24740 + Interview Questions in Mathematics Page 140 InterviewSolution

6951.	Prove that i) tan A - cot A = -2 cot2Aii) cot A = 1/2 (cot A/2 - tan A/2)
Answer» Prove that i) tan A - cot A = -2 cot2A ii) cot A = 1/2 (cot A/2 - tan A/2)

Discussion

6952.	The value of x satisfying the equation x−75=135 is___
Answer» The value of $x$ satisfying the equation $x - \frac{7}{5} = \frac{13}{5}$ is___

Discussion

6953.	Question 1 (ii)In Δ ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine:(ii) sin C, cos C
Answer» Question 1 (ii) In $Δ$ ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine: (ii) sin C, cos C

Discussion

6954.	There is a 40m long Tunnel. The cross section of the tunnel is a semicircle with a radius 6. Find the cost of painting it at the rate of ₹2/m2
Answer» There is a 40m long Tunnel. The cross section of the tunnel is a semicircle with a radius 6. Find the cost of painting it at the rate of ₹2/m²

Discussion

6955.	In the figure below, ABC is a right angled triangle and M is the midpoint of AB.(a) Prove that .(b) Prove that MC = MA = MB.
Answer» In the figure below, ABC is a right angled triangle and M is the midpoint of AB. (a) Prove that . (b) Prove that MC = MA = MB.

6955.

In the figure below, ABC is a right angled triangle and M is the midpoint of AB.(a) Prove that .(b) Prove that MC = MA = MB.

Answer»

In the figure below, ABC is a right angled triangle and M is the midpoint of AB.

(a) Prove that .

(b) Prove that MC = MA = MB.

Discussion

6956.	What is the degree of the equation that represents a straight line on the XY plane? __
Answer» What is the degree of the equation that represents a straight line on the XY plane? __

Discussion

6957.	29. solve the following pair of linear equations by the substitution method 0.2x+0.3y=1.3
Answer» 29. solve the following pair of linear equations by the substitution method 0.2x+0.3y=1.3

Discussion

6958.	cos 30∘ cos 60∘−sin 30∘ sin 60∘= __________________
Answer» $c o s 30^{\circ} c o s 60^{\circ} - s i n 30^{\circ} s i n 60^{\circ}$ = __________________

Discussion

6959.	If r is the radius and h is height of the cylinder the volume will be(a) 13πr2h(b) πr2h(c) 2πr (h + r)(d) 2πrh
Answer» If r is the radius and h is height of the cylinder the volume will be (a) $\frac{1}{3} {πr}^{2} h$ (b) ${πr}^{2} h$ (c) 2 $πr (h + r)$ (d) 2 $πrh$

Discussion

6960.	If the areas of three adjacent faces of a cuboid are 8 cm2, 18 cm3 and 25 cm3. Find the volume of the cuboid.
Answer» If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm³and 25 cm³. Find the volume of the cuboid.

Discussion

6961.	A perpendicular is drawn from a point on line x-1/2=y+1/2=z/1 to the plane x+y+z=3 such that the foot of perpendicular Q lies on plane x-y+z=3 .find coordinates of Q
Answer» A perpendicular is drawn from a point on line x-1/2=y+1/2=z/1 to the plane x+y+z=3 such that the foot of perpendicular Q lies on plane x-y+z=3 .find coordinates of Q

Discussion

6962.	The point satisfies the equation x+8y=26.
Answer» The point satisfies the equation $x + 8 y = 26.$

Discussion

6963.	In the figure below, lines RS and PQ intersect each other at point O. If ∠POR:∠ROQ=7:13 , find ∠SOQ.
Answer» In the figure below, lines RS and PQ intersect each other at point O. If $∠ P O R : ∠ R O Q = 7 : 13$ , find $∠ S O Q$ .

6963.

In the figure below, lines RS and PQ intersect each other at point O. If ∠POR:∠ROQ=7:13 , find ∠SOQ.

Answer»

In the figure below, lines RS and PQ intersect each other at point O. If $∠ P O R : ∠ R O Q = 7 : 13$ , find $∠ S O Q$ .

Discussion

6964.	What is the sum of all the exterior angles of a triangle?
Answer» What is the sum of all the exterior angles of a triangle?

Discussion

6965.	Two adjacent sides of a parallelogram ABCD are given by ⟶AB=2^i+10^j+11^k and ⟶AD=−^i+2^j+2^k. The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α is given by
Answer» Two adjacent sides of a parallelogram ABCD are given by $⟶ A B = 2^i + 10^j + 11^k$ and $⟶ A D = -^i + 2^j + 2^k .$ The side AD is rotated by an acute angle $α$ in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle $α$ is given by

Discussion

6966.	Question 1 (i)Given a parallelogram ABCD. Complete each statement along with the definition or property used.(i) AD = ..........
Answer» Question 1 (i) Given a parallelogram ABCD. Complete each statement along with the definition or property used. (i) AD = ..........

Discussion

6967.	instabitity cons†an t for \lbrack Ni(NH3)6\rbrack^{+2 }whenβ6 is 2 ×10^{12 is }
Answer» instabitity cons†an t for \lbrack Ni(NH3)6\rbrack^{+2 }whenβ6 is 2 ×10^{12 is }

Discussion

6968.	47. Find the equation of straight line passing through the point (4,3) and making intercepts on the coordinate axis whose sum is -1
Answer» 47. Find the equation of straight line passing through the point (4,3) and making intercepts on the coordinate axis whose sum is -1

Discussion

6969.	Find the value of p if the mean ofnfollowing data is 18. variate(x) 13 15 17 19 20+p 23 frequency 8 2 3 4 5p
Answer» Find the value of p if the mean ofnfollowing data is 18. variate(x) 13 15 17 19 20+p 23 frequency 8 2 3 4 5p

Discussion

6970.	Question 1 (ii)Write111 in decimal form and say what kind of decimal expansion it has.
Answer» Question 1 (ii) Write $\frac{1}{11}$ in decimal form and say what kind of decimal expansion it has.

Discussion

6971.	∫tan2x sec2x1-tan6xdx
Answer» $\int \frac{\tan^{2} x \sec^{2} x}{1 - \tan^{6} x} d x$

Discussion

6972.	The length, breadth and height of a cuboid are in the ratio 2:3:2√3. Then, the ratio of the diagonal to the height of the cuboid is
Answer» The length, breadth and height of a cuboid are in the ratio $2 : 3 : 2 \sqrt{3}$ . Then, the ratio of the diagonal to the height of the cuboid is

Discussion

6973.	Volume and surface ara of a solid hemishere are numerically equal. What is the diameter of the hemisphere ?
Answer» Volume and surface ara of a solid hemishere are numerically equal. What is the diameter of the hemisphere ?

Discussion

6974.	Solve for x: 3(9x)<8(3x)+3
Answer» Solve for $x$ : $3 (9^{x}) < 8 (3^{x}) + 3$

6974.

Solve for x: 3(9x)<8(3x)+3

Answer»

Solve for $x$ :

$3 (9^{x}) < 8 (3^{x}) + 3$

Discussion

6975.	In the given figure, ABCD is a trapezium. Find the sum of areas of △AOD and △COB.
Answer» In the given figure, ABCD is a trapezium. Find the sum of areas of $△ A O D$ and $△ C O B$ .

Discussion

6976.	Write down the abscissa, ordinate and co-ordinates of P, Q, R and S as given in the figure.
Answer» Write down the abscissa, ordinate and co-ordinates of P, Q, R and S as given in the figure.

Discussion

6977.	Use Euclid's division algorithm to find the HCF of: 135 and 225 [2 MARKS]
Answer» Use Euclid's division algorithm to find the HCF of: 135 and 225 [2 MARKS]

Discussion

6978.	x=1+a+a2+...∞(a<1) y=1+b+b2+...∞(b<1) Then the value of 1+ab+a2b2+.....∞ is [MNR 1980; MP PET 1985]
Answer» $x = 1 + a + a^{2} + . . . \infty (a < 1)$ $y = 1 + b + b^{2} + . . . \infty (b < 1)$ Then the value of $1 + a b + a^{2} b^{2} + . . . . . \infty$ is [MNR 1980; MP PET 1985]

Discussion

6979.	if the 2 different angles of a parallelogram are in ratio 4/5 :1 , then find the angles of a parallelogram
Answer» if the 2 different angles of a parallelogram are in ratio 4/5 :1 , then find the angles of a parallelogram

Discussion

6980.	Question 9 (ii)Classify √225 as rational or irrational.
Answer» Question 9 (ii) Classify $\sqrt{225}$ as rational or irrational.

Discussion

6981.	In a △ABC, let D,E and F be the points on lines BC,CA and AB which are concurrent. If CEEA=35,BDDC=57 and side AB has a length of 14 cm, then the lengths of AF and FB will be respectively :
Answer» In a $△ A B C,$ let $D, E$ and $F$ be the points on lines $B C, C A$ and $A B$ which are concurrent. If $\frac{C E}{E A} = \frac{3}{5}, \frac{B D}{D C} = \frac{5}{7}$ and side $A B$ has a length of $14 cm,$ then the lengths of $A F$ and $F B$ will be respectively :

Discussion

6982.	The abscissa of any point on y-axis is(a) 0(b) 1(c) −1(d) any number
Answer» The abscissa of any point on y-axis is (a) 0 (b) 1 (c) −1 (d) any number

Discussion

6983.	Point (0, –8) lies(a) in the II quadrant(b) in the IV quadrant(c) on the x-axis(d) on the y-axis
Answer» Point (0, –8) lies (a) in the II quadrant (b) in the IV quadrant (c) on the x-axis (d) on the y-axis

Discussion

6984.	If x > 0 and y < 0, then the point (x, y) lies in(a) I(b) III(c) II(d) IV
Answer» If x > 0 and y < 0, then the point (x, y) lies in (a) I (b) III (c) II (d) IV

Discussion

6985.	In the following diagram, AP and BQ are equal and parallel to each other. Prove that : (i) Δ AOP ≅Δ BOQ. (ii) AB and PQ bisect each other.
Answer» In the following diagram, AP and BQ are equal and parallel to each other. Prove that : (i) $Δ$ AOP $≅ Δ$ BOQ. (ii) AB and PQ bisect each other.

6985.

In the following diagram, AP and BQ are equal and parallel to each other. Prove that : (i) Δ AOP ≅Δ BOQ. (ii) AB and PQ bisect each other.

Answer»

In the following diagram, AP and BQ are equal and parallel to each other.

Prove that :

(i) $Δ$ AOP $≅ Δ$ BOQ.

(ii) AB and PQ bisect each other.

Discussion

6986.	The following table shows the marks obtained by 5 students in a class room, find the average marks of the classroom. MarksFrequency981651882541
Answer» The following table shows the marks obtained by 5 students in a class room, find the average marks of the classroom. $\begin{matrix} Marks & Frequency 98 & 1 65 & 1 88 & 2 54 & 1 \end{matrix}$

6986.

The following table shows the marks obtained by 5 students in a class room, find the average marks of the classroom. MarksFrequency981651882541

Answer»

The following table shows the marks obtained by 5 students in a class room, find the average marks of the classroom.

$\begin{matrix} Marks & Frequency 98 & 1 65 & 1 88 & 2 54 & 1 \end{matrix}$

Discussion

6987.	∑fx = 7x + 2, ∑f = 12. If the mean of the distribution is 6, what is the value of x?
Answer» $\sum$ fx = 7x + 2, $\sum$ f = 12. If the mean of the distribution is 6, what is the value of x?

Discussion

6988.	Express each of the following equations in the form ax+ by + c = 0 and indicate the values of a, b, c in each case.(i) 3x - y = x - 1(ii) x2−y3=16+y
Answer» Express each of the following equations in the form ax+ by + c = 0 and indicate the values of a, b, c in each case. (i) 3x - y = x - 1 (ii) $\frac{x}{2} - \frac{y}{3} = \frac{1}{6} + y$

Discussion

6989.	Given: log3 m=x and log3 n=y. (i) Express 32x−3 in terms of m. (ii) Write down 31−2y+3x in terms of m and n. (iii) If 2 log3 A=5x−3y; find A in terms of m and n.
Answer» Given: $l o g_{3} m = x$ and $l o g_{3} n = y$ . (i) Express $3^{2 x - 3}$ in terms of m. (ii) Write down $3^{1 - 2 y + 3 x}$ in terms of m and n. (iii) If $2 l o g_{3} A = 5 x - 3 y$ ; find A in terms of m and n.

6989.

Given: log3 m=x and log3 n=y. (i) Express 32x−3 in terms of m. (ii) Write down 31−2y+3x in terms of m and n. (iii) If 2 log3 A=5x−3y; find A in terms of m and n.

Answer»

Given: $l o g_{3} m = x$ and $l o g_{3} n = y$ .

(i) Express $3^{2 x - 3}$ in terms of m.

(ii) Write down $3^{1 - 2 y + 3 x}$ in terms of m and n.

(iii) If $2 l o g_{3} A = 5 x - 3 y$ ; find A in terms of m and n.

Discussion

6990.	To construct a unique quadrilateral ____________ the minimum number of measurements is 31. Rectangle2. Kite3. Trapezium 4. Square
Answer» To construct a unique quadrilateral ____________ the minimum number of measurements is 3 1. Rectangle 2. Kite 3. Trapezium 4. Square

Discussion

6991.	Question 11In ΔPQR, PD⊥QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, then prove that (a+b) (a-b) = (c+d) (c-d).
Answer» Question 11 In $Δ P Q R$ , $P D ⊥ Q R$ such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, then prove that (a+b) (a-b) = (c+d) (c-d).

Discussion

6992.	Two kids Goutham and Pavani are fighting for coins. Finally, Goutham won and stole a coin from Pavani's pocket which has four different coins ( a 1 rupee coin, a 2 rupee coin, a 5 rupee coin, a 10 rupee coin). What are the total number of possible outcomes when Goutham tried to steal a coin?
Answer» Two kids Goutham and Pavani are fighting for coins. Finally, Goutham won and stole a coin from Pavani's pocket which has four different coins ( a 1 rupee coin, a 2 rupee coin, a 5 rupee coin, a 10 rupee coin). What are the total number of possible outcomes when Goutham tried to steal a coin?

Discussion

6993.	The zeros of the polynomial p(x) = x2 + x – 6 are(a) 2, 3(b) –2, 3(c) 2, –3(d) –2, –3
Answer» The zeros of the polynomial p(x) = x² + x – 6 are (a) 2, 3 (b) –2, 3 (c) 2, –3 (d) –2, –3

Discussion

6994.	In the above problem, to find the area, what is the first thing you would try to obtain?
Answer» In the above problem, to find the area, what is the first thing you would try to obtain?

6994.

In the above problem, to find the area, what is the first thing you would try to obtain?

Answer»

In the above problem, to find the area, what is the first thing you would try to obtain?

Discussion

6995.	An action which results in one or several outcomes is known as _____ .
Answer» An action which results in one or several outcomes is known as _____ .

Discussion

6996.	If \vert2x-3\vert
Answer» If \vert2x-3\vert

Discussion

6997.	Find the point on the x-axis which is equidistant from (2, - 5) and (- 2, 9).
Answer» Find the point on the x-axis which is equidistant from (2, - 5) and (- 2, 9).

Discussion

6998.

A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below: Outcome 1 2 3 4 5 6 Frequency 200 30 120 100 50 100 The probability of getting a prime number is(a) 13(b) 23(c) 4960(d) 39125

Answer» A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below:

Outcome	1	2	3	4	5	6
Frequency	200	30	120	100	50	100

The probability of getting a prime number is

(a)

\frac{1}{3}

(b)

\frac{2}{3}

(c)

\frac{49}{60}

(d)

\frac{39}{125}

Discussion

6999.	Mark the correct alternative in each of the following:The point of intersect of the coordinate axes is(a) ordinate(b) abscissa(c) quadrant(d) origin
Answer» Mark the correct alternative in each of the following: The point of intersect of the coordinate axes is (a) ordinate (b) abscissa (c) quadrant (d) origin

Discussion

7000.	The value of x − yx-y when x = 2 and y = −2 is(a) 18(b) −18(c) 14(d) −14
Answer» The value of x − y^x-y when x = 2 and y = −2 is (a) 18 (b) −18 (c) 14 (d) −14

Discussion

Explore topic-wise InterviewSolutions in .

Prove that i) tan A - cot A = -2 cot2Aii) cot A = 1/2 (cot A/2 - tan A/2)

The value of x satisfying the equation x−75=135 is___

Question 1 (ii)In Δ ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine:(ii) sin C, cos C

There is a 40m long Tunnel. The cross section of the tunnel is a semicircle with a radius 6. Find the cost of painting it at the rate of ₹2/m​​​​​​2

In the figure below, ABC is a right angled triangle and M is the midpoint of AB.(a) Prove that .(b) Prove that MC = MA = MB.

What is the degree of the equation that represents a straight line on the XY plane? __

29. solve the following pair of linear equations by the substitution method 0.2x+0.3y=1.3

cos 30∘ cos 60∘−sin 30∘ sin 60∘= __________________

If r is the radius and h is height of the cylinder the volume will be(a) 13πr2h(b) πr2h(c) 2πr (h + r)(d) 2πrh

If the areas of three adjacent faces of a cuboid are 8 cm2, 18 cm3 and 25 cm3. Find the volume of the cuboid.

A perpendicular is drawn from a point on line x-1/2=y+1/2=z/1 to the plane x+y+z=3 such that the foot of perpendicular Q lies on plane x-y+z=3 .find coordinates of Q

The point satisfies the equation x+8y=26.

In the figure below, lines RS and PQ intersect each other at point O. If ∠POR:∠ROQ=7:13 , find ∠SOQ.

What is the sum of all the exterior angles of a triangle?

Two adjacent sides of a parallelogram ABCD are given by ⟶AB=2^i+10^j+11^k and ⟶AD=−^i+2^j+2^k. The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α is given by

Question 1 (i)Given a parallelogram ABCD. Complete each statement along with the definition or property used.(i) AD = ..........

instabitity cons†an t for \lbrack Ni(NH3)6\rbrack^{+2 }whenβ6 is 2 ×10^{12 is }

47. Find the equation of straight line passing through the point (4,3) and making intercepts on the coordinate axis whose sum is -1

Find the value of p if the mean ofnfollowing data is 18. variate(x) 13 15 17 19 20+p 23 frequency 8 2 3 4 5p

Question 1 (ii)Write111 in decimal form and say what kind of decimal expansion it has.

∫tan2x sec2x1-tan6xdx

The length, breadth and height of a cuboid are in the ratio 2:3:2√3. Then, the ratio of the diagonal to the height of the cuboid is

Volume and surface ara of a solid hemishere are numerically equal. What is the diameter of the hemisphere ?

Solve for x: 3(9x)&lt;8(3x)+3

In the given figure, ABCD is a trapezium. Find the sum of areas of △AOD and △COB.

Write down the abscissa, ordinate and co-ordinates of P, Q, R and S as given in the figure.

Use Euclid's division algorithm to find the HCF of: 135 and 225 [2 MARKS]

x=1+a+a2+...∞(a&lt;1) y=1+b+b2+...∞(b&lt;1) Then the value of 1+ab+a2b2+.....∞ is [MNR 1980; MP PET 1985]

if the 2 different angles of a parallelogram are in ratio 4/5 :1 , then find the angles of a parallelogram

Question 9 (ii)Classify √225 as rational or irrational.

In a △ABC, let D,E and F be the points on lines BC,CA and AB which are concurrent. If CEEA=35,BDDC=57 and side AB has a length of 14 cm, then the lengths of AF and FB will be respectively :

The abscissa of any point on y-axis is(a) 0(b) 1(c) −1(d) any number

Point (0, –8) lies(a) in the II quadrant(b) in the IV quadrant(c) on the x-axis(d) on the y-axis

If x > 0 and y < 0, then the point (x, y) lies in(a) I(b) III(c) II(d) IV

In the following diagram, AP and BQ are equal and parallel to each other. Prove that : (i) Δ AOP ≅Δ BOQ. (ii) AB and PQ bisect each other.

The following table shows the marks obtained by 5 students in a class room, find the average marks of the classroom. MarksFrequency981651882541

∑fx = 7x + 2, ∑f = 12. If the mean of the distribution is 6, what is the value of x?

Express each of the following equations in the form ax+ by + c = 0 and indicate the values of a, b, c in each case.(i) 3x - y = x - 1(ii) x2−y3=16+y

Given: log3 m=x and log3 n=y. (i) Express 32x−3 in terms of m. (ii) Write down 31−2y+3x in terms of m and n. (iii) If 2 log3 A=5x−3y; find A in terms of m and n.

To construct a unique quadrilateral ____________ the minimum number of measurements is 31. Rectangle2. Kite3. Trapezium 4. Square

Question 11In ΔPQR, PD⊥QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, then prove that (a+b) (a-b) = (c+d) (c-d).

Two kids Goutham and Pavani are fighting for coins. Finally, Goutham won and stole a coin from Pavani's pocket which has four different coins ( a 1 rupee coin, a 2 rupee coin, a 5 rupee coin, a 10 rupee coin). What are the total number of possible outcomes when Goutham tried to steal a coin?

The zeros of the polynomial p(x) = x2 + x – 6 are(a) 2, 3(b) –2, 3(c) 2, –3(d) –2, –3

In the above problem, to find the area, what is the first thing you would try to obtain?

An action which results in one or several outcomes is known as _____ .

If \vert2x-3\vert

Find the point on the x-axis which is equidistant from (2, - 5) and (- 2, 9).

A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below: Outcome 1 2 3 4 5 6 Frequency 200 30 120 100 50 100 The probability of getting a prime number is(a) 13(b) 23(c) 4960(d) 39125

Mark the correct alternative in each of the following:The point of intersect of the coordinate axes is(a) ordinate(b) abscissa(c) quadrant(d) origin

The value of x − yx-y when x = 2 and y = −2 is(a) 18(b) −18(c) 14(d) −14

There is a 40m long Tunnel. The cross section of the tunnel is a semicircle with a radius 6. Find the cost of painting it at the rate of ₹2/m2

Solve for x: 3(9x)<8(3x)+3

x=1+a+a2+...∞(a<1) y=1+b+b2+...∞(b<1) Then the value of 1+ab+a2b2+.....∞ is [MNR 1980; MP PET 1985]