
Answer» Evaluate the following integrals: $\int e^{2 x} \sin (3 x + 1) d x$

Discussion

16.	7.If A= {x : x is a natural number }, B = {x : x is an even natural number)C= {x:x is an odd natural number) andD = {x : x is a prime number ], find) An B(iv) BC(ii) AnID(vi) Cn Di) AnC
Answer» 7.If A= {x : x is a natural number }, B = {x : x is an even natural number)C= {x:x is an odd natural number) andD = {x : x is a prime number ], find) An B(iv) BC(ii) AnID(vi) Cn Di) AnC

Discussion

17.	If a, b ε R, a ≠ 0 and the quadratic equation ax2−bx+2 =0 has imaginary roots, then a + b + 2 is
Answer» If a, b $ε$ R, a $\neq$ 0 and the quadratic equation $a x^{2} - b x + 2$ =0 has imaginary roots, then a + b + 2 is

Discussion

18.	The number of ways in which 5 different fruits can be selected out of 20 different fruits if a particular fruit (Mango) is always excluded.
Answer» The number of ways in which 5 different fruits can be selected out of 20 different fruits if a particular fruit (Mango) is always excluded.

Discussion

19.	∣∣∣∣y+zzyzz+xxyxx+y∣∣∣∣ is equal to
Answer» $∣ ∣∣ ∣ \begin{matrix} y + z & z & y z & z + x & x y & x & x + y \end{matrix} ∣ ∣∣ ∣$ is equal to

Discussion

20.	यदिअंग्रेज़पुलिसकोबुलालेता?
Answer» यदि अंग्रेज़ पुलिस को बुला लेता?

Discussion

21.	∫10x√1+x2dx
Answer» $\int_{0}^{1} \frac{x}{\sqrt{1 + x^{2}}} d x$

Discussion

22.	For f(x)=ax2+bx+c the value of y at critical point is
Answer» For $f (x) = a x^{2} + b x + c$ the value of $y$ at critical point is

Discussion

23.	The value of cos−1(cos 5π3)+sin−1(sin 5π3) is
Answer» The value of ${cos}^{- 1} (cos \frac{5 π}{3}) + {sin}^{- 1} (sin \frac{5 π}{3})$ is

Discussion

24.	Number of ways of selecting 3 persons out of 12 sitting in a row,if no two selected persons were sitting together.
Answer» Number of ways of selecting 3 persons out of 12 sitting in a row,if no two selected persons were sitting together.

Discussion

25.	Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane
Answer» Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane

Discussion

26.	Write the maximum value 12sinθ−9sin2θ.
Answer» Write the maximum value $12 s i n θ - 9 s i n^{2} θ$ .

Discussion

27.	Fill in the blanks.(i) sin20∘=cos____∘(ii) tan30∘×tan___∘=1(iii) cos40∘=sin____∘
Answer» Fill in the blanks. (i) $sin 20^{\circ} = cos$ ____ $^{\circ}$ (ii) $tan 30^{\circ} \times tan$ ___ $^{\circ} = 1$ (iii) $cos 40^{\circ} = sin$ ____ $^{\circ}$

Discussion

28.	Among the following equations, the one which is not a homogeneous differential equation is .
Answer» Among the following equations, the one which is not a homogeneous differential equation is .

Discussion

29.	The curve y = x1/5 has at (0, 0)(a) a vertical tangent (b) a horizontal tangent(c) an oblique tangent (d) no tangent
Answer» The curve y = x^1/5 has at (0, 0) (a) a vertical tangent (b) a horizontal tangent (c) an oblique tangent (d) no tangent

Discussion

30.	Straight lines are drawn by joining m points on a straight line to n points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no two lines drawn are parallel and no three lines are concurrent)
Answer» Straight lines are drawn by joining $m$ points on a straight line to $n$ points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no two lines drawn are parallel and no three lines are concurrent)

Discussion

31.	if vector a and b have an angle theta between them then value of a cap - b cap will be
Answer» if vector a and b have an angle theta between them then value of a cap - b cap will be

Discussion

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

Discussion

33.	ntSolve:n nt(x-x) dy/dx + (2x-1)y = axn
Answer» ntSolve:n nt(x-x) dy/dx + (2x-1)y = axn

Discussion

34.	A={x:x∈R, x2=16 and 2x=6}. Represent the set in roster form.
Answer» $A = {x : x \in R, x^{2} = 16 and 2 x = 6}$ . Represent the set in roster form.

Discussion

35.	If (1+2x+3x2)10=k1+k2x+…+k21x20, then which of the following is/are correct?
Answer» If $(1 + 2 x + 3 x^{2})^{10} = k_{1} + k_{2} x + \dots + k_{21} x^{20}$ , then which of the following is/are correct?

Discussion

36.	The value of sin245∘=
Answer» The value of $sin 245^{\circ} =$

Discussion

37.	Let (1+x)(1+x+x2)(1+x+x2+x3)......(1+x+x2+....+x30)=a0+a1x+a2x2+........+a465x465then sum of a0+a2+a4+........+a464 is
Answer» Let $(1 + x) (1 + x + x^{2}) (1 + x + x^{2} + x^{3}) . . . . . . (1 + x + x^{2} + . . . . + x^{30}) = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . . . . + a_{465} x^{465}$ then sum of $a_{0} + a_{2} + a_{4} + . . . . . . . . + a_{464}$ is

Discussion

38.	Two newspapers A and B are published in a city. It is known that 30% of the city population read A and 25% read B, while 10% read both A and B. Further, 20% of those who read A but not B look into sports news and 40% of those who read B but not A also look into sports news, while 50% of those who read both A and B look into sports news. Then the percentage of the population who look into sport news, is
Answer» Two newspapers $A$ and $B$ are published in a city. It is known that $30 %$ of the city population read $A$ and $25 %$ read $B$ , while $10 %$ read both $A$ and $B$ . Further, $20 %$ of those who read $A$ but not $B$ look into sports news and $40 %$ of those who read $B$ but not $A$ also look into sports news, while $50 %$ of those who read both $A$ and $B$ look into sports news. Then the percentage of the population who look into sport news, is

Discussion

39.	Let k be an integer such that the triangle with vertices (k,-3k), (5, k) and (-k, 2) has area 28 sq units. Then, the orthocentre of this triangle is at the point
Answer» Let k be an integer such that the triangle with vertices (k,-3k), (5, k) and (-k, 2) has area 28 sq units. Then, the orthocentre of this triangle is at the point

Discussion

40.	In the given figure, Mayank and Monty are situated at point C and D respectively flying a kite such that the distance from the tower AB of them are in the ratio 1 : 3. If both the kites on reaching the top of the tower makes an angle of elevation of 60° and 30° respectively, then the ratio of length of string used by Mayank to the length of string used by Monty isदिये गये चित्र में, मयंक व मोंटी क्रमशः बिन्दु C व D पर स्थित हैं, जो एक पतंग उड़ा रहे हैं जबकि मीनार AB से उनकी दूरियों का अनुपात क्रमशः 1 : 3 है। यदि दोनों पतंगे मीनार के शीर्ष पर क्रमशः 60° व 30° के उन्नयन कोण निर्मित करती हैं, तब मयंक द्वारा उपयोग में ली गयी डोरी की लंबाई तथा मोंटी द्वारा उपयोग में ली गयी डोरी की लंबाई का अनुपात है
Answer» In the given figure, Mayank and Monty are situated at point C and D respectively flying a kite such that the distance from the tower AB of them are in the ratio 1 : 3. If both the kites on reaching the top of the tower makes an angle of elevation of 60° and 30° respectively, then the ratio of length of string used by Mayank to the length of string used by Monty is दिये गये चित्र में, मयंक व मोंटी क्रमशः बिन्दु C व D पर स्थित हैं, जो एक पतंग उड़ा रहे हैं जबकि मीनार AB से उनकी दूरियों का अनुपात क्रमशः 1 : 3 है। यदि दोनों पतंगे मीनार के शीर्ष पर क्रमशः 60° व 30° के उन्नयन कोण निर्मित करती हैं, तब मयंक द्वारा उपयोग में ली गयी डोरी की लंबाई तथा मोंटी द्वारा उपयोग में ली गयी डोरी की लंबाई का अनुपात है

Discussion

41.	If z=x+iy and w=(1-iz)/(z-i) then \|w\|=1 implies that, in the complex plane
Answer» If z=x+iy and w=(1-iz)/(z-i) then \|w\|=1 implies that, in the complex plane

Discussion

42.	Let α,β are real numbers for which the system of linear equations 2αx+y+z=0αx+y+2z=1β2x+y−3αz=−2 never posses unique solution then point P(α,β) lies on a conic whose
Answer» Let $α, β$ are real numbers for which the system of linear equations $2 α x + y + z = 0 α x + y + 2 z = 1 β^{2} x + y - 3 α z = - 2$ never posses unique solution then point $P (α, β)$ lies on a conic whose

Discussion

43.	The cartesian equation of a line is x−53=y+47=z−62. Its vector form is:
Answer» The cartesian equation of a line is $\frac{x - 5}{3} = \frac{y + 4}{7} = \frac{z - 6}{2}$ . Its vector form is:

Discussion

44.	Two farmers Ramkrishan and Gurucharan Singh cultivates only three varieties of rice namely Basmati, Permal and Naura. The sale (in rupees) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B.September Sales (in Rupees)BasmatiPermalNauraA=[10,00020,00030,00050,00030,00010,000]RamkishanGurcharan SinghOctober Sales (in Rupees)BasmatiPermalNauraB=[5,00010,0006,00020,00010,00010,000]RamkishanGurucharan(i) Find the combined sales in September and Octomber for each farmer in each variety.(ii) Find the decrease in sales from September to October.(iii) If both farmers receive 2 profit on gross sales, compute the profit for each farmer and for each variety sold in October.
Answer» Two farmers Ramkrishan and Gurucharan Singh cultivates only three varieties of rice namely Basmati, Permal and Naura. The sale (in rupees) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B. September Sales (in Rupees) $\begin{matrix} Basmati & Permal & Naura \end{matrix}$ $A = [\begin{matrix} 10, 000 & 20, 000 & 30, 000 50, 000 & 30, 000 & 10, 000 \end{matrix}] \begin{matrix} Ramkishan Gurcharan Singh \end{matrix}$ October Sales (in Rupees) $\begin{matrix} Basmati & Permal & Naura \end{matrix}$ $B = [\begin{matrix} 5, 000 & 10, 000 & 6, 000 20, 000 & 10, 000 & 10, 000 \end{matrix}] \begin{matrix} Ramkishan Gurucharan \end{matrix}$ $(i)$ Find the combined sales in September and Octomber for each farmer in each variety. $(i i)$ Find the decrease in sales from September to October. $(i i i)$ If both farmers receive $2$ profit on gross sales, compute the profit for each farmer and for each variety sold in October.

Discussion

45.	The equation x22−λ+y2λ−5+1=0 represents an ellipse, if
Answer» The equation $\frac{x^{2}}{2 - λ} + \frac{y^{2}}{λ - 5} + 1 = 0$ represents an ellipse, if

Discussion

46.	If A, B, C are angles of an acute angle triangle. Then minimum value of ∣∣∣∣∣(tan B+tan C)2tan2Atan2Atan2B(tan C+tan A)2tan2Btan2Ctan2C(tan A+tan B)2∣∣∣∣∣ is
Answer» If $A, B, C$ are angles of an acute angle triangle. Then minimum value of $∣ ∣∣∣ ∣ \begin{matrix} (t a n B + t a n C)^{2} & t a n^{2} A & t a n^{2} A t a n^{2} B & (t a n C + t a n A)^{2} & t a n^{2} B t a n^{2} C & t a n^{2} C & (t a n A + t a n B)^{2} \end{matrix} ∣ ∣∣∣ ∣$ is

Discussion

47.	Principal solutions are ______
Answer» Principal solutions are ______

Discussion

48.	Match the following column and mark the correct options Column−IColumn−II(I)Diadelphous(P)Sunflower(II)Syngenesious(Q)Pisum(III)Epiphyllous(R)Cassia(IV)Staminode(S)Colchicum
Answer» Match the following column and mark the correct options $\begin{matrix} C o l u m n - I & C o l u m n - I I (I) & D i a d e l p h o u s & (P) & S u n f l o w e r (I I) & S y n g e n e s i o u s & (Q) & P i s u m (I I I) & E p i p h y l l o u s & (R) & C a s s i a (I V) & S t a m i n o d e & (S) & C o l c h i c u m \end{matrix}$

Discussion

49.	The value of tan cos-1sincot-11 is ___________________.
Answer» The value of tan $[\cos^{- 1} \{\sin (\cot^{- 1} 1)\}]$ is ___________________.

Discussion

50.	How many four -digit numbers can be formed with the digits 3,5,7,8,9 which are greater than 8000, if repetition of digits is not allowed?
Answer» How many four -digit numbers can be formed with the digits 3,5,7,8,9 which are greater than 8000, if repetition of digits is not allowed?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If a+b+c=3 and a&gt;0,b&gt;0,c&gt;0, then the greatest value of a2b3c2 is

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability ).

If (1+x)n=C0+C1x+…..+Cnxn, then the value of ∑∑0≤r&lt;s≤n(Cr+Cs) is equal to

7. Range of f(x)=xsinx?

a curve is given by y=sinx. The area enclosed bt curve and x axis between x=0 and x=pie

102∫0[tan−1x]dx is equal to(where [⋅] denotes the greatest integer function)

The other domains of sine function on which it is one-one and onto provides_________ for arc sine function.

UsingCofactors of elements of third column, evaluate

If (1+i1−i)m=1, then the least positive integral value of m is

If a→, b→ and c→ are unit vectors such that a→+b→-c→=0→, then the angle between a→ and b→ is ___________.

Let A={(x,y)∈R×R|2x2+2y2−2x−2y=1},B={(x,y)∈R×R|4x2+4y2−16y+7=0} and C={(x,y)∈R×R|x2+y2−4x−2y+5≤r2}.Then the minimum value of |r| such that A∪B⊆C is equal to:

If S denotes the set of all real values of x such that (x2010+1)(1+x2+x4+⋯+x2008)=2010x2009, then the number of elements in set S is

Let A be a square matrix of order two such that A−AAT=I2. If trace (A)≠R and entries are complex numbers, number of such matrices possible are

For non-zero x, let 3f(x)+4f(1x)=1x−10. If 3∫2f(x)dx=abln(ca), where a,b,c are co-prime, then the value of (a+b+c) is

Evaluate the following integrals:∫e2x sin3x+1 dx

7.If A= {x : x is a natural number }, B = {x : x is an even natural number)C= {x:x is an odd natural number) andD = {x : x is a prime number ], find) An B(iv) BC(ii) AnID(vi) Cn Di) AnC

If a, b ε R, a ≠ 0 and the quadratic equation ax2−bx+2 =0 has imaginary roots, then a + b + 2 is

The number of ways in which 5 different fruits can be selected out of 20 different fruits if a particular fruit (Mango) is always excluded.

∣∣∣∣y+zzyzz+xxyxx+y∣∣∣∣ is equal to

यदिअंग्रेज़पुलिसकोबुलालेता?

∫10x√1+x2dx

For f(x)=ax2+bx+c the value of y at critical point is

The value of cos−1(cos 5π3)+sin−1(sin 5π3) is

Number of ways of selecting 3 persons out of 12 sitting in a row,if no two selected persons were sitting together.

Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane

Write the maximum value 12sinθ−9sin2θ.

Fill in the blanks.(i) sin20∘=cos____∘(ii) tan30∘×tan___∘=1(iii) cos40∘=sin____∘

Among the following equations, the one which is not a homogeneous differential equation is .

The curve y = x1/5 has at (0, 0)(a) a vertical tangent (b) a horizontal tangent(c) an oblique tangent (d) no tangent

Straight lines are drawn by joining m points on a straight line to n points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no two lines drawn are parallel and no three lines are concurrent)

if vector a and b have an angle theta between them then value of a cap - b cap will be

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

ntSolve:n nt(x-x) dy/dx + (2x-1)y = axn

A={x:x∈R, x2=16 and 2x=6}. Represent the set in roster form.

If (1+2x+3x2)10=k1+k2x+…+k21x20, then which of the following is/are correct?

The value of sin245∘=

Let (1+x)(1+x+x2)(1+x+x2+x3)......(1+x+x2+....+x30)=a0+a1x+a2x2+........+a465x465then sum of a0+a2+a4+........+a464 is

Let k be an integer such that the triangle with vertices (k,-3k), (5, k) and (-k, 2) has area 28 sq units. Then, the orthocentre of this triangle is at the point

If z=x+iy and w=(1-iz)/(z-i) then |w|=1 implies that, in the complex plane

Let α,β are real numbers for which the system of linear equations 2αx+y+z=0αx+y+2z=1β2x+y−3αz=−2 never posses unique solution then point P(α,β) lies on a conic whose

The cartesian equation of a line is x−53=y+47=z−62. Its vector form is:

The equation x22−λ+y2λ−5+1=0 represents an ellipse, if

If A, B, C are angles of an acute angle triangle. Then minimum value of ∣∣∣∣∣(tan B+tan C)2tan2Atan2Atan2B(tan C+tan A)2tan2Btan2Ctan2C(tan A+tan B)2∣∣∣∣∣ is

Principal solutions are ______

Match the following column and mark the correct options Column−IColumn−II(I)Diadelphous(P)Sunflower(II)Syngenesious(Q)Pisum(III)Epiphyllous(R)Cassia(IV)Staminode(S)Colchicum

The value of tan cos-1sincot-11 is ___________________.

How many four -digit numbers can be formed with the digits 3,5,7,8,9 which are greater than 8000, if repetition of digits is not allowed?

If a+b+c=3 and a>0,b>0,c>0, then the greatest value of a2b3c2 is

If (1+x)n=C0+C1x+…..+Cnxn, then the value of ∑∑0≤r<s≤n(Cr+Cs) is equal to

Fill in the blanks.(i) sin20∘=cos__∘(ii) tan30∘×tan_∘=1(iii) cos40∘=sin____∘