43030 + Interview Questions in Mathematics

1.	A coin that comes up heads with probability p and tails with probability q independently on each flip is tossed 8 times. Suppose that the probability of occurrence of three heads and five tails is equal to 125 times the probability of occurrence of five heads and three tails. Let p=mn where m and n are relatively prime. Then the value of m+n is
Answer» A coin that comes up heads with probability $p$ and tails with probability $q$ independently on each flip is tossed $8$ times. Suppose that the probability of occurrence of three heads and five tails is equal to $\frac{1}{25}$ times the probability of occurrence of five heads and three tails. Let $p = \frac{m}{n}$ where $m$ and $n$ are relatively prime. Then the value of $m + n$ is

Discussion

2.	Find the values of the following trigonometric ratios:(i) sin5π3(ii) sin 17π(iii) tan11π6(iv) cos-25π4(v) tan 7π4(vi) sin17π6(vii) cos19π6(viii) sin-11π6(ix) cosec-20π3(x) tan-13π4(xi) cos19π4(xii) sin41π4(xiii) cos39π4(xiv) sin151π6
Answer» Find the values of the following trigonometric ratios: (i) $\sin \frac{5 π}{3}$ (ii) sin 17π (iii) $\tan \frac{11 π}{6}$ (iv) $\cos (- \frac{25 π}{4})$ (v) $\tan \frac{7 π}{4}$ (vi) $\sin \frac{17 π}{6}$ (vii) $\cos \frac{19 π}{6}$ (viii) $\sin (- \frac{11 π}{6})$ (ix) $cosec (- \frac{20 π}{3})$ (x) $\tan (- \frac{13 π}{4})$ (xi) $\cos \frac{19 π}{4}$ (xii) $\sin \frac{41 π}{4}$ (xiii) $\cos \frac{39 π}{4}$ (xiv) $\sin \frac{151 π}{6}$

Discussion

3.	If y = sin-1(ex) + cos-1(ex), then dydx = ____________________.
Answer» If y = sin^-1(e^x) + cos^-1(e^x), then $\frac{d y}{d x}$ = ____________________.

Discussion

4.	The coefficient of the term independent of x in the expansion of (x+1x2/3−x1/3+1−x−1x−x1/2)10 is
Answer» The coefficient of the term independent of $x$ in the expansion of ${(\frac{x + 1}{x^{2 / 3} - x^{1 / 3} + 1} - \frac{x - 1}{x - x^{1 / 2}})}^{10}$ is

Discussion

5.	Solve for x:\|x−\|3−x\|\|−3x=8
Answer» Solve for $x : \| x - \| 3 - x \| \| - 3 x = 8$

Discussion

6.	How many triangles can be obtained by joining 12 points, five of which are collinear ?
Answer» How many triangles can be obtained by joining 12 points, five of which are collinear ?

Discussion

7.	dip circle is placed in geographic meridian at a place where dip and declination are known to be respectively30^° and 45^° . What dip will be given by dip circle?tan ,(a)23(2) tan6(3) tan(4) tan2
Answer» dip circle is placed in geographic meridian at a place where dip and declination are known to be respectively30^° and 45^° . What dip will be given by dip circle?tan ,(a)23(2) tan6(3) tan(4) tan2

Discussion

8.	∫π20log(cos x)dx=
Answer» $\int_{0}^{\frac{π}{2}} l o g (c o s x) d x =$

Discussion

9.	In each of thefollowing cases, determine the direction cosines of the normal to theplane and the distance from the origin.(a)z =2 (b) (c) (d)5y+ 8 = 0
Answer» In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin. (a)z = 2 (b) (c) (d)5y + 8 = 0

9.

In each of thefollowing cases, determine the direction cosines of the normal to theplane and the distance from the origin.(a)z =2 (b) (c) (d)5y+ 8 = 0

Answer»

In each of the
following cases, determine the direction cosines of the normal to the
plane and the distance from the origin.

(a)z =
2 (b)

(c) (d)5y
+ 8 = 0

Discussion

10.	30. A)SinA+sinB=a,cosA+cosB=b,find ,1)Sin (A+B)
Answer» 30. A)SinA+sinB=a,cosA+cosB=b,find ,1)Sin (A+B)

Discussion

11.	Let △=∣∣∣∣∣f(x)−g(x)h(x)−xyz−f(y)g(y)−h(y)∣∣∣∣∣, then which of the following statement is not correct?(where Mij and Cij are minor and co-factor of element aij and f,g,h are odd functions)
Answer» Let $△ = ∣ ∣∣∣ ∣ \begin{matrix} f (x) & - g (x) & h (x) - x & y & z - f (y) & g (y) & - h (y) \end{matrix} ∣ ∣∣∣ ∣,$ then which of the following statement is not correct? (where $M_{i j}$ and $C_{i j}$ are minor and co-factor of element $a_{i j}$ and $f, g, h$ are odd functions)

Discussion

12.	The values of a for which( a2−1)x2 + 2(a-1)x + 2 is positive for any x are
Answer» The values of a for which( $a^{2} - 1$ ) $x^{2}$ + 2(a-1)x + 2 is positive for any x are

Discussion

13.	If two events A and B are such that P(Ac)=0.3,P(B)=0.4 and P(A∩Bc)=0.5 then the value of P(BA∪Bc) is
Answer» If two events A and B are such that $P (A^{c}) = 0.3, P (B) = 0.4$ and $P (A \cap B^{c}) = 0.5$ then the value of $P (\frac{B}{A \cup B^{c}})$ is

Discussion

14.	Ratoinal number ki definition Hindi me clear kar dijiye
Answer» Ratoinal number ki definition Hindi me clear kar dijiye

Discussion

15.	Let 1440=x⋅y, where x and y are coprime to each other, then the possible pairs (x,y) is
Answer» Let $1440 = x \cdot y$ , where $x$ and $y$ are coprime to each other, then the possible pairs $(x, y)$ is

Discussion

16.	The above picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.Based on the above information, answer the following questions. If the parabolic arch is represented by a polynomial ax2+bx+c, which of the following is mandatory?
Answer» The above picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms. Based on the above information, answer the following questions. If the parabolic arch is represented by a polynomial $a x^{2} + b x + c$ , which of the following is mandatory?

Discussion

17.	Why we prove by sas in asa ?
Answer» Why we prove by sas in asa ?

Discussion

18.	In a game, 30 cards are drawn at a time out of 80 playing cards numbered from 1 to 80. The expected value of the sum of numbers on the cards drawn is 1215
Answer» In a game, 30 cards are drawn at a time out of 80 playing cards numbered from 1 to 80. The expected value of the sum of numbers on the cards drawn is 1215

Discussion

19.	Find solution of the equation ( sinx)^4 +( cos x )^7=1
Answer» Find solution of the equation ( sinx)^4 +( cos x )^7=1

Discussion

20.	If S=1+83+279+6427+⋯∞, then the value of 8S is
Answer» If $S = 1 + \frac{8}{3} + \frac{27}{9} + \frac{64}{27} + \dots \infty,$ then the value of $8 S$ is

Discussion

21.	If A is skew symmetric and B is symmetric matrix, then skew symmetric matrix isOptions:a) AB+BAb) A^2+B^2c) AB-BAd) A^2-B^2
Answer» If A is skew symmetric and B is symmetric matrix, then skew symmetric matrix is Options: a) AB+BA b) A^2+B^2 c) AB-BA d) A^2-B^2

Discussion

22.	The total no. of positive integral solutions of the equation \lbrack x÷9\rbrack= \lbrack x÷11\rbrack i
Answer» The total no. of positive integral solutions of the equation \lbrack x÷9\rbrack= \lbrack x÷11\rbrack i

Discussion

23.	If f(x)=2cosx+ax+4 is strictly increasing over R, then[2 marks]
Answer» If $f (x) = 2 cos x + a x + 4$ is strictly increasing over $R,$ then [2 marks]

Discussion

24.	if x+1/3-root 5, then the value of (root x + 1/root x ) is:
Answer» if x+1/3-root 5, then the value of (root x + 1/root x ) is:

Discussion

25.	Let f(x)={√{x} , x∉Z 1 , x∈Z and g(x)={x}2, the area bounded by f(x) and g(x) for x∈[0,n]; (n∈Z) is denoted by S(n), then which of the following is correct?
Answer» Let $f (x) = {\begin{matrix} \sqrt{{x}}, x \notin Z 1, x \in Z \end{matrix}$ and $g (x) = {x}^{2},$ the area bounded by $f (x)$ and $g (x)$ for $x \in [0, n]; (n \in Z)$ is denoted by $S (n)$ , then which of the following is correct?

Discussion

26.	The locus of the point of intersection of the lines x cosθ + y sinθ = a and x sinθ – y cosθ = b is a circle of radius __________.
Answer» The locus of the point of intersection of the lines x cosθ + y sinθ = a and x sinθ – y cosθ = b is a circle of radius __________.

Discussion

27.	If cotA+cosec A=3 and A is an acute angle, then the value of cosA is
Answer» If $cot A + cosec A = 3$ and $A$ is an acute angle, then the value of $cos A$ is

Discussion

28.	Question 11The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is(A) (0, 1)(B) (0, –1)(C) (–1, 0)(D) (1, 0)
Answer» Question 11 The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is (A) (0, 1) (B) (0, –1) (C) (–1, 0) (D) (1, 0)

Discussion

29.	Find the equations of the tangent andnormal to the hyperbola atthe point.
Answer» Find the equations of the tangent and normal to the hyperbola at the point.

Discussion

30.	The function f(x)=log(x+√x2+1), is
Answer» The function $f (x) = l o g (x + \sqrt{x^{2} + 1})$ , is

Discussion

31.	If sin A-B=12 and cos A+B=12, 0° <A+B≥90°, A<B find A and B.
Answer» If $\sin (A - B) = \frac{1}{2} and \cos (A + B) = \frac{1}{2}, 0 ° < A + B \geq 90 °, A < B$ find A and B.

Discussion

32.	12 persons are to be arranged around two round table such that one table can accommodate seven persons and another five persons only. Number of ways of arrangement if two particular persons A and B want to be together and consecutive is
Answer» 12 persons are to be arranged around two round table such that one table can accommodate seven persons and another five persons only. Number of ways of arrangement if two particular persons A and B want to be together and consecutive is

Discussion

33.	2sq. unit25bs(2)0(p)26. If (h, k) is orthocentre of triangle formed by lines 3y3x 2y and x+7, then (h- k) is(e)0 (9)I ()If a vertex of an equilateral triangle is the origin and theside opposite to it has the equation x + y = 1 then theorthocentre of the triangle is:(p)Sls(B)(4)(0)(d) None of these
Answer» 2sq. unit25bs(2)0(p)26. If (h, k) is orthocentre of triangle formed by lines 3y3x 2y and x+7, then (h- k) is(e)0 (9)I ()If a vertex of an equilateral triangle is the origin and theside opposite to it has the equation x + y = 1 then theorthocentre of the triangle is:(p)Sls(B)(4)(0)(d) None of these

Discussion

34.	If a line makes angle 45 60 and 60 with the positive direction of x y and z axes find the direction cosines and direction ratio
Answer» If a line makes angle 45 60 and 60 with the positive direction of x y and z axes find the direction cosines and direction ratio

Discussion

35.	The value oflimx→03√1+sinx−3√1−sinxxis
Answer» $The value of {lim}_{x \to 0} \frac{\sqrt[3]{1 + s i n x} - \sqrt[3]{1 - s i n x}}{x} i s$

Discussion

36.	The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45∘. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of 30∘ to the horizontal plane, the angle of elevation of the top of the hill becomes 75∘. Then the height of the hill (in meters) is
Answer» The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be $45^{\circ}$ . After walking a distance of $80$ meters towards the top, up a slope inclined at an angle of $30^{\circ}$ to the horizontal plane, the angle of elevation of the top of the hill becomes $75^{\circ}$ . Then the height of the hill (in meters) is

Discussion

37.	A car park can fit 15 rows of cars with 5 cars in each row. Find the number of cars that can fit into the car park.75
Answer» A car park can fit 15 rows of cars with 5 cars in each row. Find the number of cars that can fit into the car park. 75

Discussion

38.	Show that f(x)=tan−1(sinx+cosx) is an increasing function in (0,π4).
Answer» Show that $f (x) = t a n^{- 1} (s i n x + c o s x)$ is an increasing function in $(0, \frac{π}{4})$ .

Discussion

39.	The real value of α for which the expression 1-i sin α1+2i sin α is purely real, is(a) n+1 π2(b) 2n+1 π2(c) nπ(d) none of these where n ∈ N.
Answer» The real value of α for which the expression $\frac{1 - i \sin α}{1 + 2 i \sin α}$ is purely real, is (a) $(n + 1) \frac{π}{2}$ (b) $(2 n + 1) \frac{π}{2}$ (c) nπ (d) none of these where n ∈ N.

Discussion

40.	If tangents are drawn to the ellipse x2+2y2=2 at all points on the ellipse other than its four vertices, then the mid points of the tangents intercepted between the coordinates axes lie on the curve :
Answer» If tangents are drawn to the ellipse $x^{2} + 2 y^{2} = 2$ at all points on the ellipse other than its four vertices, then the mid points of the tangents intercepted between the coordinates axes lie on the curve :

Discussion

41.	Let ΔABC be an isosceles right-angled triangle where AB⊥BC, if the equation of hypotenuse is 2x+3y=4, then the sum of slopes of AB and AC can be equal to
Answer» Let $Δ A B C$ be an isosceles right-angled triangle where $A B ⊥ B C$ , if the equation of hypotenuse is $2 x + 3 y = 4$ , then the sum of slopes of $A B$ and $A C$ can be equal to

Discussion

42.	From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is (i) Red and a king (ii) Either red or a king
Answer» From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is (i) Red and a king (ii) Either red or a king

42.

From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is (i) Red and a king (ii) Either red or a king

Answer»

From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is

(i) Red and a king

(ii) Either red or a king

Discussion

43.	Find a number which when divided by 3,5,7 leaves remainder 1,2,3 repectively
Answer» Find a number which when divided by 3,5,7 leaves remainder 1,2,3 repectively

Discussion

44.	Number of solution of the equation 2e\|x\|tan−1(\|x\|)=1 is
Answer» Number of solution of the equation $2 e^{\| x \|} {tan}^{- 1} (\| x \|) = 1$ is

Discussion

45.	Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
Answer» Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

Discussion

46.	Find solutions of f(x)=g(x) ifF(x)=sin(2x+1) and g(x)=\|2x+1\|
Answer» Find solutions of f(x)=g(x) if F(x)=sin(2x+1) and g(x)=\|2x+1\|

Discussion

47.	The value of 1∫0sin−1xxdx is
Answer» The value of $1 \int 0 \frac{{sin}^{- 1} x}{x} d x$ is

Discussion

48.	The value of the expression sin2xcos3x+sin3xcos8x+sin5xcos16xsin2xsin3x+sin3xsin8x+sin5xsin16x is
Answer» The value of the expression $\frac{sin 2 x cos 3 x + sin 3 x cos 8 x + sin 5 x cos 16 x}{sin 2 x sin 3 x + sin 3 x sin 8 x + sin 5 x sin 16 x}$ is

Discussion

49.	The slope of a line is double of the slope of another line. If tangent of the angle between them is , find the slopes of he lines.
Answer» The slope of a line is double of the slope of another line. If tangent of the angle between them is , find the slopes of he lines.

Discussion

50.	The value of limn→∞n∑i=1(i)p+q+1n∑i=1(i)qn∑i=1(i)p is equal to (where p,q≥1)
Answer» The value of $lim n \to \infty \frac{n \sum i = 1 (i)^{p + q + 1}}{n \sum i = 1 (i)^{q} n \sum i = 1 (i)^{p}}$ is equal to (where $p, q \geq 1$ )

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the values of the following trigonometric ratios:(i) sin5π3(ii) sin 17π(iii) tan11π6(iv) cos-25π4(v) tan 7π4(vi) sin17π6(vii) cos19π6(viii) sin-11π6(ix) cosec-20π3(x) tan-13π4(xi) cos19π4(xii) sin41π4(xiii) cos39π4(xiv) sin151π6

If y = sin-1(ex) + cos-1(ex), then dydx = ____________________.

The coefficient of the term independent of x in the expansion of (x+1x2/3−x1/3+1−x−1x−x1/2)10 is

Solve for x:|x−|3−x||−3x=8

How many triangles can be obtained by joining 12 points, five of which are collinear ?

dip circle is placed in geographic meridian at a place where dip and declination are known to be respectively30^° and 45^° . What dip will be given by dip circle?tan ,(a)23(2) tan6(3) tan(4) tan2

∫π20log(cos x)dx=

In each of thefollowing cases, determine the direction cosines of the normal to theplane and the distance from the origin.(a)z =2 (b) (c) (d)5y+ 8 = 0

30. A)SinA+sinB=a,cosA+cosB=b,find ,1)Sin (A+B)

Let △=∣∣∣∣∣f(x)−g(x)h(x)−xyz−f(y)g(y)−h(y)∣∣∣∣∣, then which of the following statement is not correct?(where Mij and Cij are minor and co-factor of element aij and f,g,h are odd functions)

The values of a for which( a2−1)x2 + 2(a-1)x + 2 is positive for any x are

If two events A and B are such that P(Ac)=0.3,P(B)=0.4 and P(A∩Bc)=0.5 then the value of P(BA∪Bc) is

Ratoinal number ki definition Hindi me clear kar dijiye

Let 1440=x⋅y, where x and y are coprime to each other, then the possible pairs (x,y) is

Why we prove by sas in asa ?

In a game, 30 cards are drawn at a time out of 80 playing cards numbered from 1 to 80. The expected value of the sum of numbers on the cards drawn is 1215

Find solution of the equation ( sinx)^4 +( cos x )^7=1

If S=1+83+279+6427+⋯∞, then the value of 8S is

If A is skew symmetric and B is symmetric matrix, then skew symmetric matrix isOptions:a) AB+BAb) A^2+B^2c) AB-BAd) A^2-B^2

The total no. of positive integral solutions of the equation \lbrack x÷9\rbrack= \lbrack x÷11\rbrack i

If f(x)=2cosx+ax+4 is strictly increasing over R, then[2 marks]

if x+1/3-root 5, then the value of (root x + 1/root x ) is:

Let f(x)={√{x} , x∉Z 1 , x∈Z and g(x)={x}2, the area bounded by f(x) and g(x) for x∈[0,n]; (n∈Z) is denoted by S(n), then which of the following is correct?

The locus of the point of intersection of the lines x cosθ + y sinθ = a and x sinθ – y cosθ = b is a circle of radius __________.

If cotA+cosec A=3 and A is an acute angle, then the value of cosA is

Question 11The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is(A) (0, 1)(B) (0, –1)(C) (–1, 0)(D) (1, 0)

Find the equations of the tangent andnormal to the hyperbola atthe point.

The function f(x)=log(x+√x2+1), is

If sin A-B=12 and cos A+B=12, 0° &lt;A+B≥90°, A&lt;B find A and B.

12 persons are to be arranged around two round table such that one table can accommodate seven persons and another five persons only. Number of ways of arrangement if two particular persons A and B want to be together and consecutive is

2sq. unit25bs(2)0(p)26. If (h, k) is orthocentre of triangle formed by lines 3y3x 2y and x+7, then (h- k) is(e)0 (9)I ()If a vertex of an equilateral triangle is the origin and theside opposite to it has the equation x + y = 1 then theorthocentre of the triangle is:(p)Sls(B)(4)(0)(d) None of these

If a line makes angle 45 60 and 60 with the positive direction of x y and z axes find the direction cosines and direction ratio

The value oflimx→03√1+sinx−3√1−sinxxis

A car park can fit 15 rows of cars with 5 cars in each row. Find the number of cars that can fit into the car park.75

Show that f(x)=tan−1(sinx+cosx) is an increasing function in (0,π4).

The real value of α for which the expression 1-i sin α1+2i sin α is purely real, is(a) n+1 π2(b) 2n+1 π2(c) nπ(d) none of these where n ∈ N.

If tangents are drawn to the ellipse x2+2y2=2 at all points on the ellipse other than its four vertices, then the mid points of the tangents intercepted between the coordinates axes lie on the curve :

Let ΔABC be an isosceles right-angled triangle where AB⊥BC, if the equation of hypotenuse is 2x+3y=4, then the sum of slopes of AB and AC can be equal to

From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is (i) Red and a king (ii) Either red or a king

Find a number which when divided by 3,5,7 leaves remainder 1,2,3 repectively

Number of solution of the equation 2e|x|tan−1(|x|)=1 is

Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

Find solutions of f(x)=g(x) ifF(x)=sin(2x+1) and g(x)=|2x+1|

The value of 1∫0sin−1xxdx is

The value of the expression sin2xcos3x+sin3xcos8x+sin5xcos16xsin2xsin3x+sin3xsin8x+sin5xsin16x is

The slope of a line is double of the slope of another line. If tangent of the angle between them is , find the slopes of he lines.

The value of limn→∞n∑i=1(i)p+q+1n∑i=1(i)qn∑i=1(i)p is equal to (where p,q≥1)

If sin A-B=12 and cos A+B=12, 0° <A+B≥90°, A<B find A and B.