43030 + Interview Questions in Mathematics

1.	The maximum distance between the points (acosα,asinα) and (acosβ,asinβ) is
Answer» The maximum distance between the points $(a cos α, a sin α)$ and $(a cos β, a sin β)$ is

Discussion

2.	The sum of the roots of the equation √5x2−6x+8−√5x2−6x−7=1 is
Answer» The sum of the roots of the equation $\sqrt{5 x^{2} - 6 x + 8} - \sqrt{5 x^{2} - 6 x - 7} = 1$ is

Discussion

3.	If the Boolean expression (p ⊕ q) ∧ (∼ p ⊙ q) is equivalent to p ∧ q, where ⊕, ⊙∈{∧, ∨}, then the ordered pair (⊕, ⊙) is:
Answer» If the Boolean expression $(p \oplus q) \land (\sim p ⊙ q)$ is equivalent to $p \land q$ , where $\oplus, ⊙ \in {\land, \lor}$ , then the ordered pair $(\oplus, ⊙)$ is:

Discussion

4.	Total number of integral values of a such that x^2 + ax + a + 1 = 0 has integral roots is equal to
Answer» Total number of integral values of a such that x^2 + ax + a + 1 = 0 has integral roots is equal to

Discussion

5.	Y=x²+x is maximum for
Answer» Y=x²+x is maximum for

Discussion

6.	Let a,b,c be the roots of the equation px3+qx2+rx+s=0. If ∣∣∣∣∣−bcb2+bcc2+bca2+ac−acc2+aca2+abb2+ab−ab∣∣∣∣∣=27, a+b+c≥0 and a2+b2+c2=3, then the value of 3p+q is
Answer» Let $a, b, c$ be the roots of the equation $p x^{3} + q x^{2} + r x + s = 0$ . If $∣ ∣∣∣ ∣ \begin{matrix} - b c & b^{2} + b c & c^{2} + b c a^{2} + a c & - a c & c^{2} + a c a^{2} + a b & b^{2} + a b & - a b \end{matrix} ∣ ∣∣∣ ∣ = 27, a + b + c \geq 0$ and $a^{2} + b^{2} + c^{2} = 3,$ then the value of $3 p + q$ is

Discussion

7.	If x,y,z∈R and x+y+z =5, xy +yz+zx=3, probability for x to be positive only is
Answer» If $x, y, z \in R$ and x+y+z =5, xy +yz+zx=3, probability for x to be positive only is

Discussion

8.	cosec18∘ is a root of the equation
Answer» $cosec 18^{\circ}$ is a root of the equation

Discussion

9.	If A=[cosθsinθsinθ−cosθ],B=[10−11],C=ABAT,then ATCnA equals to(nϵZ+)
Answer» $I f A = [\begin{matrix} c o s θ & s i n θ s i n θ & - c o s θ \end{matrix}], B = [\begin{matrix} 1 & 0 - 1 & 1 \end{matrix}], C = A B A^{T}, t h e n A^{T} C^{n} A e q u a l s t o (n ϵ Z^{+})$

Discussion

10.	A curve is such that the mid point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y−axis lies on the line y=x. If the equation of curve is y=ax+bx2+c and it passes through (1,0), then the value of a−b−c is
Answer» A curve is such that the mid point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the $y -$ axis lies on the line $y = x .$ If the equation of curve is $y = a x + b x^{2} + c$ and it passes through $(1, 0),$ then the value of $a - b - c$ is

Discussion

11.	The value of sin/7 + sin2/7 + sin4/7 is
Answer» The value of sin/7 + sin2/7 + sin4/7 is

Discussion

12.	Define a function as a set of ordered pairs.
Answer» Define a function as a set of ordered pairs.

Discussion

13.	The value of ∫π015+4 cos xdx is
Answer» The value of $\int_{0}^{π} \frac{1}{5 + 4 cos x} dx$ is

Discussion

14.	Find the equation to the straight line (i) cutting off intercepts 3 and 2 from the axes. (ii) cutting off intercepts - 5 and 6 from the axes.
Answer» Find the equation to the straight line (i) cutting off intercepts 3 and 2 from the axes. (ii) cutting off intercepts - 5 and 6 from the axes.

14.

Find the equation to the straight line (i) cutting off intercepts 3 and 2 from the axes. (ii) cutting off intercepts - 5 and 6 from the axes.

Answer»

Find the equation to the straight line

(i) cutting off intercepts 3 and 2 from the axes.

(ii) cutting off intercepts - 5 and 6 from the axes.

Discussion

15.	Find f + g, f - g, cf(cϵR,c≠0). fg. 1f and fg in each of the following : (i) f(x)=x3+1 and g(x)=x+1 (ii) f(x)=√x−1 and g(x)=√x+1
Answer» Find f + g, f - g, $c f (c ϵ R, c \neq 0)$ . fg. $\frac{1}{f}$ and $\frac{f}{g}$ in each of the following : (i) $f (x) = x^{3} + 1$ and $g (x) = x + 1$ (ii) $f (x) = \sqrt{x - 1}$ and $g (x) = \sqrt{x + 1}$

Discussion

16.	If y= a sin 3x + b cos 3x, prove that (d2y/dx2) + 4(dy/dx) + 3y= 10 cos 3x
Answer» If y= a sin 3x + b cos 3x, prove that (d2y/dx2) + 4(dy/dx) + 3y= 10 cos 3x

Discussion

17.	69. how to find conjugate of a complex number
Answer» 69. how to find conjugate of a complex number

Discussion

18.	If the area of △ on the argand plane, whose vertices are -z,iz,z-iz, is 600 sq. units, then \|z\| =
Answer» If the area of $△$ on the argand plane, whose vertices are -z,iz,z-iz, is 600 sq. units, then \|z\| =

Discussion

19.	Find the value of k, if f(x) is continuous at x = 0:f(x) = (Sin3x/2)/x , x not equal to 0 k , x = 0
Answer» Find the value of k, if f(x) is continuous at x = 0: f(x) = (Sin3x/2)/x , x not equal to 0 k , x = 0

Discussion

20.	If a fair coin is tossed n times, then the total number of possible outcomes are
Answer» If a fair coin is tossed n times, then the total number of possible outcomes are

Discussion

21.	Which among the following represents the graph of y=√x+1
Answer» Which among the following represents the graph of $y = \sqrt{x + 1}$

Discussion

22.	Prove the following by using the principle of mathematical induction for all n ∈ N: n (n + 1) (n + 5) is a multiple of 3.
Answer» Prove the following by using the principle of mathematical induction for all n ∈ N: n (n + 1) (n + 5) is a multiple of 3.

Discussion

23.	Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 669 more balls are added, then all the balls can be arranged in the shape of a square such that each of its sides contains 8 balls less than each side of triangle had. The initial number of balls lies in the interval
Answer» Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If $669$ more balls are added, then all the balls can be arranged in the shape of a square such that each of its sides contains $8$ balls less than each side of triangle had. The initial number of balls lies in the interval

Discussion

24.	The value of logtan17∘+logtan37∘+logtan53∘+logtan73∘ is
Answer» The value of $log tan 17^{\circ} + log tan 37^{\circ} + log tan 53^{\circ} + log tan 73^{\circ}$ is

Discussion

25.	If 100∑n=1[nn+1−n−1n]=k, then the value of 101k is
Answer» If $100 \sum n = 1 [\frac{n}{n + 1} - \frac{n - 1}{n}] = k$ , then the value of $101 k$ is

Discussion

26.	Let A=\{x_1,x_2,x_3\} and B =\{y_{1,},y_2,y_3\} then find the number of one - one mapping from A to B such that F(x_i)≠ y_{} , i=1,2,3
Answer» Let A=\{x_1,x_2,x_3\} and B =\{y_{1,},y_2,y_3\} then find the number of one - one mapping from A to B such that F(x_i)≠ y_{} , i=1,2,3

Discussion

27.	17.Foci (± 3、0), a = 4
Answer» 17.Foci (± 3、0), a = 4

Discussion

28.	Find the distance between parallel lines (i) 15 x + 8 y – 34 = 0 and 15 x + 8 y + 31 = 0 (ii) l ( x + y ) + p = 0 and l ( x + y ) – r = 0
Answer» Find the distance between parallel lines (i) 15 x + 8 y – 34 = 0 and 15 x + 8 y + 31 = 0 (ii) l ( x + y ) + p = 0 and l ( x + y ) – r = 0

Discussion

29.	If [x] is the greatest integer less than or equal to x, for all x∈R, then evaluate limx→1+1−\|x\|+sin\|1−x\|\|1−x\|[1−x]
Answer» If $[x]$ is the greatest integer less than or equal to $x$ , for all $x \in R$ , then evaluate $lim x \to 1^{+} \frac{1 - \| x \| + sin \| 1 - x \|}{\| 1 - x \| [1 - x]}$

Discussion

30.	How to find domain and range of a algebraic function
Answer» How to find domain and range of a algebraic function

Discussion

31.	In ΔABC,−−→AB=^i+3^j−2^k, −−→AC=3^i−^j−2^k. If the bisector of ∠BAC meets BC at D and G is the centroid of ΔABC, then \|−−→GD\|=
Answer» In $Δ A B C, - - \to A B =^i + 3^j - 2^k, - - \to A C = 3^i -^j - 2^k .$ If the bisector of $∠ B A C$ meets $B C$ at $D$ and $G$ is the centroid of $Δ A B C$ , then $\| - - \to G D \| =$

Discussion

32.	Let a, b, c be distinct non – negative numbers. If the vectors a^i+a^j+c^k,^i+^k and c^i+c^j+b^k lie in a plane, then c is
Answer» Let a, b, c be distinct non – negative numbers. If the vectors $a^i + a^j + c^k,^i +^k$ and $c^i + c^j + b^k$ lie in a plane, then c is

Discussion

33.	27. The point on the curve x2- 2y which is nearest to the point (0, 5) is(A) (2V2,4) (B) (2^2,0) (C) (o.0) (D) (2,2)
Answer» 27. The point on the curve x2- 2y which is nearest to the point (0, 5) is(A) (2V2,4) (B) (2^2,0) (C) (o.0) (D) (2,2)

Discussion

34.	If the area bounded by y=tan−1x,y=cot−1x and y−axis is k sq. unit, then the value of ek is equal to
Answer» If the area bounded by $y = {tan}^{- 1} x, y = {cot}^{- 1} x$ and $y -$ axis is $k$ sq. unit, then the value of $e^{k}$ is equal to

Discussion

35.	Probability that A speaks truth is.A coin is tossed. A reports that a head appears. The probability thatactually there was head isA. B. C. D.
Answer» Probability that A speaks truth is. A coin is tossed. A reports that a head appears. The probability that actually there was head is A. B. C. D.

35.

Probability that A speaks truth is.A coin is tossed. A reports that a head appears. The probability thatactually there was head isA. B. C. D.

Answer»

Probability that A speaks truth is.
A coin is tossed. A reports that a head appears. The probability that
actually there was head is

A.

B.

C.

D.

Discussion

36.	If the area of a rectangular field is 3600 square units and the length and breadth of the field are coprime to each other, then the possible value of length(s) is (are)
Answer» If the area of a rectangular field is $3600$ square units and the length and breadth of the field are coprime to each other, then the possible value of length(s) is (are)

Discussion

37.	Solve the inequality
Answer» Solve the inequality

Discussion

38.	Find the area enclosed between the parabola y 2 = 4 ax and the line y = mx
Answer» Find the area enclosed between the parabola y 2 = 4 ax and the line y = mx

Discussion

39.	If z=(1+i)(1−i√3)(−2−2i)(i)(3), then
Answer» If $z = (1 + i) (1 - i \sqrt{3}) (- 2 - 2 i) (i) (3),$ then

Discussion

40.	find the range of {x}^2 + 4{x} + 5 where {} are fractional integer function
Answer» find the range of {x}^2 + 4{x} + 5 where {} are fractional integer function

Discussion

41.	Unjumble the letters and find out the word.1. dmeama2. eusirssem3. ermic4. oubrnjo
Answer» Unjumble the letters and find out the word. 1. dmeama 2. eusirssem 3. ermic 4. oubrnjo

Discussion

42.	The coefficients of 5th, 6th and 7th terms in the expansion of (1+x)n are in A.P., find n.
Answer» The coefficients of 5th, 6th and 7th terms in the expansion of $(1 + x)^{n}$ are in A.P., find n.

Discussion

43.	A single letter is selected at random from the word "PROBABILITY”. The probability that the selected letter is a vowel is [MNR 1986; UPSEAT 2000]
Answer» A single letter is selected at random from the word "PROBABILITY”. The probability that the selected letter is a vowel is [MNR 1986; UPSEAT 2000]

43.

A single letter is selected at random from the word "PROBABILITY”. The probability that the selected letter is a vowel is [MNR 1986; UPSEAT 2000]

Answer»

A single letter is selected at random from the word "PROBABILITY”. The probability that the selected letter is a vowel is

[MNR 1986; UPSEAT 2000]

Discussion

44.	Show that the given differential equation is homogeneous and then solve it. (x2+xy)dy=(x2+y2)dx.
Answer» Show that the given differential equation is homogeneous and then solve it. $(x^{2} + x y) d y = (x^{2} + y^{2}) d x .$

Discussion

45.	Write the value of cos1∘+cos2∘+...+cos180∘.
Answer» Write the value of $c o s 1^{\circ} + c o s 2^{\circ} + . . . + c o s 180^{\circ} .$

Discussion

46.	If x and y are real numbers which satisfy the relation x2+9y2−4x+6y+4=0, then the maximum value of (4x−9y)2 is
Answer» If $x$ and $y$ are real numbers which satisfy the relation $x^{2} + 9 y^{2} - 4 x + 6 y + 4 = 0,$ then the maximum value of $\frac{(4 x - 9 y)}{2}$ is

Discussion

47.	2.Ís 3 ! + 4-71?
Answer» 2.Ís 3 ! + 4-71?

Discussion

48.	If f(x)=cos (log x), then f(x) f(y)−12{f(xy)+f(xy)} has the value
Answer» If $f (x) = c o s (l o g x)$ , then $f (x) f (y) - \frac{1}{2} {f (\frac{x}{y}) + f (x y)}$ has the value

Discussion

49.	The sides of a triangle are given as a=3, b=5, c=7, then the smallest angle of triangle is:
Answer» $The sides of a triangle are given as a = 3, b = 5, c = 7, then the smallest angle of triangle i s :$

Discussion

50.	If (5+2√6)n=m+f, where n and m are positive integers and 0 ≤ f < 1, then 11−f−f is equal to:
Answer» If $(5 + 2 \sqrt{6})^{n} = m + f$ , where n and m are positive integers and 0 $\leq$ f < 1, then $\frac{1}{1 - f} - f$ is equal to:

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The maximum distance between the points (acosα,asinα) and (acosβ,asinβ) is

The sum of the roots of the equation √5x2−6x+8−√5x2−6x−7=1 is

If the Boolean expression (p ⊕ q) ∧ (∼ p ⊙ q) is equivalent to p ∧ q, where ⊕, ⊙∈{∧, ∨}, then the ordered pair (⊕, ⊙) is:

Total number of integral values of a such that x^2 + ax + a + 1 = 0 has integral roots is equal to

Y=x²+x is maximum for

Let a,b,c be the roots of the equation px3+qx2+rx+s=0. If ∣∣∣∣∣−bcb2+bcc2+bca2+ac−acc2+aca2+abb2+ab−ab∣∣∣∣∣=27, a+b+c≥0 and a2+b2+c2=3, then the value of 3p+q is

If x,y,z∈R and x+y+z =5, xy +yz+zx=3, probability for x to be positive only is

cosec18∘ is a root of the equation

If A=[cosθsinθsinθ−cosθ],B=[10−11],C=ABAT,then ATCnA equals to(nϵZ+)

A curve is such that the mid point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y−axis lies on the line y=x. If the equation of curve is y=ax+bx2+c and it passes through (1,0), then the value of a−b−c is

The value of sin/7 + sin2/7 + sin4/7 is

Define a function as a set of ordered pairs.

The value of ∫π015+4 cos xdx is

Find the equation to the straight line (i) cutting off intercepts 3 and 2 from the axes. (ii) cutting off intercepts - 5 and 6 from the axes.

Find f + g, f - g, cf(cϵR,c≠0). fg. 1f and fg in each of the following : (i) f(x)=x3+1 and g(x)=x+1 (ii) f(x)=√x−1 and g(x)=√x+1

If y= a sin 3x + b cos 3x, prove that (d2y/dx2) + 4(dy/dx) + 3y= 10 cos 3x

69. how to find conjugate of a complex number

If the area of △ on the argand plane, whose vertices are -z,iz,z-iz, is 600 sq. units, then |z| =

Find the value of k, if f(x) is continuous at x = 0:f(x) = (Sin3x/2)/x , x not equal to 0 k , x = 0

If a fair coin is tossed n times, then the total number of possible outcomes are

Which among the following represents the graph of y=√x+1

Prove the following by using the principle of mathematical induction for all n ∈ N: n (n + 1) (n + 5) is a multiple of 3.

The value of logtan17∘+logtan37∘+logtan53∘+logtan73∘ is

If 100∑n=1[nn+1−n−1n]=k, then the value of 101k is

Let A=\{x_1,x_2,x_3\} and B =\{y_{1,},y_2,y_3\} then find the number of one - one mapping from A to B such that F(x_i)≠ y_{} , i=1,2,3

17.Foci (± 3、0), a = 4

Find the distance between parallel lines (i) 15 x + 8 y – 34 = 0 and 15 x + 8 y + 31 = 0 (ii) l ( x + y ) + p = 0 and l ( x + y ) – r = 0

If [x] is the greatest integer less than or equal to x, for all x∈R, then evaluate limx→1+1−|x|+sin|1−x||1−x|[1−x]

How to find domain and range of a algebraic function

In ΔABC,−−→AB=^i+3^j−2^k, −−→AC=3^i−^j−2^k. If the bisector of ∠BAC meets BC at D and G is the centroid of ΔABC, then |−−→GD|=

Let a, b, c be distinct non – negative numbers. If the vectors a^i+a^j+c^k,^i+^k and c^i+c^j+b^k lie in a plane, then c is

27. The point on the curve x2- 2y which is nearest to the point (0, 5) is(A) (2V2,4) (B) (2^2,0) (C) (o.0) (D) (2,2)

If the area bounded by y=tan−1x,y=cot−1x and y−axis is k sq. unit, then the value of ek is equal to

Probability that A speaks truth is.A coin is tossed. A reports that a head appears. The probability thatactually there was head isA. B. C. D.

If the area of a rectangular field is 3600 square units and the length and breadth of the field are coprime to each other, then the possible value of length(s) is (are)

Solve the inequality

Find the area enclosed between the parabola y 2 = 4 ax and the line y = mx

If z=(1+i)(1−i√3)(−2−2i)(i)(3), then

find the range of {x}^2 + 4{x} + 5 where {} are fractional integer function

Unjumble the letters and find out the word.1. dmeama2. eusirssem3. ermic4. oubrnjo

The coefficients of 5th, 6th and 7th terms in the expansion of (1+x)n are in A.P., find n.

A single letter is selected at random from the word "PROBABILITY”. The probability that the selected letter is a vowel is [MNR 1986; UPSEAT 2000]

Show that the given differential equation is homogeneous and then solve it. (x2+xy)dy=(x2+y2)dx.

Write the value of cos1∘+cos2∘+...+cos180∘.

If x and y are real numbers which satisfy the relation x2+9y2−4x+6y+4=0, then the maximum value of (4x−9y)2 is

2.Ís 3 ! + 4-71?

If f(x)=cos (log x), then f(x) f(y)−12{f(xy)+f(xy)} has the value

The sides of a triangle are given as a=3, b=5, c=7, then the smallest angle of triangle is:

If (5+2√6)n=m+f, where n and m are positive integers and 0 ≤ f &lt; 1, then 11−f−f is equal to:

If (5+2√6)n=m+f, where n and m are positive integers and 0 ≤ f < 1, then 11−f−f is equal to: