43030 + Interview Questions in Mathematics Page 2 InterviewSolution

51.	The number of four letter words that can be formed using the letters of the word BARRACK is
Answer» The number of four letter words that can be formed using the letters of the word $B A R R A C K$ is

Discussion

52.	If Sr denotes the sum of the infinite geometric series whose first term is r and common ratio is 11+r, where r∈N, then the value of 10∑r=1S2r is
Answer» If $S_{r}$ denotes the sum of the infinite geometric series whose first term is $r$ and common ratio is $\frac{1}{1 + r}$ , where $r \in N$ , then the value of $10 \sum r = 1 S_{r}^{2}$ is

Discussion

53.	The number of integral values of k for which the line, 3x+4y=kintersects the circle, x2+y2−2x−4y+4=0 at two distinct points is
Answer» The number of integral values of $k$ for which the line, $3 x + 4 y = k$ intersects the circle, $x^{2} + y^{2} - 2 x - 4 y + 4 = 0$ at two distinct points is

Discussion

54.	Question 1If cosA=45, then the value of tan A is(A) 35(B) 34(C) 43(D) 53
Answer» Question 1 If $c o s A = \frac{4}{5}$ , then the value of tan A is (A) $\frac{3}{5}$ (B) $\frac{3}{4}$ (C) $\frac{4}{3}$ (D) $\frac{5}{3}$

Discussion

55.	A variable plane intersects the coordinate axes at A,B,C and is at a constant distance p from O(0,0,0). Then the locus of the centroid of the tetrahedron OABC is
Answer» A variable plane intersects the coordinate axes at $A, B, C$ and is at a constant distance $p$ from $O (0, 0, 0) .$ Then the locus of the centroid of the tetrahedron $O A B C$ is

Discussion

56.	Express the function f:X→R given by f(x)=x3+1 as set of ordered pairs, where X = {-1, 0, 3, 9, 7}.
Answer» Express the function $f : X \to R$ given by $f (x) = x^{3} + 1$ as set of ordered pairs, where X = {-1, 0, 3, 9, 7}.

Discussion

57.	If two cards are drawn one by one without replacement from a well shuffled deck of cards, then the probability that both of these cards are king is
Answer» If two cards are drawn one by one without replacement from a well shuffled deck of cards, then the probability that both of these cards are king is

Discussion

58.	What does direction ratio actually mean???? Because the definition saying that 3 numbers proportional to the direction cosines of a line is called a direction ratio is not So imaginable ...
Answer» What does direction ratio actually mean???? Because the definition saying that 3 numbers proportional to the direction cosines of a line is called a direction ratio is not So imaginable ...

Discussion

59.	Difference between width and breadth
Answer» Difference between width and breadth

Discussion

60.	Draw the graph of the following linear equations in two variables: x+y=4
Answer» Draw the graph of the following linear equations in two variables: $x + y = 4$

Discussion

61.	(i) Which term of the sequence 24,2314,2212,2234,…… is the first negative term ? (ii) Which term of the sequence 12+8i,11+6i,10+4i,…… is (a) purely real (b) purely imaginary ?
Answer» (i) Which term of the sequence $24, 23 \frac{1}{4}, 22 \frac{1}{2}, 22 \frac{3}{4}, \dots \dots$ is the first negative term ? (ii) Which term of the sequence $12 + 8 i, 11 + 6 i, 10 + 4 i, \dots \dots$ is (a) purely real (b) purely imaginary ?

61.

(i) Which term of the sequence 24,2314,2212,2234,…… is the first negative term ? (ii) Which term of the sequence 12+8i,11+6i,10+4i,…… is (a) purely real (b) purely imaginary ?

Answer»

(i) Which term of the sequence $24, 23 \frac{1}{4}, 22 \frac{1}{2}, 22 \frac{3}{4}, \dots \dots$ is the first negative term ?

(ii) Which term of the sequence $12 + 8 i, 11 + 6 i, 10 + 4 i, \dots \dots$ is (a) purely real (b) purely imaginary ?

Discussion

62.	Value of sin(45+θ)cos(15+θ)−cos(45+θ)sin(15+θ):-
Answer» Value of $s i n (45 + θ) c o s (15 + θ) - c o s (45 + θ) s i n (15 + θ)$ :-

Discussion

63.	1)f(x^2)=x^3+x^2+x+1,x>0 find (16)2)f(2x+5)=x^4+x^2+1, find f(3)
Answer» 1)f(x^2)=x^3+x^2+x+1,x>0 find (16) 2)f(2x+5)=x^4+x^2+1, find f(3)

Discussion

64.	In triangle ABC , AB =AC and BC=AB +AI , where I is the incentre of triangle ABC . Thenfind the measure of angle A.
Answer» In triangle ABC , AB =AC and BC=AB +AI , where I is the incentre of triangle ABC . Then find the measure of angle A.

Discussion

65.	The points on the parabola y2=12x whose focal distance is 4, are
Answer» The points on the parabola $y^{2} = 12 x$ whose focal distance is 4, are

Discussion

66.	The area (in sq. units) of a pentagon whose vertices are (4,3),(−5,6),(0,−7),(3,−6) and (−7,−2) is
Answer» The area (in sq. units) of a pentagon whose vertices are $(4, 3), (- 5, 6), (0, - 7), (3, - 6)$ and $(- 7, - 2)$ is

Discussion

67.	A rod AB of the length 30 units slips on the coordinate axes such that A lies on x−axis and B lies on y−axis. Then, the locus of C if BC=2AC is
Answer» A rod $A B$ of the length $30$ units slips on the coordinate axes such that $A$ lies on $x -$ axis and $B$ lies on $y -$ axis. Then, the locus of $C$ if $B C = 2 A C$ is

Discussion

68.	Answer the following as true or false: (i) Two vectors having same magnitude are collinear.
Answer» Answer the following as true or false: (i) Two vectors having same magnitude are collinear.

Discussion

69.	The cricketer, whose record is exemplary, bagged an eight-year endorsement contract with a sportswear giant.
Answer» The cricketer, whose record is exemplary, bagged an eight-year endorsement contract with a sportswear giant.

Discussion

70.	The A. M. of n observations is M. If the sum of n - 4 observations is a, then the mean of remaining 4 observations is
Answer» The A. M. of n observations is M. If the sum of n - 4 observations is a, then the mean of remaining 4 observations is

Discussion

71.	List IList II (A)If limn→∞(n2+1n+1−an)−b=0,thenthe value of b is(P)0(B)If x2y+y3=2 and the value of d2ydx2 at x=1 is −m8, then the value of m is(Q)1(C)If f(x)={x,x≤1x2+bx+c,x>1 and f′(x)exists for all x∈R, then the value of c is(R)2(D)If f(x)=x∫0tsin1t dt, then the number ofpoint(s) of discontinuity of f(x) in (0,π) is(S)−1(T)4(U)3Which of the following is the only CORRECT combination?
Answer» $\begin{matrix} List I & List II (A) & If lim n \to \infty (\frac{n^{2} + 1}{n + 1} - a n) - b = 0, then the value of b is & (P) & 0 (B) & If x^{2} y + y^{3} = 2 and the value of \frac{d^{2} y}{d x^{2}} at x = 1 is - \frac{m}{8}, then the value of m is & (Q) & 1 (C) & If f (x) = {\begin{matrix} x, & x \leq 1 x^{2} + b x + c, & x > 1 \end{matrix} and f^{'} (x) exists for all x \in R, then the value of c is & (R) & 2 (D) & If f (x) = x \int 0 t sin \frac{1}{t} d t, then the number of point(s) of discontinuity of f (x) in (0, π) is & (S) & - 1 (T) & 4 (U) & 3 \end{matrix}$ Which of the following is the only CORRECT combination?

Discussion

72.	The roster form of the set {x:x is a real number and x3=3x2−2x}
Answer» The roster form of the set ${x : x$ is a real number and $x^{3} = 3 x^{2} - 2 x}$

Discussion

73.	The number of triangles in the given figure is
Answer» The number of triangles in the given figure is

Discussion

74.	Let P(x0,y0) be a point on the curve C:(x2−11)(y+1)+4=0, where x0,y0∈N. Then the area (in sq. units) of the triangle formed by the normal drawn to the curve C at P and the co-ordinate axes is
Answer» Let $P (x_{0}, y_{0})$ be a point on the curve $C : (x^{2} - 11) (y + 1) + 4 = 0,$ where $x_{0}, y_{0} \in N .$ Then the area (in sq. units) of the triangle formed by the normal drawn to the curve $C$ at $P$ and the co-ordinate axes is

Discussion

75.	(2nC1)2+2×(2nC2)2+3.(2nC3)2.....+2n(2nC2n)2,When n = 100
Answer» $(^{2 n} C_{1})^{2} + 2 \times (^{2 n} C_{2})^{2} + 3. (^{2 n} C_{3})^{2} . . . . . + 2 n (^{2 n} C_{2 n})^{2}$ ,When n = 100

Discussion

76.	Using Binomial Theorem, evaluate (101)4
Answer» Using Binomial Theorem, evaluate (101)⁴

Discussion

77.	The number of points of intersection of f(x)=2sinx,x∈[0,4π] and y=1.5 are
Answer» The number of points of intersection of $f (x) = 2 sin x, x \in [0, 4 π]$ and $y = 1.5$ are

Discussion

78.	Tangent at any point on the curve x2y3=a5 has an intercept between the axes. This intercept is divided in the ratio m:n, such that m>n and m,n are co-prime, then 4m+2n=
Answer» Tangent at any point on the curve $x^{2} y^{3} = a^{5}$ has an intercept between the axes. This intercept is divided in the ratio $m : n,$ such that $m > n$ and $m, n$ are co-prime, then $4 m + 2 n =$

Discussion

79.	Number of solutions of the equation 2x+x=2sinx+sinx in [0,10π] is
Answer» Number of solutions of the equation $2^{x} + x = 2^{sin x} + sin x$ in $[0, 10 π]$ is

Discussion

80.	Mark the correct alternative in the following question:The relation S defined on the set R of all real number by the rule aSb iff a ≥ b is(a) an equivalence relation(b) reflexive, transitive but not symmetric(c) symmetric, transitive but not reflexive(d) neither transitive nor reflexive but symmetric
Answer» Mark the correct alternative in the following question: The relation S defined on the set R of all real number by the rule aSb iff a $\geq$ b is (a) an equivalence relation (b) reflexive, transitive but not symmetric (c) symmetric, transitive but not reflexive (d) neither transitive nor reflexive but symmetric

Discussion

81.	2x+6y = 8
Answer» 2x+6y = 8

Discussion

82.	If x = 3 is one root of the quadratic equation x2 – 2kx – 6 = 0, then find the value of k.
Answer» If x = 3 is one root of the quadratic equation x² – 2kx – 6 = 0, then find the value of k.

Discussion

83.	If the sum and product of 20 terms in G.P. are 16 and 1024 respectively, then the sum of its reciprocals is
Answer» If the sum and product of $20$ terms in G.P. are $16$ and $1024$ respectively, then the sum of its reciprocals is

Discussion

84.	The equation of the plane containing the line x−11=y−22=z−33 and parallel to the line x−23=y−31=z−12 is Ax+By+Cz=0 then the value of A+B+C=
Answer» The equation of the plane containing the line $\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and parallel to the line $\frac{x - 2}{3} = \frac{y - 3}{1} = \frac{z - 1}{2}$ is $A x + B y + C z = 0$ then the value of $A + B + C =$

Discussion

85.	If (1+i)22−i=x+iy, find x+y.
Answer» $If \frac{(1 + i)^{2}}{2 - i} = x + i y, find x + y .$

Discussion

86.	If the roots of a quadratic equation are −6 and 7, then the quadratic equation is
Answer» If the roots of a quadratic equation are $- 6$ and $7$ , then the quadratic equation is

Discussion

87.	Which of the following sets are the subsets of A={k:k is a factor of 48}?
Answer» Which of the following sets are the subsets of $A = {k : k is a factor of 48} ?$

Discussion

88.	The value of sin−1(cos53π5) is
Answer» The value of ${sin}^{- 1} (cos \frac{53 π}{5})$ is

Discussion

89.	Second term of an AP is 9 If the sum of first 6 terms is equal to1/4th the sum of next 6 terms then the fourth term is
Answer» Second term of an AP is 9 If the sum of first 6 terms is equal to1/4th the sum of next 6 terms then the fourth term is

Discussion

90.	8. Consider that the graph of y=f(x) is symmetric about the lines x=2 and x=4 then the period of f(x) is
Answer» 8. Consider that the graph of y=f(x) is symmetric about the lines x=2 and x=4 then the period of f(x) is

Discussion

91.	Write the order of the differential equation representing the family of curves y = ax + a3.
Answer» Write the order of the differential equation representing the family of curves y = ax + a³.

Discussion

92.	If x∈R, then the range of log5/4(5x2−8x+4) is
Answer» If $x \in R$ , then the range of ${log}_{5 / 4} (5 x^{2} - 8 x + 4)$ is

Discussion

93.	Value of x for logx 100 - 2 logx 2 = 2 is
Answer» Value of x for log^x100 - 2 log_x2 = 2 is

Discussion

94.	If a→ , b→ are two vectors such that a→=1,b→=2 and a→×b⇀=2 then the angle between a→ and b→ is _____________.
Answer» If $\vec{a}, \vec{b}$ are two vectors such that $\|\vec{a}\| = 1, \|\vec{b}\| = 2 and \|\vec{a} \times \overset{⇀}{b}\| = \sqrt{2}$ then the angle between $\vec{a} and \vec{b}$ is _____________.

Discussion

95.	Find the value of tan−1(tan(−6)).
Answer» Find the value of ${tan}^{- 1} (tan (- 6)) .$

Discussion

96.	If cot a - tan a = 2 , then a = ? /2, /4, /8, /15
Answer» If cot a - tan a = 2 , then a = ? /2, /4, /8, /15

Discussion

97.	Let f,g and h be the lengths of the perpendiculars from the circumcentre of ΔABC on the sides a,b, and c respectively, and af+bg+ch=1λabcfgh, then λ is :
Answer» Let $f, g$ and $h$ be the lengths of the perpendiculars from the circumcentre of $Δ A B C$ on the sides $a, b,$ and $c$ respectively, and $\frac{a}{f} + \frac{b}{g} + \frac{c}{h} = \frac{1}{λ} \frac{a b c}{f g h},$ then $λ$ is :

Discussion

98.	If the slope of OA is 1, slope of OB is 7 and OA=OB, where A and B are points in the first quadrant and ' O ' is the origin then the absolute value of 10 times the slope of AB is
Answer» If the slope of $O A$ is 1, slope of $O B$ is 7 and $O A = O B$ , where $A$ and $B$ are points in the first quadrant and ' $O$ ' is the origin then the absolute value of $10$ times the slope of $A B$ is

Discussion

99.	The roots of the equation x2+\|x\|−2=0 is/are
Answer» The roots of the equation $x^{2} + \| x \| - 2 = 0$ is/are

Discussion

100.	If x=3secθ−2 and y=3tanθ+2, then which of the following equation in x,y is correct?
Answer» If $x = 3 sec θ - 2$ and $y = 3 tan θ + 2$ , then which of the following equation in $x, y$ is correct?

Discussion

Explore topic-wise InterviewSolutions in .

The number of four letter words that can be formed using the letters of the word BARRACK is

If Sr denotes the sum of the infinite geometric series whose first term is r and common ratio is 11+r, where r∈N, then the value of 10∑r=1S2r is

The number of integral values of k for which the line, 3x+4y=kintersects the circle, x2+y2−2x−4y+4=0 at two distinct points is

Question 1If cosA=45, then the value of tan A is(A) 35(B) 34(C) 43(D) 53

A variable plane intersects the coordinate axes at A,B,C and is at a constant distance p from O(0,0,0). Then the locus of the centroid of the tetrahedron OABC is

Express the function f:X→R given by f(x)=x3+1 as set of ordered pairs, where X = {-1, 0, 3, 9, 7}.

If two cards are drawn one by one without replacement from a well shuffled deck of cards, then the probability that both of these cards are king is

What does direction ratio actually mean???? Because the definition saying that 3 numbers proportional to the direction cosines of a line is called a direction ratio is not So imaginable ...

Difference between width and breadth

Draw the graph of the following linear equations in two variables: x+y=4

(i) Which term of the sequence 24,2314,2212,2234,…… is the first negative term ? (ii) Which term of the sequence 12+8i,11+6i,10+4i,…… is (a) purely real (b) purely imaginary ?

Value of sin(45+θ)cos(15+θ)−cos(45+θ)sin(15+θ):-

1)f(x^2)=x^3+x^2+x+1,x>0 find (16)2)f(2x+5)=x^4+x^2+1, find f(3)

In triangle ABC , AB =AC and BC=AB +AI , where I is the incentre of triangle ABC . Thenfind the measure of angle A.

The points on the parabola y2=12x whose focal distance is 4, are

The area (in sq. units) of a pentagon whose vertices are (4,3),(−5,6),(0,−7),(3,−6) and (−7,−2) is

A rod AB of the length 30 units slips on the coordinate axes such that A lies on x−axis and B lies on y−axis. Then, the locus of C if BC=2AC is

Answer the following as true or false: (i) Two vectors having same magnitude are collinear.

The cricketer, whose record is exemplary, bagged an eight-year endorsement contract with a sportswear giant.

The A. M. of n observations is M. If the sum of n - 4 observations is a, then the mean of remaining 4 observations is

The roster form of the set {x:x is a real number and x3=3x2−2x}

The number of triangles in the given figure is

Let P(x0,y0) be a point on the curve C:(x2−11)(y+1)+4=0, where x0,y0∈N. Then the area (in sq. units) of the triangle formed by the normal drawn to the curve C at P and the co-ordinate axes is

(2nC1)2+2×(2nC2)2+3.(2nC3)2.....+2n(2nC2n)2,When n = 100

Using Binomial Theorem, evaluate (101)4

The number of points of intersection of f(x)=2sinx,x∈[0,4π] and y=1.5 are

Tangent at any point on the curve x2y3=a5 has an intercept between the axes. This intercept is divided in the ratio m:n, such that m&gt;n and m,n are co-prime, then 4m+2n=

Number of solutions of the equation 2x+x=2sinx+sinx in [0,10π] is

2x+6y = 8

If x = 3 is one root of the quadratic equation x2 – 2kx – 6 = 0, then find the value of k.

If the sum and product of 20 terms in G.P. are 16 and 1024 respectively, then the sum of its reciprocals is

The equation of the plane containing the line x−11=y−22=z−33 and parallel to the line x−23=y−31=z−12 is Ax+By+Cz=0 then the value of A+B+C=

If (1+i)22−i=x+iy, find x+y.

If the roots of a quadratic equation are −6 and 7, then the quadratic equation is

Which of the following sets are the subsets of A={k:k is a factor of 48}?

The value of sin−1(cos53π5) is

Second term of an AP is 9 If the sum of first 6 terms is equal to1/4th the sum of next 6 terms then the fourth term is

8. Consider that the graph of y=f(x) is symmetric about the lines x=2 and x=4 then the period of f(x) is

Write the order of the differential equation representing the family of curves y = ax + a3.

If x∈R, then the range of log5/4(5x2−8x+4) is

Value of x for logx 100 - 2 logx 2 = 2 is

If a→ , b→ are two vectors such that a→=1,b→=2 and a→×b⇀=2 then the angle between a→ and b→ is _____________.

Find the value of tan−1(tan(−6)).

If cot a - tan a = 2 , then a = ? /2, /4, /8, /15

Let f,g and h be the lengths of the perpendiculars from the circumcentre of ΔABC on the sides a,b, and c respectively, and af+bg+ch=1λabcfgh, then λ is :

If the slope of OA is 1, slope of OB is 7 and OA=OB, where A and B are points in the first quadrant and ' O ' is the origin then the absolute value of 10 times the slope of AB is

The roots of the equation x2+|x|−2=0 is/are

If x=3secθ−2 and y=3tanθ+2, then which of the following equation in x,y is correct?

Tangent at any point on the curve x2y3=a5 has an intercept between the axes. This intercept is divided in the ratio m:n, such that m>n and m,n are co-prime, then 4m+2n=