43030 + Interview Questions in Mathematics

1.	I) 10, 0, 101, 56, 72 II) 1021, 1011, 1058, 1100 (III) 256, 282, 320, 198, 200 (IV) 0, 93, 46, 10, 32, 46 Which of the given data sets have maximum range
Answer» I) 10, 0, 101, 56, 72 II) 1021, 1011, 1058, 1100 (III) 256, 282, 320, 198, 200 (IV) 0, 93, 46, 10, 32, 46 Which of the given data sets have maximum range

Discussion

2.	If the tangents drawn to the hyperbola 4y2=x2+1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid point of AB is :
Answer» If the tangents drawn to the hyperbola $4 y^{2} = x^{2} + 1$ intersect the co-ordinate axes at the distinct points $A$ and $B$ , then the locus of the mid point of $A B$ is :

Discussion

3.	Prove that √2+√2+√2+2 cos 8θ=2 cos θ. Or Prove that (1+cosπ8)(1+cos3π8)(1+cos5π8)(1+cos7π8)=18
Answer» Prove that $\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 c o s 8 θ}}} = 2 c o s θ .$ Or Prove that $(1 + c o s \frac{π}{8}) (1 + c o s \frac{3 π}{8}) (1 + c o s \frac{5 π}{8}) (1 + c o s \frac{7 π}{8}) = \frac{1}{8}$

3.

Prove that √2+√2+√2+2 cos 8θ=2 cos θ. Or Prove that (1+cosπ8)(1+cos3π8)(1+cos5π8)(1+cos7π8)=18

Answer»

Prove that $\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 c o s 8 θ}}} = 2 c o s θ .$

Or

Prove that $(1 + c o s \frac{π}{8}) (1 + c o s \frac{3 π}{8}) (1 + c o s \frac{5 π}{8}) (1 + c o s \frac{7 π}{8}) = \frac{1}{8}$

Discussion

4.	Find the equation of chord centered at the point (1, 2) in the circle x2 + y2 = 9.
Answer» Find the equation of chord centered at the point (1, 2) in the circle $x^{2} + y^{2} = 9.$

Discussion

5.	Between any two real roots of the equation ex sin x = 1, the equation ex cos x = - 1 has
Answer» Between any two real roots of the equation $e^{x}$ sin x = 1, the equation $e^{x}$ cos x = - 1 has

Discussion

6.	The solution set of x−2>0,x−9<0 and x2−9≥0 is
Answer» The solution set of $x - 2 > 0, x - 9 < 0$ and $x^{2} - 9 \geq 0$ is

Discussion

7.	The distance of the point (1,3,–7) from the plane passing through the point (1,–1,–1), having normal perpendicular to both the lines x−11=y+2−2=z−43 and x−22=y+1−1=z+7−1, is:
Answer» The distance of the point $(1, 3, - 7)$ from the plane passing through the point $(1, - 1, - 1),$ having normal perpendicular to both the lines $\frac{x - 1}{1} = \frac{y + 2}{- 2} = \frac{z - 4}{3}$ and $\frac{x - 2}{2} = \frac{y + 1}{- 1} = \frac{z + 7}{- 1}$ , is:

Discussion

8.	If the tangent to the ellipse x2+4y2=16 at the point P(ϕ) is normal to the circle x2+y2−8x−4y=0, then possible values(s) of ϕ is/are
Answer» If the tangent to the ellipse $x^{2} + 4 y^{2} = 16$ at the point $P (ϕ)$ is normal to the circle $x^{2} + y^{2} - 8 x - 4 y = 0,$ then possible values(s) of $ϕ$ is/are

Discussion

9.	Total number of ways in which 256 identical balls can be placed in 16 numbered boxes (1,2,3,.,16) such that rth box contains at least r balls is (1≤r≤16)
Answer» Total number of ways in which 256 identical balls can be placed in 16 numbered boxes (1,2,3,.,16) such that $r^{t h}$ box contains at least r balls is $(1 \leq r \leq 16)$

Discussion

10.	If two numbers a,b are such that a:b=8:3 and a−5:b+6=5:3, then a−7:b+7 is equal to
Answer» If two numbers $a, b$ are such that $a : b = 8 : 3$ and $a - 5 : b + 6 = 5 : 3$ , then $a - 7 : b + 7$ is equal to

Discussion

11.	Number of irrational terms in the binomial expansion of (31/5+71/3)100 is
Answer» Number of irrational terms in the binomial expansion of $(3^{1 / 5} + 7^{1 / 3})^{100}$ is

Discussion

12.	In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:
Answer» In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:

Discussion

13.	If kx2+ky2−4x−6y−2k=0 represents a real circle, then the set of values of k is
Answer» If $k x^{2} + k y^{2} - 4 x - 6 y - 2 k = 0$ represents a real circle, then the set of values of $k$ is

Discussion

14.	Integrate the rational functions. ∫1x(xn+1)dx
Answer» Integrate the rational functions. $\int \frac{1}{x (x^{n} + 1)} d x$

Discussion

15.	Interval in which {x} is monotonically increasing function, where { } is fractional part function -
Answer» Interval in which {x} is monotonically increasing function, where { } is fractional part function -

Discussion

16.	The equations of the tangents to the hyperbola x2−4y2=36 which are perpendicular to the line x−y+4=0 are:
Answer» The equations of the tangents to the hyperbola $x^{2} - 4 y^{2} = 36$ which are perpendicular to the line $x - y + 4 = 0$ are:

Discussion

17.	The value of x satisfying logax+log√ax+log3√ax+....loga√ax=a+12 will be
Answer» The value of x satisfying ${log}_{a} x + {log}_{\sqrt{a}} x + {log}_{3 \sqrt{a}} x + . . . . {log}_{a \sqrt{a}} x = \frac{a + 1}{2}$ will be

Discussion

18.	Let (1+x2)2(1+x)n=A0+A1x+A2x2+..............If A0,A1,A2 are in A.P., then the value of n is
Answer» Let $(1 + x^{2})^{2} (1 + x)^{n} = A_{0} + A_{1} x + A_{2} x^{2} + . . . . . . . . . . . . . . I f A_{0}, A_{1}, A_{2}$ are in A.P., then the value of n is

Discussion

19.	cot−1(√1+x2−1x)= _________
Answer» ${cot}^{- 1} (\frac{\sqrt{1 + x^{2}} - 1}{x}) =$ _________

Discussion

20.	If a tangent of slope 3 on the ellipse x2a2+y2b2=1 is normal to the circle 2x2+2y2+8x+1=0, then the maximum value of ab is
Answer» If a tangent of slope $3$ on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is normal to the circle $2 x^{2} + 2 y^{2} + 8 x + 1 = 0,$ then the maximum value of $a b$ is

Discussion

21.	The number of ordered real pairs (x,y) with 0<x,y<1 satisfying the simultaneous equation 1+√1−x2x=1+2y1−y+√1−y2 and 25(1−x2)=17−10√1−y2 is
Answer» The number of ordered real pairs $(x, y)$ with $0 < x, y < 1$ satisfying the simultaneous equation $\frac{1 + \sqrt{1 - x^{2}}}{x} = 1 + \frac{2 y}{1 - y + \sqrt{1 - y^{2}}}$ and $25 (1 - x^{2}) = 17 - 10 \sqrt{1 - y^{2}}$ is

Discussion

22.	if 1+sin A+sin2 A+...upto infinity=2(square root of 3)+4,then A=
Answer» if 1+sin A+sin² A+...upto infinity=2(square root of 3)+4,then A=

Discussion

23.	limx→144x−12√x−1
Answer» ${lim}_{x \to \frac{1}{4}} \frac{4 x - 1}{2 \sqrt{x} - 1}$

Discussion

24.	How many words, with or without meaning, can be formed by using all the letters of the word `DELHI', using each letter exactly once ?
Answer» How many words, with or without meaning, can be formed by using all the letters of the word `DELHI', using each letter exactly once ?

Discussion

25.	Number of greatest binomial coefficients in the expansion of (1+x)2n and (1+x)2n+1 are p and q respectively (where n is a positive integer). Find the value of p+2q ___
Answer» Number of greatest binomial coefficients in the expansion of $(1 + x)^{2 n}$ and $(1 + x)^{2 n + 1}$ are p and q respectively (where n is a positive integer). Find the value of p+2q ___

Discussion

26.	Determine the values of p and q so that the prime factorisation of 2520 is a expressible as 2^33^pq*7.
Answer» Determine the values of p and q so that the prime factorisation of 2520 is a expressible as 2^33^pq*7.

Discussion

27.	If the equations x2+2x+3=0 and ax2+bx+c=0 , a , b , c ^I R , have a common root, then a: b: c is
Answer» If the equations $x^{2} + 2 x + 3 = 0 a n d a x^{2} + b x + c = 0$ , a , b , c $^I$ R , have a common root, then a: b: c is

Discussion

28.	The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,3,7,9 (repetition of digits allowed) is equal to :
Answer» The number of natural numbers less than $7, 000$ which can be formed by using the digits $0, 1, 3, 7, 9$ (repetition of digits allowed) is equal to :

Discussion

29.	(48x−8)+6=29 Given the above equation, what is the value of 6x−1?
Answer» $(48 x - 8) + 6 = 29$ Given the above equation, what is the value of 6x $- 1$ ?

Discussion

30.	I have a problem solving the question below if m=2 find the difference between the value of 4m to the power of 3 and 3m to the power of 4
Answer» I have a problem solving the question below if m=2 find the difference between the value of 4m to the power of 3 and 3m to the power of 4

Discussion

31.	∣∣∣∣∣1xx2x21xxx21∣∣∣∣∣=(1−x3)2
Answer» $∣ ∣∣∣ ∣ \begin{matrix} 1 & x & x^{2} x^{2} & 1 & x x & x^{2} & 1 \end{matrix} ∣ ∣∣∣ ∣ = (1 - x^{3})^{2}$

Discussion

32.	Graph of f(x) is given. Find the graph of f(x)−2
Answer» Graph of f(x) is given. Find the graph of $f (x) - 2$

Discussion

33.	A light ray coming along the line 3x + 4y = 5 gets reflected from the line ax + by = 1 and goes along the line 5x – 12y = 10. Then,
Answer» A light ray coming along the line 3x + 4y = 5 gets reflected from the line ax + by = 1 and goes along the line 5x – 12y = 10. Then,

Discussion

34.	In a G.P. first term and common ratio both are equal to 12(√3+i). Then the modulus value of nth term of the G.P. is
Answer» In a $G . P .$ first term and common ratio both are equal to $\frac{1}{2} (\sqrt{3} + i) .$ Then the modulus value of $n^{t h}$ term of the $G . P .$ is

Discussion

35.	From the given equation, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. y=ex(acosx+bsinx)
Answer» From the given equation, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. $y = e^{x} (a c o s x + b s i n x)$

Discussion

36.	Using coafactors of the elements of second row, evaluate Δ=∣∣∣∣538201123∣∣∣∣
Answer» Using coafactors of the elements of second row, evaluate $Δ = ∣ ∣∣ ∣ \begin{matrix} 5 & 3 & 8 2 & 0 & 1 1 & 2 & 3 \end{matrix} ∣ ∣∣ ∣$

Discussion

37.	Find √289
Answer» Find $\sqrt{289}$

Discussion

38.	∫2x(f′(x)+f(x)log2)dx is equal to
Answer» $\int 2^{x} (f^{'} (x) + f (x) log 2) d x$ is equal to

Discussion

39.	What is limiting value of average value?
Answer» What is limiting value of average value?

Discussion

40.	The domain of the function f(x)=√5\|x\|−x2−6 is
Answer» The domain of the function $f (x) = \sqrt{5 \| x \| - x^{2} - 6}$ is

Discussion

41.	Represent to solution set of each of the following in equations graphically in two dimensional plane : 0≤2x−5y+10
Answer» Represent to solution set of each of the following in equations graphically in two dimensional plane : $0 \leq 2 x - 5 y + 10$

41.

Represent to solution set of each of the following in equations graphically in two dimensional plane : 0≤2x−5y+10

Answer»

Represent to solution set of each of the following in equations graphically in two dimensional plane :

$0 \leq 2 x - 5 y + 10$

Discussion

42.	Find the equation of a parabola with vertex at the origin and the directrix,y=2.
Answer» Find the equation of a parabola with vertex at the origin and the directrix,y=2.

Discussion

43.	Mark incorrect statement
Answer» Mark incorrect statement

Discussion

44.	Martin is ordering pizzas and cupcakes for a house party. He calls the Eat All bakery, and places order for x pizzas and y cupcakes. If a pizza costs 12$ and a cupcake costs 7$ and he had planned a budget of 90$ at the most, then which of the following inequalities models the situation in the best possible way?
Answer» Martin is ordering pizzas and cupcakes for a house party. He calls the Eat All bakery, and places order for x pizzas and y cupcakes. If a pizza costs $12 $$ and a cupcake costs $7 $$ and he had planned a budget of $90 $$ at the most, then which of the following inequalities models the situation in the best possible way?

Discussion

45.	Which of the following expression(s) is/are not representing a polynomial for n∈N.
Answer» Which of the following expression(s) is/are not representing a polynomial for $n \in N$ .

Discussion

46.	Evaluate the definite integrals. ∫ππ2ex(1−sin x1−cos x)dx.
Answer» Evaluate the definite integrals. $\int_{\frac{π}{2}}^{π} e^{x} (\frac{1 - s i n x}{1 - c o s x}) d x .$

46.

Evaluate the definite integrals. ∫ππ2ex(1−sin x1−cos x)dx.

Answer»

Evaluate the definite integrals.

$\int_{\frac{π}{2}}^{π} e^{x} (\frac{1 - s i n x}{1 - c o s x}) d x .$

Discussion

47.	Determine whether the binary operation ∗ on the set N of natural numbers defined by a∗b=2ab is associative or not.
Answer» Determine whether the binary operation $$ on the set N of natural numbers defined by $a b = 2^{a b}$ is associative or not.

Discussion

48.	If A={x:x is a prime number between 2 and 16}, then number of subsets of A with exactly two elements is
Answer» If $A = {x : x$ is a prime number between $2$ and $16},$ then number of subsets of $A$ with exactly two elements is

Discussion

49.	5 girls and 5 boys are to be seated around a circular table such that no 2 girls sit toghether. The no of ways in which they can be seated is?
Answer» 5 girls and 5 boys are to be seated around a circular table such that no 2 girls sit toghether. The no of ways in which they can be seated is?

Discussion

50.	The numerical value of (1+cotx−cosec x)(1+tanx+secx) is
Answer» The numerical value of $(1 + cot x - cosec x) (1 + tan x + sec x)$ is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

I) 10, 0, 101, 56, 72 II) 1021, 1011, 1058, 1100 (III) 256, 282, 320, 198, 200 (IV) 0, 93, 46, 10, 32, 46 Which of the given data sets have maximum range

If the tangents drawn to the hyperbola 4y2=x2+1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid point of AB is :

Prove that √2+√2+√2+2 cos 8θ=2 cos θ. Or Prove that (1+cosπ8)(1+cos3π8)(1+cos5π8)(1+cos7π8)=18

Find the equation of chord centered at the point (1, 2) in the circle x2 + y2 = 9.

Between any two real roots of the equation ex sin x = 1, the equation ex cos x = - 1 has

The solution set of x−2&gt;0,x−9&lt;0 and x2−9≥0 is

The distance of the point (1,3,–7) from the plane passing through the point (1,–1,–1), having normal perpendicular to both the lines x−11=y+2−2=z−43 and x−22=y+1−1=z+7−1, is:

If the tangent to the ellipse x2+4y2=16 at the point P(ϕ) is normal to the circle x2+y2−8x−4y=0, then possible values(s) of ϕ is/are

Total number of ways in which 256 identical balls can be placed in 16 numbered boxes (1,2,3,.,16) such that rth box contains at least r balls is (1≤r≤16)

If two numbers a,b are such that a:b=8:3 and a−5:b+6=5:3, then a−7:b+7 is equal to

Number of irrational terms in the binomial expansion of (31/5+71/3)100 is

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:

If kx2+ky2−4x−6y−2k=0 represents a real circle, then the set of values of k is

Integrate the rational functions. ∫1x(xn+1)dx

Interval in which {x} is monotonically increasing function, where { } is fractional part function -

The equations of the tangents to the hyperbola x2−4y2=36 which are perpendicular to the line x−y+4=0 are:

The value of x satisfying logax+log√ax+log3√ax+....loga√ax=a+12 will be

Let (1+x2)2(1+x)n=A0+A1x+A2x2+..............If A0,A1,A2 are in A.P., then the value of n is

cot−1(√1+x2−1x)= _________

If a tangent of slope 3 on the ellipse x2a2+y2b2=1 is normal to the circle 2x2+2y2+8x+1=0, then the maximum value of ab is

The number of ordered real pairs (x,y) with 0&lt;x,y&lt;1 satisfying the simultaneous equation 1+√1−x2x=1+2y1−y+√1−y2 and 25(1−x2)=17−10√1−y2 is

if 1+sin A+sin2 A+...upto infinity=2(square root of 3)+4,then A=

limx→144x−12√x−1

How many words, with or without meaning, can be formed by using all the letters of the word `DELHI', using each letter exactly once ?

Number of greatest binomial coefficients in the expansion of (1+x)2n and (1+x)2n+1 are p and q respectively (where n is a positive integer). Find the value of p+2q ___

Determine the values of p and q so that the prime factorisation of 2520 is a expressible as 2^3*3^p*q*7.

If the equations x2+2x+3=0 and ax2+bx+c=0 , a , b , c ^I R , have a common root, then a: b: c is

The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,3,7,9 (repetition of digits allowed) is equal to :

(48x−8)+6=29 Given the above equation, what is the value of 6x−1?

I have a problem solving the question below if m=2 find the difference between the value of 4m to the power of 3 and 3m to the power of 4

∣∣∣∣∣1xx2x21xxx21∣∣∣∣∣=(1−x3)2

Graph of f(x) is given. Find the graph of f(x)−2

A light ray coming along the line 3x + 4y = 5 gets reflected from the line ax + by = 1 and goes along the line 5x – 12y = 10. Then,

In a G.P. first term and common ratio both are equal to 12(√3+i). Then the modulus value of nth term of the G.P. is

From the given equation, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.​ y=ex(acosx+bsinx)

Using coafactors of the elements of second row, evaluate Δ=∣∣∣∣538201123∣∣∣∣

Find √289

∫2x(f′(x)+f(x)log2)dx is equal to

What is limiting value of average value?

The domain of the function f(x)=√5|x|−x2−6 is

Represent to solution set of each of the following in equations graphically in two dimensional plane : 0≤2x−5y+10

Find the equation of a parabola with vertex at the origin and the directrix,y=2.

Mark incorrect statement

Which of the following expression(s) is/are not representing a polynomial for n∈N.

Evaluate the definite integrals. ∫ππ2ex(1−sin x1−cos x)dx.

Determine whether the binary operation ∗ on the set N of natural numbers defined by a∗b=2ab is associative or not.

If A={x:x is a prime number between 2 and 16}, then number of subsets of A with exactly two elements is

5 girls and 5 boys are to be seated around a circular table such that no 2 girls sit toghether. The no of ways in which they can be seated is?

The numerical value of (1+cotx−cosec x)(1+tanx+secx) is

The solution set of x−2>0,x−9<0 and x2−9≥0 is

The number of ordered real pairs (x,y) with 0<x,y<1 satisfying the simultaneous equation 1+√1−x2x=1+2y1−y+√1−y2 and 25(1−x2)=17−10√1−y2 is

Determine the values of p and q so that the prime factorisation of 2520 is a expressible as 2^33^pq*7.

From the given equation, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. y=ex(acosx+bsinx)