43030 + Interview Questions in Mathematics

1.	A card is drawn and replaced in an ordinary set of 52 cards.Minimum number of times a card must be drawn so that there is atleast an even chance of drawing a heart?
Answer» A card is drawn and replaced in an ordinary set of 52 cards.Minimum number of times a card must be drawn so that there is atleast an even chance of drawing a heart?

Discussion

2.	If u=∫eaxcos bx dx and v=∫eaxsinbxdx, then (a2+b2)(u2+v2)=
Answer» If $u = \int e^{a x} c o s b x d x$ and $v = \int e^{a x} s i n b x d x$ , then $(a^{2} + b^{2}) (u^{2} + v^{2}) =$

Discussion

3.	If f(x)=3x2−5x−1 and (f∘g)(x)=3x2+7x+1, then which of the following option is INCORRECT?
Answer» If $f (x) = 3 x^{2} - 5 x - 1$ and $(f \circ g) (x) = 3 x^{2} + 7 x + 1,$ then which of the following option is $INCORRECT ?$

Discussion

4.	6. 3
Answer» 6. 3

Discussion

5.	If ∫2cosx−sinx+λcosx+sinx−2dx=Aℓn\|cosx+sinx−2\|+Bx+C. Then the ordered triplet A,B,λ is
Answer» If $\int \frac{2 c o s x - s i n x + λ}{c o s x + s i n x - 2} d x = A ℓ n \| c o s x + s i n x - 2 \| + B x + C$ . Then the ordered triplet $A, B, λ$ is

Discussion

6.	If xϵ(π4,3π4)then∫sin x−cos x√1−sin 2xesin xcos x dx=
Answer» If $x ϵ (\frac{π}{4}, \frac{3 π}{4}) t h e n \int \frac{s i n x - c o s x}{\sqrt{1 - s i n 2 x}} e^{s i n x} c o s x d x =$

Discussion

7.	Initially content at ABC is 000. The MOD number of the above shown counter is _____8
Answer» Initially content at ABC is 000. The MOD number of the above shown counter is _____ 8

Discussion

8.	Let f(x)=(1+b2)x2+2bx+1 and m(b) the minimum value of f(x) for a given b. As b varies, the range of m(b) is
Answer» Let $f (x) = (1 + b^{2}) x^{2} + 2 b x + 1$ and m(b) the minimum value of f(x) for a given b. As b varies, the range of m(b) is

Discussion

9.	The value of limn→∞⎡⎢⎢⎣1√(2n−12)+1√(4n−22)+1√(6n−32)+...+1n⎤⎥⎥⎦ is equal to
Answer» The value of $lim n \to \infty ⎡ ⎢⎢ ⎣ \frac{1}{\sqrt{(2 n - 1^{2})}} + \frac{1}{\sqrt{(4 n - 2^{2})}} + \frac{1}{\sqrt{(6 n - 3^{2})}} + . . . + \frac{1}{n} ⎤ ⎥⎥ ⎦$ is equal to

Discussion

10.	A five digit number is formed with digits 0. 1. 2. 3. 4 without repetition. A number is selected at random, then the probability that it is divisible by 4 is
Answer» A five digit number is formed with digits 0. 1. 2. 3. 4 without repetition. A number is selected at random, then the probability that it is divisible by 4 is

Discussion

11.	Let U={1,2,3,4,5,5,6,7,8,9,10} and A={1,3,5,7,9}. Find A′.
Answer» Let $U = {1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10}$ and $A = {1, 3, 5, 7, 9}$ . Find $A^{'}$ .

Discussion

12.	Notice the stanza divisions. Do you find a shift to a new idea in successive stanza?
Answer» Notice the stanza divisions. Do you find a shift to a new idea in successive stanza?

Discussion

13.	∫√1−√x1+√xdx.
Answer» $\int \sqrt{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}} d x .$

Discussion

14.	Which of the following boolean expresion is a tautology?
Answer» Which of the following boolean expresion is a tautology?

Discussion

15.	Showthat isdivisible by 64, whenever nis a positive integer.
Answer» Show that is divisible by 64, whenever n is a positive integer.

Discussion

16.	Let f:[−3,1]→R be given asf(x)={min{(x+6),x2},−3≤x≤0max{√x,x2},0≤x≤1.If the area bounded by y=f(x) and x− axis is A, then the value of 6A is equal to
Answer» Let $f : [- 3, 1] \to R$ be given as $f (x) = {\begin{matrix} min {(x + 6), x^{2}}, & - 3 \leq x \leq 0 max {\sqrt{x}, x^{2}}, & 0 \leq x \leq 1. \end{matrix}$ If the area bounded by $y = f (x)$ and $x -$ axis is $A,$ then the value of $6 A$ is equal to

Discussion

17.	The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio (3+2√2):(3−2√2).
Answer» The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio $(3 + 2 \sqrt{2}) : (3 - 2 \sqrt{2})$ .

Discussion

18.	Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse
Answer» Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse

Discussion

19.	The area of the region S={(x,y):3x2≤4y≤6x+24} is
Answer» The area of the region $S = {(x, y) : 3 x^{2} \leq 4 y \leq 6 x + 24}$ is

Discussion

20.	A line passing through point A (-5, -4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x−y−5=0 at B,C and D respectively If (15AB)2+(10AC)2=(6AD)2, then the equation of line is
Answer» A line passing through point A (-5, -4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and $x - y - 5 = 0$ at B,C and D respectively If ${(\frac{15}{A B})}^{2} + {(\frac{10}{A C})}^{2} = {(\frac{6}{A D})}^{2}$ , then the equation of line is

Discussion

21.	∫dxcosx−sinx is equal to
Answer» $\int \frac{d x}{cos x - sin x}$ is equal to

Discussion

22.	The value of 50C03−50C14+50C25+⋯+50C5053 is equal to
Answer» The value of $\frac{^{50} C_{0}}{3} - \frac{^{50} C_{1}}{4} + \frac{^{50} C_{2}}{5} + \dots + \frac{^{50} C_{50}}{53}$ is equal to

Discussion

23.	The equation of circle which has radius of 6 units and is centred at (5,8), is
Answer» The equation of circle which has radius of $6$ units and is centred at $(5, 8),$ is

Discussion

24.	Let X and Y be two arbitrary, 3×3, non-zero, skew symmetric matrices and Z be an arbitrary 3×3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?
Answer» Let $X$ and $Y$ be two arbitrary, $3 \times 3$ , non-zero, skew symmetric matrices and $Z$ be an arbitrary $3 \times 3$ , non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?

Discussion

25.	If (1+x)15=a0+a1x+……+a15x15, then ∑15r=1rarar−1 is
Answer» If $(1 + x)^{15} = a_{0} + a_{1} x + \dots \dots + a_{15} x^{15}$ , then $\sum_{r = 1}^{15} r \frac{a_{r}}{a_{r} - 1}$ is

Discussion

26.	P, q, r, s are vector of equal magnitude. If p+q-r=0 angle between p and q is 1. If p+q-s=0 angle between p and s is 2 .the ratio of 1 and 2 is
Answer» P, q, r, s are vector of equal magnitude. If p+q-r=0 angle between p and q is 1. If p+q-s=0 angle between p and s is 2 .the ratio of 1 and 2 is

Discussion

27.	2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
Answer» 2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

Discussion

28.	cos 70°sin 20°+cos 55° cosec 35°tan 5° tan 25° tan 45° tan 65° tan 85°
Answer» $\{\frac{\cos 70 °}{\sin 20 °} + \frac{\cos 55 ° cosec 35 °}{\tan 5 ° \tan 25 ° \tan 45 ° \tan 65 ° \tan 85 °}\}$

Discussion

29.	5^a=8^b=10^c, find c :-
Answer» 5^a=8^b=10^c, find c :-

Discussion

30.	A palindrome is a word, number, phrase or sequence of words that reads the same backwards as forwards e.g. "SOLOS".The number of palindromes that can be formed using the letters ''AABBBBCCCDDDD'' is
Answer» A palindrome is a word, number, phrase or sequence of words that reads the same backwards as forwards e.g. "SOLOS". The number of palindromes that can be formed using the letters ''AABBBBCCCDDDD'' is

Discussion

31.	Let f(x)=5−\|x−2\| and g(x)=\|x+1\|,x∈R. If f(x) attains maximum value at α and g(x) attains minimum value at β, then limx→−αβ(x−1)(x2−5x+6)x2−6x+8 is equal to:
Answer» Let $f (x) = 5 - \| x - 2 \|$ and $g (x) = \| x + 1 \|, x \in R .$ If $f (x)$ attains maximum value at $α$ and $g (x)$ attains minimum value at $β,$ then $lim x \to - α β \frac{(x - 1) (x^{2} - 5 x + 6)}{x^{2} - 6 x + 8}$ is equal to:

Discussion

32.	∫x31+x2dx=a1+x232+b1+x2+C, then(a) a=13, b=1(b) a=-13, b=1(c) a=-13, b=-1(d) a=13, b=-1
Answer» $\int \frac{x^{3}}{\sqrt{1 + x^{2}}} d x = a {(1 + x^{2})}^{\frac{3}{2}} + b \sqrt{1 + x^{2}} + C$ , then $(a) a = \frac{1}{3}, b = 1 (b) a = - \frac{1}{3}, b = 1 (c) a = - \frac{1}{3}, b = - 1 (d) a = \frac{1}{3}, b = - 1$

Discussion

33.	If , show that
Answer» If , show that

Discussion

34.	(sina-cosa)^2=1-sin2a
Answer» (sina-cosa)^2=1-sin2a

Discussion

35.	Given ax2+bx+c≥0,bx2+cx+a≥0,cx2+ax+b≥0 where a≠b≠c and a,b,cϵR. Now a2+b2+c2ab+bc+ca cannot take the value(s)
Answer» Given $a x^{2} + b x + c \geq 0, b x^{2} + c x + a \geq 0, c x^{2} + a x + b \geq 0$ where $a \neq b \neq c$ and $a, b, c ϵ R$ . Now $\frac{a^{2} + b^{2} + c^{2}}{a b + b c + c a}$ cannot take the value(s)

Discussion

36.	Equation of the diameter of the circle x2+y2−2x+4y=0 which passes through the origin is
Answer» Equation of the diameter of the circle $x^{2} + y^{2} - 2 x + 4 y = 0$ which passes through the origin is

Discussion

37.	Sum of the real values of 'a' for which the equation (a2−3a+2)x2+(a2−4a+3)x+(a2−6a+5)=0 has three distinct roots
Answer» Sum of the real values of 'a' for which the equation $(a^{2} - 3 a + 2) x^{2} + (a^{2} - 4 a + 3) x + (a^{2} - 6 a + 5) = 0$ has three distinct roots

Discussion

38.	How many integral values of x disprove the existence of log3(x2−2x−3)?
Answer» How many integral values of $x$ disprove the existence of ${log}_{3} (x^{2} - 2 x - 3)$ ?

Discussion

39.	n(n+1)(n+5) is a multiple of 3 Please give the answers of this question. I hAve seen the solutions but I am not able to understand the last k+1 part.
Answer» n(n+1)(n+5) is a multiple of 3 Please give the answers of this question. I hAve seen the solutions but I am not able to understand the last k+1 part.

39.

n(n+1)(n+5) is a multiple of 3 Please give the answers of this question. I hAve seen the solutions but I am not able to understand the last k+1 part.

Answer»

n(n+1)(n+5) is a multiple of 3

Please give the answers of this question. I hAve seen the solutions but I am not able to understand the last k+1 part.

Discussion

40.	Find the distance of the point (2, 12, 5) from the point of intersection of the line r→=2i^-4j^+2k^+λ3i^+4j^+2k^ and r→.i^-2j^+k^=0. [CBSE 2014]
Answer» Find the distance of the point (2, 12, 5) from the point of intersection of the line $\vec{r} = 2 \hat{i} - 4 \hat{j} + 2 \hat{k} + λ (3 \hat{i} + 4 \hat{j} + 2 \hat{k})$ and $\vec{r} . (\hat{i} - 2 \hat{j} + \hat{k}) = 0$ . [CBSE 2014]

Discussion

41.	Find the values of other five trigonometric functions if , x lies in second quadrant.
Answer» Find the values of other five trigonometric functions if , x lies in second quadrant.

Discussion

42.	If equations x2+bx+c=0 and bx2+cx+1=0 have a common root then
Answer» If equations $x^{2} + b x + c = 0$ and $b x^{2} + c x + 1 = 0$ have a common root then

Discussion

43.	Which of the following types of functions are called monotonic functions
Answer» Which of the following types of functions are called monotonic functions

Discussion

44.	Let Tr be the rth term of a sequence. If, for r = 1,2,3,.... . 3Tr+1=Tr and T7=1243, then the value of ∑∞r=1(Tr.Tr+1) is
Answer» Let $T_{r}$ be the $r^{t h}$ term of a sequence. If, for r = 1,2,3,.... . $3 T_{r + 1} = T_{r}$ and $T_{7} = \frac{1}{243},$ then the value of $\sum_{r = 1}^{\infty} (T_{r} . T_{r + 1})$ is

Discussion

45.	2. Let f be defined by f(x)=x-4 and g be defined by g(x)={x-16/x+4 when x is not equal to -4 Or when x=-4 } Find such that f(x)=g(x) for all x.
Answer» 2. Let f be defined by f(x)=x-4 and g be defined by g(x)={x-16/x+4 when x is not equal to -4 Or when x=-4 } Find such that f(x)=g(x) for all x.

Discussion

46.	cot7 1/2degree is equal to
Answer» cot7 1/2degree is equal to

Discussion

47.	The mean age of 50 persons was found to be 32 years. Later it was detected that the age 28 was wrongly noted as 35, the age 57 was wrongly noted as 30 and the age 60 was wrongly noted as 32. Then the correct mean age is
Answer» The mean age of 50 persons was found to be 32 years. Later it was detected that the age 28 was wrongly noted as 35, the age 57 was wrongly noted as 30 and the age 60 was wrongly noted as 32. Then the correct mean age is

Discussion

48.	If 10∑i=1(xi−5)=20 and 10∑i=1(xi−5)2=660, y=S.D. of 10 items x1,x2,x3.....,x10, then [y] is equal to (where [.] represents the greatest integer function)
Answer» If $10 \sum i = 1 (x_{i} - 5) = 20$ and $10 \sum i = 1 (x_{i} - 5)^{2} = 660,$ $y = S . D .$ of $10$ items $x_{1}, x_{2}, x_{3} . . . . ., x_{10}$ , then $[y]$ is equal to (where $[.]$ represents the greatest integer function)

Discussion

49.	If X={x:x is a solution of x2+2x+1=0}, then
Answer» If $X = {x : x is a solution of x^{2} + 2 x + 1 = 0},$ then

Discussion

50.	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

Explore topic-wise InterviewSolutions in Current Affairs.

A card is drawn and replaced in an ordinary set of 52 cards.Minimum number of times a card must be drawn so that there is atleast an even chance of drawing a heart?

If u=∫eaxcos bx dx and v=∫eaxsinbxdx, then (a2+b2)(u2+v2)=

If f(x)=3x2−5x−1 and (f∘g)(x)=3x2+7x+1, then which of the following option is INCORRECT?

6. 3

If ∫2cosx−sinx+λcosx+sinx−2dx=Aℓn|cosx+sinx−2|+Bx+C. Then the ordered triplet A,B,λ is

If xϵ(π4,3π4)then∫sin x−cos x√1−sin 2xesin xcos x dx=

Initially content at ABC is 000. The MOD number of the above shown counter is _____8

Let f(x)=(1+b2)x2+2bx+1 and m(b) the minimum value of f(x) for a given b. As b varies, the range of m(b) is

The value of limn→∞⎡⎢⎢⎣1√(2n−12)+1√(4n−22)+1√(6n−32)+...+1n⎤⎥⎥⎦ is equal to

A five digit number is formed with digits 0. 1. 2. 3. 4 without repetition. A number is selected at random, then the probability that it is divisible by 4 is

Let U={1,2,3,4,5,5,6,7,8,9,10} and A={1,3,5,7,9}. Find A′.

Notice the stanza divisions. Do you find a shift to a new idea in successive stanza?

∫√1−√x1+√xdx.

Which of the following boolean expresion is a tautology?

Showthat isdivisible by 64, whenever nis a positive integer.

Let f:[−3,1]→R be given asf(x)={min{(x+6),x2},−3≤x≤0max{√x,x2},0≤x≤1.If the area bounded by y=f(x) and x− axis is A, then the value of 6A is equal to

The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio (3+2√2):(3−2√2).

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse

The area of the region S={(x,y):3x2≤4y≤6x+24} is

A line passing through point A (-5, -4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x−y−5=0 at B,C and D respectively If (15AB)2+(10AC)2=(6AD)2, then the equation of line is

∫dxcosx−sinx is equal to

The value of 50C03−50C14+50C25+⋯+50C5053 is equal to

The equation of circle which has radius of 6 units and is centred at (5,8), is

Let X and Y be two arbitrary, 3×3, non-zero, skew symmetric matrices and Z be an arbitrary 3×3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?

If (1+x)15=a0+a1x+……+a15x15, then ∑15r=1rarar−1 is

P, q, r, s are vector of equal magnitude. If p+q-r=0 angle between p and q is 1. If p+q-s=0 angle between p and s is 2 .the ratio of 1 and 2 is

2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

cos 70°sin 20°+cos 55° cosec 35°tan 5° tan 25° tan 45° tan 65° tan 85°

5^a=8^b=10^c, find c :-

A palindrome is a word, number, phrase or sequence of words that reads the same backwards as forwards e.g. "SOLOS".The number of palindromes that can be formed using the letters ''AABBBBCCCDDDD'' is

Let f(x)=5−|x−2| and g(x)=|x+1|,x∈R. If f(x) attains maximum value at α and g(x) attains minimum value at β, then limx→−αβ(x−1)(x2−5x+6)x2−6x+8 is equal to:

∫x31+x2dx=a1+x232+b1+x2+C, then(a) a=13, b=1(b) a=-13, b=1(c) a=-13, b=-1(d) a=13, b=-1

If , show that

(sina-cosa)^2=1-sin2a

Given ax2+bx+c≥0,bx2+cx+a≥0,cx2+ax+b≥0 where a≠b≠c and a,b,cϵR. Now a2+b2+c2ab+bc+ca cannot take the value(s)

Equation of the diameter of the circle x2+y2−2x+4y=0 which passes through the origin is

Sum of the real values of 'a' for which the equation (a2−3a+2)x2+(a2−4a+3)x+(a2−6a+5)=0 has three distinct roots

How many integral values of x disprove the existence of log3(x2−2x−3)?

n(n+1)(n+5) is a multiple of 3 Please give the answers of this question. I hAve seen the solutions but I am not able to understand the last k+1 part.

Find the distance of the point (2, 12, 5) from the point of intersection of the line r→=2i^-4j^+2k^+λ3i^+4j^+2k^ and r→.i^-2j^+k^=0. [CBSE 2014]

Find the values of other five trigonometric functions if , x lies in second quadrant.

If equations x2+bx+c=0 and bx2+cx+1=0 have a common root then

Which of the following types of functions are called monotonic functions

Let Tr be the rth term of a sequence. If, for r = 1,2,3,.... . 3Tr+1=Tr and T7=1243, then the value of ∑∞r=1(Tr.Tr+1) is

2. Let f be defined by f(x)=x-4 and g be defined by g(x)={x-16/x+4 when x is not equal to -4 Or when x=-4 } Find such that f(x)=g(x) for all x.

cot7 1/2degree is equal to

The mean age of 50 persons was found to be 32 years. Later it was detected that the age 28 was wrongly noted as 35, the age 57 was wrongly noted as 30 and the age 60 was wrongly noted as 32. Then the correct mean age is

If 10∑i=1(xi−5)=20 and 10∑i=1(xi−5)2=660, y=S.D. of 10 items x1,x2,x3.....,x10, then [y] is equal to (where [.] represents the greatest integer function)

If X={x:x is a solution of x2+2x+1=0}, then

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