43030 + Interview Questions in Mathematics Page 64 InterviewSolution

3151.	A plane passing through the point (3,1,1) contains two lines whose direction ratios are 1,−2,2 and 2,3,−1 respectively. If this plane also passes through the point (α,−3,5), then α is equal to:
Answer» A plane passing through the point $(3, 1, 1)$ contains two lines whose direction ratios are $1, - 2, 2$ and $2, 3, - 1$ respectively. If this plane also passes through the point $(α, - 3, 5)$ , then $α$ is equal to:

Discussion

3152.	Find the relationship between a and b so that the function f defined by is continuous at x = 3.
Answer» Find the relationship between a and b so that the function f defined by is continuous at x = 3.

Discussion

3153.	If the system of equations 4x + py 21 and px 2y 15 hasunique solution, then which of the following could be the valueof p?
Answer» If the system of equations 4x + py 21 and px 2y 15 has unique solution, then which of the following could be the value of p?

Discussion

3154.	The Newton-Raphson method formula for finding the square root of a real number N from the equation x2−N=0 is
Answer» The Newton-Raphson method formula for finding the square root of a real number N from the equation $x^{2} - N = 0$ is

Discussion

3155.	The number of value(s) of x for which the function f(x)=log10\|sinx\|+log10\|cosx\| is not defined in the interval [0,10π] is equal to
Answer» The number of value(s) of $x$ for which the function $f (x) = {log}_{10} \| sin x \| + {log}_{10} \| cos x \|$ is not defined in the interval $[0, 10 π]$ is equal to

Discussion

3156.	There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
Answer» There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

Discussion

3157.	Theprobability that a student is not a swimmer is.Then the probability that out of five students, four are swimmers is(A) (B) (C) (D) Noneof these
Answer» The probability that a student is not a swimmer is. Then the probability that out of five students, four are swimmers is (A) (B) (C) (D) None of these

3157.

Theprobability that a student is not a swimmer is.Then the probability that out of five students, four are swimmers is(A) (B) (C) (D) Noneof these

Answer»

The
probability that a student is not a swimmer is.
Then the probability that out of five students, four are swimmers is

(A) (B)

(C) (D) None
of these

Discussion

3158.	If a≠b≠c, write the condition for which the equations (b−c)x+(c−a) y+(a−b)=0 and (b3−c3)x+(c3−a3)y+(a3−b3=0 represent the same line.
Answer» If $a \neq b \neq c,$ write the condition for which the equations $(b - c) x + (c - a)$ $y + (a - b) = 0$ and $(b^{3} - c^{3}) x + (c^{3} - a^{3}) y + (a^{3} - b^{3} = 0$ represent the same line.

Discussion

3159.	If I=3π∫0[tanx]dx, where [.] represents the greatest integer function, then the value of ∣∣∣2Iπ∣∣∣ is
Answer» If $I = 3 π \int 0 [tan x] d x,$ where $[.]$ represents the greatest integer function, then the value of $∣ ∣ ∣ \frac{2 I}{π} ∣ ∣ ∣$ is

Discussion

3160.	Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?
Answer» Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

Discussion

3161.	What is ungrouped data ?
Answer» What is ungrouped data ?

Discussion

3162.	35. If b tan theta=a ,then the value of a sin theta-b cos theta/a sin theta+b cos theta is
Answer» 35. If b tan theta=a ,then the value of a sin theta-b cos theta/a sin theta+b cos theta is

Discussion

3163.	The value of limn→∞(a−1+n√ba)n, (a>0,b>0) is equal to
Answer» The value of $lim n \to \infty {(\frac{a - 1 + \sqrt[n]{b}}{a})}^{n}, (a > 0, b > 0)$ is equal to

Discussion

3164.	If α, β and γ are the real roots of a³ − 6a²+ 3a + 1 = 0, determine the sum of possible values of α²β + β²γ + γ²α.
Answer» If α, β and γ are the real roots of a³ − 6a²+ 3a + 1 = 0, determine the sum of possible values of α²β + β²γ + γ²α.

Discussion

3165.	AA1,BB1,CC1 are the medians of triangle ABC whose centroid is G.If the points A,C1,G and B1 are concyclic,then which of the following options is correct?
Answer» $A A_{1}, B B_{1}, C C_{1}$ are the medians of triangle $A B C$ whose centroid is $G$ .If the points $A, C_{1}, G$ and $B_{1}$ are concyclic,then which of the following options is correct?

Discussion

3166.	Prove that cosα+cosα+β+cosα+2β+...+cosα+n-1β=cosα+n-12βsinnβ2sinβ2 for all n∈N. [NCERT EXEMPLAR]
Answer» $Prove that \cos α + \cos (α + β) + \cos (α + 2 β) + . . . + \cos [α + (n - 1) β] = \frac{\cos \{α + (\frac{n - 1}{2}) β\} \sin (\frac{n β}{2})}{\sin (\frac{β}{2})} for all n \in N .$ [NCERT EXEMPLAR]

Discussion

3167.	If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of A and B occurs) = 59, then find the value of p.
Answer» If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of A and B occurs) = $\frac{5}{9}$ , then find the value of p.

Discussion

3168.	The least integer greater than log215⋅log1/62⋅log316 is
Answer» The least integer greater than ${log}_{2} 15 \cdot {log}_{1 / 6} 2 \cdot {log}_{3} \frac{1}{6}$ is

Discussion

3169.	Will the value of rnot will remain same or constant in all cases or it will change??
Answer» Will the value of rnot will remain same or constant in all cases or it will change??

Discussion

3170.	Find the area of the region bounded by y 2 = 9 x , x = 2, x = 4 and the x -axis in the first quadrant.
Answer» Find the area of the region bounded by y 2 = 9 x , x = 2, x = 4 and the x -axis in the first quadrant.

Discussion

3171.	The differential equation(s) of family of curves whose tangent form an angle of π4 with the hyperbola xy=c2 is/are given by
Answer» The differential equation(s) of family of curves whose tangent form an angle of $\frac{π}{4}$ with the hyperbola $x y = c^{2}$ is/are given by

Discussion

3172.	Solve the following equation- 2 sin^2 x +3^1/2 cos x + 1 = 0
Answer» Solve the following equation- 2 sin^2 x +3^1/2 cos x + 1 = 0

Discussion

3173.	If the system of linear equationsx−4y+7z=7g 3y−5z=h−2x+5y−9z=kis consistent, then :
Answer» If the system of linear equations $\begin{matrix} x - 4 y + 7 z = 7 g 3 y - 5 z = h - 2 x + 5 y - 9 z = k \end{matrix}$ is consistent, then :

Discussion

3174.	zeroes of polynomial x^2+kx +k,k not equal to zero.options a) can't both be positive b) can't both be negative c) data insufficient d) one positive and one negative
Answer» zeroes of polynomial x^2+kx +k,k not equal to zero.options a) can't both be positive b) can't both be negative c) data insufficient d) one positive and one negative

Discussion

3175.	Show that for any sets A and B, A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)
Answer» Show that for any sets A and B, A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)

Discussion

3176.	31.Three persons A,B and C throw a die in succession till one gets a six and wins the game.find their respective probabilities of winning
Answer» 31.Three persons A,B and C throw a die in succession till one gets a six and wins the game.find their respective probabilities of winning

Discussion

3177.	∫(x+2x+4)2exdx is equal to
Answer» $\int {(\frac{x + 2}{x + 4})}^{2} e^{x} d x$ is equal to

Discussion

3178.	In triangle ABC, if cotA,cotB,cotC are in A.P., then a2,b2,c2 are in:
Answer» In triangle $A B C$ , if $cot A, cot B, cot C$ are in $A . P .$ , then $a^{2}, b^{2}, c^{2}$ are in:

Discussion

3179.	equals
Answer» equals

3179.

equals

Answer»

equals

Discussion

3180.	A point “P” is located in three dimensional coordinate plane such that the angles made by OP with positive direction of X - axis is 30∘ and Y- axis is 60∘ then find the angle made by OP with positive direction of Z - axis, where “O” is origin.
Answer» A point “P” is located in three dimensional coordinate plane such that the angles made by OP with positive direction of X - axis is $30^{\circ}$ and Y- axis is $60^{\circ}$ then find the angle made by OP with positive direction of Z - axis, where “O” is origin.

Discussion

3181.	Tangent at any point on the hyperbola x2a2−y2b2=1 cut the axis at A and B respectively. If the rectangle OAPB (where O is origin) is completed then locus of point P is given by
Answer» Tangent at any point on the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ cut the axis at A and B respectively. If the rectangle OAPB (where O is origin) is completed then locus of point P is given by

Discussion

3182.	IQ of a person is given by the formula Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.
Answer» IQ of a person is given by the formula Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.

Discussion

3183.	If the length of the common chord of two circles of radii 3 and 4 units, which intersect orthogonally is k5, then the value of k is
Answer» If the length of the common chord of two circles of radii $3$ and $4$ units, which intersect orthogonally is $\frac{k}{5},$ then the value of $k$ is

Discussion

3184.	Findthe coefficient of a5b7in (a –2b)12
Answer» Find the coefficient of a⁵b⁷ in (a – 2b)¹²

Discussion

3185.	,xin quadrant III
Answer» , x in quadrant III

Discussion

3186.	If the sum to n terms of the series 312×22+522×32+732×42+…… is 0.99, then the value of n is
Answer» If the sum to $n$ terms of the series $\frac{3}{1^{2} \times 2^{2}} + \frac{5}{2^{2} \times 3^{2}} + \frac{7}{3^{2} \times 4^{2}} + \dots \dots$ is $0.99$ , then the value of $n$ is

Discussion

3187.	If limx→0(ax+bx+cx+dx4)1/x=8, then the minimum value of the determinant ∣∣∣a+ibc+id−c+ida−ib∣∣∣ is
Answer» If $lim x \to 0 {(\frac{a^{x} + b^{x} + c^{x} + d^{x}}{4})}^{1 / x} = 8,$ then the minimum value of the determinant $∣ ∣ ∣ \begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix} ∣ ∣ ∣$ is

Discussion

3188.	Prove that: cot π8=2+1
Answer» Prove that: $\cot \frac{π}{8} = \sqrt{2} + 1$

Discussion

3189.	5C1+5C2+5C3+5C4+5C5 is equal to
Answer» $^{5} C_{1} +^{5} C_{2} +^{5} C_{3} +^{5} C_{4} +^{5} C_{5}$ is equal to

Discussion

3190.	36. If f(X+1/y) + f(x-1/y)=2f(X)f(1/y) for all X,y belong to R-{0} and f(0)=1/2 then f(4) is
Answer» 36. If f(X+1/y) + f(x-1/y)=2f(X)f(1/y) for all X,y belong to R-{0} and f(0)=1/2 then f(4) is

Discussion

3191.	Find the sixth term in the expansion y12+x13n, if the binomial coefficient of the third term from the end is 45.
Answer» Find the sixth term in the expansion ${(y^{\frac{1}{2}} + x^{\frac{1}{3}})}^{n}$ , if the binomial coefficient of the third term from the end is 45.

Discussion

3192.	How many real numbers satisfy the relation [x]=32x. __
Answer» How many real numbers satisfy the relation $[x] = \frac{3}{2} x$ . __

Discussion

3193.	Mark the correct alternative in each of the following:The linear inequality representing the solution set given in Fig. 15.44 is (a) x<5(b) x>5(c) x≥5(d) x≤5
Answer» Mark the correct alternative in each of the following: The linear inequality representing the solution set given in Fig. 15.44 is (a) $\|x\|$ $<$ 5 (b) $\|x\|$ $>$ 5 (c) $\|x\|$ $\geq$ 5 (d) $\|x\|$ $\leq$ 5

Discussion

3194.	In throwing 3 dice what is the probability that atleast 2 of the dice show same numbers?
Answer» In throwing 3 dice what is the probability that atleast 2 of the dice show same numbers?

Discussion

3195.	A child has a die whose 6 faces show the letters given below: A B C A D A The die is thrown once. What is the probability of getting (i) A, (ii) D?
Answer» A child has a die whose 6 faces show the letters given below: $A B C A D A$ The die is thrown once. What is the probability of getting (i) A, (ii) D?

Discussion

3196.	What is the differentiation of f(x)=y-2÷(3-x).
Answer» What is the differentiation of f(x)=y-2÷(3-x).

Discussion

3197.	If z=−5+3i and the value of z4+9z3+26z2−14z+8 is k, where k∈R, then the value of −k is
Answer» If $z = - 5 + 3 i$ and the value of $z^{4} + 9 z^{3} + 26 z^{2} - 14 z + 8$ is $k$ , where $k \in R$ , then the value of $- k$ is

Discussion

3198.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes. Outcome 3 heads 2 heads 1 head No head Frequency 23 72 77 28 If the three coins are simultaneously tossed again, compute the(i) probability of 2 heads coming up.(ii) probability of 3 tails coming up.

Answer» Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes.

Outcome	3 heads	2 heads	1 head	No head
Frequency	23	72	77	28

If the three coins are simultaneously tossed again, compute the

(i) probability of 2 heads coming up.

(ii) probability of 3 tails coming up.

Discussion

3199.	If a * b denotes the larger of 'a' and 'b' and if a o b = (a * b)+ 3, then write the value of (5) o (10), where * and o are binary operations.
Answer» If a * b denotes the larger of 'a' and 'b' and if a o b = (a * b)+ 3, then write the value of (5) o (10), where * and o are binary operations.

3199.

If a * b denotes the larger of 'a' and 'b' and if a o b = (a * b)+ 3, then write the value of (5) o (10), where * and o are binary operations.

Answer»

If a * b denotes the larger of 'a' and 'b' and if a o b = (a * b)+ 3, then write the value of

(5) o (10), where * and o are binary operations.

Discussion

3200.	The solution of the differential equation, dydx=(x−y)2, when y(1)=1, is :
Answer» The solution of the differential equation, $\frac{d y}{d x} = (x - y)^{2}$ , when $y (1) = 1$ , is :

Discussion

Explore topic-wise InterviewSolutions in .

A plane passing through the point (3,1,1) contains two lines whose direction ratios are 1,−2,2 and 2,3,−1 respectively. If this plane also passes through the point (α,−3,5), then α is equal to:

Find the relationship between a and b so that the function f defined by is continuous at x = 3.

If the system of equations 4x + py 21 and px 2y 15 hasunique solution, then which of the following could be the valueof p?

The Newton-Raphson method formula for finding the square root of a real number N from the equation x2−N=0 is

The number of value(s) of x for which the function f(x)=log10|sinx|+log10|cosx| is not defined in the interval [0,10π] is equal to

There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

Theprobability that a student is not a swimmer is.Then the probability that out of five students, four are swimmers is(A) (B) (C) (D) Noneof these

If a≠b≠c, write the condition for which the equations (b−c)x+(c−a) y+(a−b)=0 and (b3−c3)x+(c3−a3)y+(a3−b3=0 represent the same line.

If I=3π∫0[tanx]dx, where [.] represents the greatest integer function, then the value of ∣∣∣2Iπ∣∣∣ is

What is ungrouped data ?

35. If b tan theta=a ,then the value of a sin theta-b cos theta/a sin theta+b cos theta is

The value of limn→∞(a−1+n√ba)n, (a&gt;0,b&gt;0) is equal to

If α, β and γ are the real roots of a³ − 6a²+ 3a + 1 = 0, determine the sum of possible values of α²β + β²γ + γ²α.

AA1,BB1,CC1 are the medians of triangle ABC whose centroid is G.If the points A,C1,G and B1 are concyclic,then which of the following options is correct?

Prove that cosα+cosα+β+cosα+2β+...+cosα+n-1β=cosα+n-12βsinnβ2sinβ2 for all n∈N. [NCERT EXEMPLAR]

If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of A and B occurs) = 59, then find the value of p.

The least integer greater than log215⋅log1/62⋅log316 is

Will the value of rnot will remain same or constant in all cases or it will change??

Find the area of the region bounded by y 2 = 9 x , x = 2, x = 4 and the x -axis in the first quadrant.

The differential equation(s) of family of curves whose tangent form an angle of π4 with the hyperbola xy=c2 is/are given by

Solve the following equation- 2 sin^2 x +3^1/2 cos x + 1 = 0

If the system of linear equationsx−4y+7z=7g 3y−5z=h−2x+5y−9z=kis consistent, then :

zeroes of polynomial x^2+kx +k,k not equal to zero.options a) can't both be positive b) can't both be negative c) data insufficient d) one positive and one negative

Show that for any sets A and B, A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)

31.Three persons A,B and C throw a die in succession till one gets a six and wins the game.find their respective probabilities of winning

∫(x+2x+4)2exdx is equal to

In triangle ABC, if cotA,cotB,cotC are in A.P., then a2,b2,c2 are in:

equals

A point “P” is located in three dimensional coordinate plane such that the angles made by OP with positive direction of X - axis is 30∘ and Y- axis is 60∘ then find the angle made by OP with positive direction of Z - axis, where “O” is origin.

Tangent at any point on the hyperbola x2a2−y2b2=1 cut the axis at A and B respectively. If the rectangle OAPB (where O is origin) is completed then locus of point P is given by

IQ of a person is given by the formula Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.

If the length of the common chord of two circles of radii 3 and 4 units, which intersect orthogonally is k5, then the value of k is

Findthe coefficient of a5b7in (a –2b)12

,xin quadrant III

If the sum to n terms of the series 312×22+522×32+732×42+…… is 0.99, then the value of n is

If limx→0(ax+bx+cx+dx4)1/x=8, then the minimum value of the determinant ∣∣∣a+ibc+id−c+ida−ib∣∣∣ is

Prove that: cot π8=2+1

5C1+5C2+5C3+5C4+5C5 is equal to

36. If f(X+1/y) + f(x-1/y)=2f(X)f(1/y) for all X,y belong to R-{0} and f(0)=1/2 then f(4) is

Find the sixth term in the expansion y12+x13n, if the binomial coefficient of the third term from the end is 45.

How many real numbers satisfy the relation [x]=32x. __

Mark the correct alternative in each of the following:The linear inequality representing the solution set given in Fig. 15.44 is (a) x&lt;5(b) x&gt;5(c) x≥5(d) x≤5

In throwing 3 dice what is the probability that atleast 2 of the dice show same numbers?

A child has a die whose 6 faces show the letters given below: A B C A D A The die is thrown once. What is the probability of getting (i) A, (ii) D?

What is the differentiation of f(x)=y-2÷(3-x).

If z=−5+3i and the value of z4+9z3+26z2−14z+8 is k, where k∈R, then the value of −k is

If a * b denotes the larger of 'a' and 'b' and if a o b = (a * b)+ 3, then write the value of (5) o (10), where * and o are binary operations.

The solution of the differential equation, dydx=(x−y)2, when y(1)=1, is :

The value of limn→∞(a−1+n√ba)n, (a>0,b>0) is equal to

Mark the correct alternative in each of the following:The linear inequality representing the solution set given in Fig. 15.44 is (a) x<5(b) x>5(c) x≥5(d) x≤5