43030 + Interview Questions in Mathematics

1.	The equation, x210−a+y24−a=1 represents ellipse if
Answer» $The equation, \frac{x^{2}}{10 - a} + \frac{y^{2}}{4 - a} = 1 represents ellipse if$

Discussion

2.	Find the 7th term in the following sequence whose nth term is
Answer» Find the 7^th term in the following sequence whose n^th term is

Discussion

3.	The number of positive real value(s) of x such that x−3i3−ix is purely real is
Answer» The number of positive real value(s) of $x$ such that $\frac{x - 3 i}{3 - i x}$ is purely real is

Discussion

4.	Determine the nature of the roots of the following quadratic equations:(i) 2x2 − 3x + 5 = 0(ii) 2x2 − 6x + 3 = 0(iii) 35x2-23x+1=0(iv) 3x2-43x+4=0(v) 3x2-26x+2=0(vi) 4x2+43x+3=0
Answer» Determine the nature of the roots of the following quadratic equations: (i) 2x² − 3x + 5 = 0 (ii) 2x² − 6x + 3 = 0 (iii) $\frac{3}{5} x^{2} - \frac{2}{3} x + 1 = 0$ (iv) $3 x^{2} - 4 \sqrt{3} x + 4 = 0$ (v) $3 x^{2} - 2 \sqrt{6} x + 2 = 0$ (vi) $4 x^{2} + 4 \sqrt{3} x + 3 = 0$

Discussion

5.	If the lines p1 x+q1 y=1, p2 x+q2 y=1 and p3 x+q3 y=1 be concurrent, show that the points (p1, q1), (p2, q2) and p3, q3) are coolinear.
Answer» If the lines $p_{1} x + q_{1} y = 1, p_{2} x + q_{2} y = 1$ and $p_{3} x + q_{3} y = 1$ be concurrent, show that the points $(p_{1}, q_{1}), (p_{2}, q_{2})$ and $p_{3}, q_{3})$ are coolinear.

Discussion

6.	∫ x+sin x1+cox x dx is equal to (a) log1+cosx+C (b) log x+sin x+C(c) x-tanx2+C (d) x tanx2+C
Answer» $\int \frac{x + \sin x}{1 + c o x x} d x i s e q u a l t o (a) \log \|1 + \cos x\| + C (b) \log \|x + \sin x\| + C (c) x - \tan \frac{x}{2} + C (d) x \tan \frac{x}{2} + C$

Discussion

7.	The anti derivative ofequals(A) (B) (C) (D)
Answer» The anti derivative of equals (A) (B) (C) (D)

7.

The anti derivative ofequals(A) (B) (C) (D)

Answer»

The anti derivative of
equals

(A) (B)

(C) (D)

Discussion

8.	9.Which of the given values of x and y make the following pair of matrices equal25y+1 2-3x」,L8x=-y=7(A)2(B)Not possible to find23-2y=3(C) y=7,x=(D)x=-,33
Answer» 9.Which of the given values of x and y make the following pair of matrices equal25y+1 2-3x」,L8x=-y=7(A)2(B)Not possible to find23-2y=3(C) y=7,x=(D)x=-,33

Discussion

9.	If limx→0(1−cos2x)(sin5x)x2sin3x=a, then the value of 3a is equal to
Answer» If $lim x \to 0 \frac{(1 - cos 2 x) (sin 5 x)}{x^{2} sin 3 x} = a,$ then the value of $3 a$ is equal to

Discussion

10.	The equation of the ellipse whose centre is at origin and which passes through the points (-3, 1) and (2, -2) is
Answer» The equation of the ellipse whose centre is at origin and which passes through the points (-3, 1) and (2, -2) is

10.

The equation of the ellipse whose centre is at origin and which passes through the points (-3, 1) and (2, -2) is

Answer»

The equation of the ellipse whose centre is at origin and which passes through the points (-3, 1) and (2, -2) is

Discussion

11.	A continuous, even periodic function f with period 8 is such that f(0) = 0, f(1) = –2, f(2) = 1, f(3) = 2, f(4) = 3, then the value of cos–1(cos(f(9) + 2f(20))) is equal to
Answer» A continuous, even periodic function f with period 8 is such that f(0) = 0, f(1) = –2, f(2) = 1, f(3) = 2, f(4) = 3, then the value of cos–1(cos(f(9) + 2f(20))) is equal to

Discussion

12.	If the equations ax2+2bx+3c=0and 3x2+8x+15=0 have a common root where a,b,c, are lengths of sides of ABC then sin2 A + sin2 B + sin2 C=
Answer» If the equations $a x^{2} + 2 b x + 3 c = 0$ and 3 $x^{2} + 8 x + 15 = 0$ have a common root where a,b,c, are lengths of sides of ABC then $s i n^{2} A$ + $s i n^{2} B$ + $s i n^{2} C =$

Discussion

13.	Anurn 5 red and 5 black balls .A ball is drawn at random its colour is noted and is returned to the urn moreover two additional balls of the colour drawn are put in the urn and then a ball is drawn at random .what is the probability that second ball is red?
Answer» Anurn 5 red and 5 black balls .A ball is drawn at random its colour is noted and is returned to the urn moreover two additional balls of the colour drawn are put in the urn and then a ball is drawn at random .what is the probability that second ball is red?

Discussion

14.	If tan α=17, tan β=13, then cos 2α is equal to
Answer» If $t a n α = \frac{1}{7}, t a n β = \frac{1}{3}$ , then $c o s 2 α$ is equal to

Discussion

15.	For any angle x∈[−π4,π3];cotx∈
Answer» For any angle $x \in [- \frac{π}{4}, \frac{π}{3}]; cot x \in$

Discussion

16.	Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
Answer» Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Discussion

17.	In a class of 100 students there are 70 boys whose average marks in a subject is 75. If the average mark of the complete class is 72, then the average marks of the girls is
Answer» In a class of $100$ students there are $70$ boys whose average marks in a subject is $75$ . If the average mark of the complete class is $72$ , then the average marks of the girls is

Discussion

18.	Answer each of the following questions in one word or one sentence or as per exact requirement of for question: In a ΔABC, if b=20, c=21 and sin A=35, find a.
Answer» Answer each of the following questions in one word or one sentence or as per exact requirement of for question: $I n a Δ A B C, i f b = 20, c = 21 a n d s i n A = \frac{3}{5}, f i n d a .$

18.

Answer each of the following questions in one word or one sentence or as per exact requirement of for question: In a ΔABC, if b=20, c=21 and sin A=35, find a.

Answer»

Answer each of the following questions in one word or one sentence or as per exact requirement of for question:

$I n a Δ A B C, i f b = 20, c = 21 a n d s i n A = \frac{3}{5}, f i n d a .$

Discussion

19.	Find all the points of discontinuity of f(x) defined by f(x)=\|x\|-\|x+1\|.
Answer» Find all the points of discontinuity of f(x) defined by f(x)=\|x\|-\|x+1\|.

Discussion

20.	Let A={2,3,4,5,...,17,18}. Let ≃ be the equivalence relation on A×A, cartesian product of A with itself, defined by (a,b)≃(c,d) if ad=bc. Then the number of ordered pairs of the equivalence class of (3,2) is
Answer» Let $A = {2, 3, 4, 5, . . ., 17, 18} .$ Let $≃$ be the equivalence relation on $A \times A,$ cartesian product of $A$ with itself, defined by $(a, b) ≃ (c, d)$ if $a d = b c .$ Then the number of ordered pairs of the equivalence class of $(3, 2)$ is

Discussion

21.	If A = {1, 2, 3, 4}, B = {3, 4} and C = {2, 3} then n ((A ∩ B x C)
Answer» If A = {1, 2, 3, 4}, B = {3, 4} and C = {2, 3} then n ((A ∩ B x C)

Discussion

22.	An item is manufactured by three machines X, Y and Z. Out of the total number of items manufactured during a specified period, 40% are manufactured on X, 40% on Y and 20% on Z. 3% of the items produced on X and 2% of items produced on Y are defective, and 3% of these produced on Z is defective. All the items are stored at one godown. One item is drawn at random and is found to be defective. What is the probability that it was manufactured on machine Y?
Answer» An item is manufactured by three machines X, Y and Z. Out of the total number of items manufactured during a specified period, 40% are manufactured on X, 40% on Y and 20% on Z. 3% of the items produced on X and 2% of items produced on Y are defective, and 3% of these produced on Z is defective. All the items are stored at one godown. One item is drawn at random and is found to be defective. What is the probability that it was manufactured on machine Y?

Discussion

23.	the lines 2x- 3 y + 7 = 0and 4 x - 6y - 5 =0 a tangent to the same circle the radius of the circle is
Answer» the lines 2x- 3 y + 7 = 0and 4 x - 6y - 5 =0 a tangent to the same circle the radius of the circle is

Discussion

24.	Question 1(i)Check whether the following are quadratic equations:(i)(x+1)2=2(x−3)
Answer» Question 1(i) Check whether the following are quadratic equations: $(i) (x + 1)^{2} = 2 (x - 3)$

Discussion

25.	When A=11/3 π then, what is (cosA-sinA)
Answer» When A=11/3 π then, what is (cosA-sinA)

Discussion

26.	Let the function f(x) be defined as f(x) =lnx-1/x-e, x not equal to eK, x=eRhe value of k for which the function is continuous at x=e is equal to
Answer» Let the function f(x) be defined as f(x) =lnx-1/x-e, x not equal to e K, x=e Rhe value of k for which the function is continuous at x=e is equal to

Discussion

27.	For any positive real number x, write the value ofxab1abxbc1bcxca1ca
Answer» For any positive real number x, write the value of ${\{{(x^{a})}^{b}\}}^{\frac{1}{a b}} {\{{(x^{b})}^{c}\}}^{\frac{1}{b c}} {\{{(x^{c})}^{a}\}}^{\frac{1}{c a}}$

Discussion

28.	Write the domain of the real function f defined by f(x) = 25-x2. [NCERT EXEMPLAR]
Answer» Write the domain of the real function f defined by f(x) = $\sqrt{25 - x^{2}}$ . [NCERT EXEMPLAR]

Discussion

29.	If tanA = a tanB and sin A = b sinB,then prove that cos^2 A = b^2 - 1 / a^2 - 1.
Answer» If tanA = a tanB and sin A = b sinB,then prove that cos^2 A = b^2 - 1 / a^2 - 1.

Discussion

30.	find the next term in the sequence 0, 2, 24, 252,______ (1)620 (3)1040 (3)3120 (4)5430 (with solutions)
Answer» find the next term in the sequence 0, 2, 24, 252,______ (1)620 (3)1040 (3)3120 (4)5430 (with solutions)

Discussion

31.	If the variance of 10 natural numbers 1,1,1,…,1,k is less than 10, then the maximum possible value of k is
Answer» If the variance of $10$ natural numbers $1, 1, 1, \dots, 1, k$ is less than $10,$ then the maximum possible value of $k$ is

Discussion

32.	The distance of the point (1, 0, 2) from the point of intersection of the line x−23=y+14=z−212 and the plane x - y + z = 16, is .
Answer» The distance of the point (1, 0, 2) from the point of intersection of the line $\frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 2}{12}$ and the plane x - y + z = 16, is .

Discussion

33.	If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Answer» If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term

Discussion

34.	The minimum value of the function M=π216sin−1(−x)+cos−1x is
Answer» The minimum value of the function $M = \frac{π^{2}}{16 {sin}^{- 1} (- x)} + {cos}^{- 1} x$ is

Discussion

35.	P,Q,R,S,T,U,V and W are sitting round the circle and are facing the centre :1. P is second to the right of T who is the neighbour of R and V.2. S is not the neighbour of P.3. V is the neighbour of U.4. Q is not between S and W.5. W is not between U and S.Which two of the following are not neighbours?
Answer» $P, Q, R, S, T, U, V$ and $W$ are sitting round the circle and are facing the centre : $1. P$ is second to the right of $T$ who is the neighbour of $R$ and $V .$ $2. S$ is not the neighbour of $P .$ $3. V$ is the neighbour of $U .$ $4. Q$ is not between $S$ and $W .$ $5. W$ is not between $U$ and $S .$ Which two of the following are not neighbours?

Discussion

36.	Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows.(i) a = 10, d = 10(ii) a = -2, d = 0
Answer» Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (i) a = 10, d = 10 (ii) a = -2, d = 0

Discussion

37.	A person standing at the junction (crossing) of two straight paths represented by the equations 2 x – 3 y + 4 = 0 and 3 x + 4 y – 5 = 0 wants to reach the path whose equation is 6 x – 7 y + 8 = 0 in the least time. Find equation of the path that he should follow.
Answer» A person standing at the junction (crossing) of two straight paths represented by the equations 2 x – 3 y + 4 = 0 and 3 x + 4 y – 5 = 0 wants to reach the path whose equation is 6 x – 7 y + 8 = 0 in the least time. Find equation of the path that he should follow.

Discussion

38.	Let f:R → R be defined by f(x)=\|x-2n\| for x ϵ [2n-1,2n+1], n ϵ Z. Then f is periodic with period ___
Answer» Let f:R $\to$ R be defined by f(x)=\|x-2n\| for x $ϵ$ [2n-1,2n+1], n $ϵ$ Z. Then f is periodic with period ___

Discussion

39.	∣∣∣∣1ab−a1c−b−c1∣∣∣∣=
Answer» $∣ ∣∣ ∣ \begin{matrix} 1 & a & b - a & 1 & c - b & - c & 1 \end{matrix} ∣ ∣∣ ∣ =$

Discussion

40.	If B = {1, 3, 5, 7, 9}, the set-builder representation of B is
Answer» If B = {1, 3, 5, 7, 9}, the set-builder representation of B is

Discussion

41.	The range of f(x)=x+1x ∀ x≠0 is
Answer» The range of $f (x) = x + \frac{1}{x} \forall x \neq 0$ is

Discussion

42.	limx→0 cos(sin x)−1x2 is equal to
Answer» $lim x \to 0 \frac{cos (sin x) - 1}{x^{2}}$ is equal to

Discussion

43.	List I has four entries and List II has five entries. Each entry of List I is to be matched with one or more than one entries of List II. List IList II (A)Centre(s) of the circle(s) having radius 5 and(P)(4,6)touching the line 3x+4y−11=0 at (1,2) is (are)(B)End points of one of the diameters of(Q)(1,1)x2+y2−6x−8y+20=0 are(C)The line equidistant from both the lines(R)(3,−3)4x+2y+2=0 and 6x+3y−21=0,passes through(D)If one of the sides of a square is 3x−4y−12=0(S)(−2,7)and its centre is (0,0), then its diagonalpasses through(T)(−2,−2) Which of the following is the only CORRECT combination?
Answer» $List I$ has four entries and $List II$ has five entries. Each entry of $List I$ is to be matched with one or more than one entries of $List II .$ $\begin{matrix} List I & List II (A) & Centre(s) of the circle(s) having radius 5 and & (P) & (4, 6) touching the line 3 x + 4 y - 11 = 0 at (1, 2) is (are) (B) & End points of one of the diameters of & (Q) & (1, 1) x^{2} + y^{2} - 6 x - 8 y + 20 = 0 are (C) & The line equidistant from both the lines & (R) & (3, - 3) 4 x + 2 y + 2 = 0 and 6 x + 3 y - 21 = 0, passes through (D) & If one of the sides of a square is 3 x - 4 y - 12 = 0 & (S) & (- 2, 7) and its centre is (0, 0), then its diagonal passes through (T) & (- 2, - 2) \end{matrix}$ Which of the following is the only CORRECT combination?

Discussion

44.	Show that the equation of the line passing through the origin and making an angle θ with the line .
Answer» Show that the equation of the line passing through the origin and making an angle θ with the line .

Discussion

45.	The value of 8∫2\|x−5\|dx is
Answer» The value of $8 \int 2 \| x - 5 \| d x$ is

Discussion

46.	Graph of f(x) is given. Draw the graph of [f(x)]
Answer» Graph of f(x) is given. Draw the graph of [f(x)]

46.

Graph of f(x) is given. Draw the graph of [f(x)]

Answer»

Graph of f(x) is given. Draw the graph of [f(x)]

Discussion

47.	Differentiate the following functions with respect to x : x4−2 sin x+3 cos x
Answer» Differentiate the following functions with respect to x : $x^{4} - 2 s i n x + 3 c o s x$

47.

Differentiate the following functions with respect to x : x4−2 sin x+3 cos x

Answer»

Differentiate the following functions with respect to x :

$x^{4} - 2 s i n x + 3 c o s x$

Discussion

48.	What is modulus function
Answer» What is modulus function

Discussion

49.	Angle between 2 planes ¯r.^n1=d1,¯r.^n2=d2, can always be given by
Answer» Angle between 2 planes $¯ r ._{1} = d_{1}, ¯ r ._{2} = d_{2}$ , can always be given by

Discussion

50.	Prove that: sinx+1-cosx/cosx-1+sinx=1+sinx/cosx
Answer» Prove that: sinx+1-cosx/cosx-1+sinx=1+sinx/cosx

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The equation, x210−a+y24−a=1 represents ellipse if

Find the 7th term in the following sequence whose nth term is

The number of positive real value(s) of x such that x−3i3−ix is purely real is

Determine the nature of the roots of the following quadratic equations:(i) 2x2 − 3x + 5 = 0(ii) 2x2 − 6x + 3 = 0(iii) 35x2-23x+1=0(iv) 3x2-43x+4=0(v) 3x2-26x+2=0(vi) 4x2+43x+3=0

If the lines p1 x+q1 y=1, p2 x+q2 y=1 and p3 x+q3 y=1 be concurrent, show that the points (p1, q1), (p2, q2) and p3, q3) are coolinear.

∫ x+sin x1+cox x dx is equal to (a) log1+cosx+C (b) log x+sin x+C(c) x-tanx2+C (d) x tanx2+C

The anti derivative ofequals(A) (B) (C) (D)

9.Which of the given values of x and y make the following pair of matrices equal25y+1 2-3x」,L8x=-y=7(A)2(B)Not possible to find23-2y=3(C) y=7,x=(D)x=-,33

If limx→0(1−cos2x)(sin5x)x2sin3x=a, then the value of 3a is equal to

The equation of the ellipse whose centre is at origin and which passes through the points (-3, 1) and (2, -2) is

A continuous, even periodic function f with period 8 is such that f(0) = 0, f(1) = –2, f(2) = 1, f(3) = 2, f(4) = 3, then the value of cos–1(cos(f(9) + 2f(20))) is equal to

If the equations ax2+2bx+3c=0and 3x2+8x+15=0 have a common root where a,b,c, are lengths of sides of ABC then sin2 A + sin2 B + sin2 C=

Anurn 5 red and 5 black balls .A ball is drawn at random its colour is noted and is returned to the urn moreover two additional balls of the colour drawn are put in the urn and then a ball is drawn at random .what is the probability that second ball is red?

If tan α=17, tan β=13, then cos 2α is equal to

For any angle x∈[−π4,π3];cotx∈

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

In a class of 100 students there are 70 boys whose average marks in a subject is 75. If the average mark of the complete class is 72, then the average marks of the girls is

Answer each of the following questions in one word or one sentence or as per exact requirement of for question: In a ΔABC, if b=20, c=21 and sin A=35, find a.

Find all the points of discontinuity of f(x) defined by f(x)=|x|-|x+1|.

Let A={2,3,4,5,...,17,18}. Let ≃ be the equivalence relation on A×A, cartesian product of A with itself, defined by (a,b)≃(c,d) if ad=bc. Then the number of ordered pairs of the equivalence class of (3,2) is

If A = {1, 2, 3, 4}, B = {3, 4} and C = {2, 3} then n ((A ∩ B x C)

the lines 2x- 3 y + 7 = 0and 4 x - 6y - 5 =0 a tangent to the same circle the radius of the circle is

Question 1(i)Check whether the following are quadratic equations:(i)(x+1)2=2(x−3)

When A=11/3 π then, what is (cosA-sinA)

Let the function f(x) be defined as f(x) =lnx-1/x-e, x not equal to eK, x=eRhe value of k for which the function is continuous at x=e is equal to

For any positive real number x, write the value ofxab1abxbc1bcxca1ca

Write the domain of the real function f defined by f(x) = 25-x2. [NCERT EXEMPLAR]

If tanA = a tanB and sin A = b sinB,then prove that cos^2 A = b^2 - 1 / a^2 - 1.

find the next term in the sequence 0, 2, 24, 252,______ (1)620 (3)1040 (3)3120 (4)5430 (with solutions)

If the variance of 10 natural numbers 1,1,1,…,1,k is less than 10, then the maximum possible value of k is

The distance of the point (1, 0, 2) from the point of intersection of the line x−23=y+14=z−212 and the plane x - y + z = 16, is .

If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term

The minimum value of the function M=π216sin−1(−x)+cos−1x is

Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows.(i) a = 10, d = 10(ii) a = -2, d = 0

A person standing at the junction (crossing) of two straight paths represented by the equations 2 x – 3 y + 4 = 0 and 3 x + 4 y – 5 = 0 wants to reach the path whose equation is 6 x – 7 y + 8 = 0 in the least time. Find equation of the path that he should follow.

Let f:R → R be defined by f(x)=|x-2n| for x ϵ [2n-1,2n+1], n ϵ Z. Then f is periodic with period ___

∣∣∣∣1ab−a1c−b−c1∣∣∣∣=

If B = {1, 3, 5, 7, 9}, the set-builder representation of B is

The range of f(x)=x+1x ∀ x≠0 is

limx→0 cos(sin x)−1x2 is equal to

Show that the equation of the line passing through the origin and making an angle θ with the line .

The value of 8∫2|x−5|dx is

Graph of f(x) is given. Draw the graph of [f(x)]

Differentiate the following functions with respect to x : x4−2 sin x+3 cos x

What is modulus function

Angle between 2 planes ¯r.^n1=d1,¯r.^n2=d2, can always be given by

Prove that: sinx+1-cosx/cosx-1+sinx=1+sinx/cosx