32581 + Interview Questions in Mathematics

1.	Mode is(a) least frequency value(b) middle most value(c) most frequent value(d) None of these
Answer» Mode is (a) least frequency value (b) middle most value (c) most frequent value (d) None of these

Discussion

2.	Given that √2 is a zero of the cubic polynomial 6x3+√2x2−10x−4√2, find its other two zeroes.
Answer» Given that $\sqrt{2}$ is a zero of the cubic polynomial $6 x^{3} + \sqrt{2} x^{2} - 10 x - 4 \sqrt{2}$ , find its other two zeroes.

Discussion

3.	Rohit takes 2 hours to reach the airport travelling at a speed of 40 km/h. At what speed should Rohit travel to reach the airport in 80 min?
Answer» Rohit takes 2 hours to reach the airport travelling at a speed of 40 km/h. At what speed should Rohit travel to reach the airport in 80 min?

Discussion

4.	A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and the base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder.
Answer» A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and the base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder.

Discussion

5.	4)boat goes 24 km upstream and 28 km downstream in 6 hrs .It goes 30 km upstream and 21km downstream in hrs .Find the speed of the boat in still water and also speed of the stream
Answer» 4)boat goes 24 km upstream and 28 km downstream in 6 hrs .It goes 30 km upstream and 21 km downstream in hrs .Find the speed of the boat in still water and also speed of the stream

Discussion

6.	With the axes of coordinates chosen along two adjacent sides of a rectangle, two opposite vertices have coordinates (0, 0) and (4, 3). What are the coordinates of the other two vertices?
Answer» With the axes of coordinates chosen along two adjacent sides of a rectangle, two opposite vertices have coordinates (0, 0) and (4, 3). What are the coordinates of the other two vertices?

Discussion

7.	Find the roots of the quadratic equation √2x2+7x+5√2=0 using factorisation method.
Answer» Find the roots of the quadratic equation $\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0$ using factorisation method.

Discussion

8.	cot θ tan 90°-θ-sec90°-θcosec θ+sin265°+sin225°+3 tan 5°tan 45°tan 85°
Answer» $\cot θ \tan (90 ° - θ) - \sec (90 ° - θ) cosec θ + \sin^{2} 65 ° + \sin^{2} 25 ° + \sqrt{3} \tan 5 ° \tan 45 ° \tan 85 °$

Discussion

9.	In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is(a) 9 cm(b) 15 cm(c) 353 cm(d) 25 cm
Answer» In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is (a) 9 cm (b) 15 cm (c) $\sqrt{353}$ cm (d) 25 cm

Discussion

10.	12. A sponge contain water of 60%of its volume.find approximately,how much water will be found in 20 such sponge shaped like cylinder with two hemispherical ends if completely lengths of each sponge is 5cm and diameter is 2.8cm?
Answer» 12. A sponge contain water of 60%of its volume.find approximately,how much water will be found in 20 such sponge shaped like cylinder with two hemispherical ends if completely lengths of each sponge is 5cm and diameter is 2.8cm?

Discussion

11.	If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, then a = _______ and b = _______.
Answer» If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, then a = _______ and b = _______.

Discussion

12.	If the y-coordinate of a point is zero then this point always lies(a) on the y-axis(b) on the x-axis(c) in the I quadrant(d) in the IV quadrant
Answer» If the y-coordinate of a point is zero then this point always lies (a) on the y-axis (b) on the x-axis (c) in the I quadrant (d) in the IV quadrant

Discussion

13.	Th sum of the first 30 terms of the arithmetic sequence 10, 18, 26... is ___.
Answer» Th sum of the first 30 terms of the arithmetic sequence 10, 18, 26... is ___.

Discussion

14.	If the centre of a circle is (2a, a-7), then the values of 'a', if the circle passes through the point (11,-9) and has diameter 10√2 units will be:
Answer» If the centre of a circle is (2a, a-7), then the values of 'a', if the circle passes through the point (11,-9) and has diameter $10 \sqrt{2}$ units will be:

Discussion

15.	Find the sum of the following APs.(i) 2, 7, 12,…., to 10 terms(ii) − 37, − 33, − 29 ,…, to 12 terms
Answer» Find the sum of the following APs. (i) 2, 7, 12,…., to 10 terms (ii) − 37, − 33, − 29 ,…, to 12 terms

Discussion

16.	ABCD is a trapezium in which AB \|\| CD. The diagonals AC and BD intersect at O. Prove that : (i) ∆AOB ∼ ∆COD (ii) If OA = 6 cm, OC = 8 cm,Find:(a) Area ∆AOBArea ∆COD(b) Area ∆AODArea ∆COD
Answer» ABCD is a trapezium in which AB \|\| CD. The diagonals AC and BD intersect at O. Prove that : (i) ∆AOB ∼ ∆COD (ii) If OA = 6 cm, OC = 8 cm, Find: (a) $\frac{Area (∆ AOB)}{Area (∆ COD)}$ (b) $\frac{Area (∆ AOD)}{Area (∆ COD)}$

Discussion

17.	An experiment succeeds thrice as often as it fails. Find the probability that in the next live trials, there will be at least 3 successes.
Answer» An experiment succeeds thrice as often as it fails. Find the probability that in the next live trials, there will be at least 3 successes.

Discussion

18.	If cos 3θ=√32, 0° < 3θ < 90°, then find the value of θ.
Answer» $If c o s 3 θ = \frac{\sqrt{3}}{2}$ , 0° < $3 θ$ < 90°, then find the value of $θ$ .

Discussion

19.	Question 5 (ix) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (ix) (cosecA−sinA)(secA−cosA)=1(tanA+cotA) [Hint : Simplify L.H.S and R.H.S separately]
Answer» Question 5 (ix) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. $(i x) (c o s e c A - s i n A) (s e c A - c o s A) = \frac{1}{(t a n A + c o t A)}$ [Hint : Simplify L.H.S and R.H.S separately]

Discussion

20.	find the zero of 3x^2-1
Answer» find the zero of 3x^2-1

Discussion

21.	Consider the following pattern.Choose the option that comes next in the pattern.
Answer» Consider the following pattern. Choose the option that comes next in the pattern.

Discussion

22.	If A, B, C are the interior angles of a ΔABC, then which of the following is not true?
Answer» If A, B, C are the interior angles of a ΔABC, then which of the following is not true?

Discussion

23.	In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?
Answer» In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

23.

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

Answer»

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

Discussion

24.	The mean of first 10 whole numbers is:
Answer» The mean of first 10 whole numbers is:

Discussion

25.	Two circles intersect in points P and Q. A secant passing through P intersects the circles in A and B respectively. Tangents to the circles at A and B intersect at T. Prove that A, Q, B and T lie on a circle.
Answer» Two circles intersect in points P and Q. A secant passing through P intersects the circles in A and B respectively. Tangents to the circles at A and B intersect at T. Prove that A, Q, B and T lie on a circle.

Discussion

26.	A 6 ft tall man finds that the angle of elevation of a 24 ft high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.
Answer» A 6 ft tall man finds that the angle of elevation of a 24 ft high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.

Discussion

27.	Two circles touch each other externally. The sum of their areas is 490 π cm2. Their centres are separated by 28 cm. The difference of their perimeters is ___________.
Answer» Two circles touch each other externally. The sum of their areas is 490 π cm². Their centres are separated by 28 cm. The difference of their perimeters is ___________.

Discussion

28.	In a right angled triangle, the orthocenter lies on ______________.
Answer» In a right angled triangle, the orthocenter lies on ______________.

Discussion

29.	Express 0.1¯23 as a rational number in simplest form.
Answer» Express $0.1 ¯ 23$ as a rational number in simplest form.

Discussion

30.	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) x-2a x-2b=4ab(vii) 9a2b2x2-24abcdx+16c2d2=0, a≠0, b≠0(viii) 2a2+b2x2+2a+bx+1=0(ix) b+cx2-a+b+cx+a=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) $(x - 2 a) (x - 2 b) = 4 a b$ (vii) $9 a^{2} b^{2} x^{2} - 24 a b c d x + 16 c^{2} d^{2} = 0, a \neq 0, b \neq 0$ (viii) $2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0$ (ix) $(b + c) x^{2} - (a + b + c) x + a = 0$

Discussion

31.	Kevin hired a cab and followed the path as shown in the figure. Find the difference between the total distance and the displacement covered by him if all the distances in the figure are in kilometres? Ans - _
Answer» Kevin hired a cab and followed the path as shown in the figure. Find the difference between the total distance and the displacement covered by him if all the distances in the figure are in kilometres? Ans - _

Discussion

32.	How can I draw a triangle of circum radius 3cm and two angles 32 1/2 degree and 37 1/2 degree
Answer» How can I draw a triangle of circum radius 3cm and two angles 32 1/2 degree and 37 1/2 degree

Discussion

33.	Pair the cards correctly.
Answer» Pair the cards correctly.

Discussion

34.	Evaluate(I) (II) (III) cos 48° − sin 42°(IV)cosec 31° − sec 59°
Answer» Evaluate (I) (II) (III) cos 48° − sin 42° (IV)cosec 31° − sec 59°

34.

Evaluate(I) (II) (III) cos 48° − sin 42°(IV)cosec 31° − sec 59°

Answer»

Evaluate

(I)

(II)

(III) cos 48° − sin 42°

(IV)cosec 31° − sec 59°

Discussion

35.	Hypotenuse is the side opposite to the angle that measures __ degrees in a triangle.
Answer» Hypotenuse is the side opposite to the angle that measures __ degrees in a triangle.

Discussion

36.	Evaluate the following :(i) sin 20°cos 70°(ii) cos 19°sin 71°(iii) sin 21°cos 69°(iv) tan 10°cot 80°(v) sec 11°cosec 79°
Answer» Evaluate the following : (i) $\frac{\sin 20 °}{\cos 70 °}$ (ii) $\frac{\cos 19 °}{\sin 71 °}$ (iii) $\frac{\sin 21 °}{\cos 69 °}$ (iv) $\frac{\tan 10 °}{\cot 80 °}$ (v) $\frac{\sec 11 °}{cosec 79 °}$

Discussion

37.	Find the sum of the terms of the finite AP : 1, 3, 5, 7,…,199
Answer» Find the sum of the terms of the finite AP : 1, 3, 5, 7,…,199

Discussion

38.	'Telecom Ltd.' issued 20,000 Equity Shares of ₹ 10 each at a premium of ₹ 5 per share, payable as: ₹ 7 (including premium) on application, ₹ 5 on allotment and the balance after three months of allotment. A shareholder to whom 200 shares were allotted failed to pay the allotment and call money and his shares were forfeited. 160 of the forfeited shares were reissued for ₹ 1,600.Give necessary entries in company's Journal and the Balance Sheet.
Answer» 'Telecom Ltd.' issued 20,000 Equity Shares of ₹ 10 each at a premium of ₹ 5 per share, payable as: ₹ 7 (including premium) on application, ₹ 5 on allotment and the balance after three months of allotment. A shareholder to whom 200 shares were allotted failed to pay the allotment and call money and his shares were forfeited. 160 of the forfeited shares were reissued for ₹ 1,600. Give necessary entries in company's Journal and the Balance Sheet.

Discussion

39.	For AP show that ap+ap+2q=2ap+q
Answer» For AP show that $a_{p} + a_{p + 2 q} = 2 a_{p + q}$

Discussion

40.	In the given figure, O is the centre of the circle. Tap on the angle whose value will be 2x∘.
Answer» In the given figure, O is the centre of the circle. Tap on the angle whose value will be $2 x^{\circ} .$

Discussion

41.	The volume of concrete required to build the terrace, ifI. the terrace consists of 20 steps each 100 units long.II. each step has a rise of 12m and a breadth of 12m.
Answer» The volume of concrete required to build the terrace, if I. the terrace consists of 20 steps each 100 units long. II. each step has a rise of $\frac{1}{2} m$ and a breadth of $\frac{1}{2} m$ .

Discussion

42.	How do we draw a triangle with two of the angle 40° and 120° and circumradius 3 centimetres?
Answer» How do we draw a triangle with two of the angle 40° and 120° and circumradius 3 centimetres?

Discussion

43.	There are 10 songs on a playlist, in which you started playing the first track. You've turned shuffle on. What is the probability that the second track will be played next?
Answer» There are 10 songs on a playlist, in which you started playing the first track. You've turned shuffle on. What is the probability that the second track will be played next?

Discussion

44.	Evaluate each of the following(cosec2 45° sec2 30°) (sin2 30° + 4 cot2 45° − sec2 60°)
Answer» Evaluate each of the following (cosec² 45° sec² 30°) (sin² 30° + 4 cot² 45° − sec² 60°)

Discussion

45.	If y = 1 is a common root of the equations ay2+ay+3=0 and y2+y+b=0, then ab equals(a) 3(b) −7/2(c) 6(d) −3
Answer» If y = 1 is a common root of the equations $a y^{2} + a y + 3 = 0 and y^{2} + y + b = 0$ , then ab equals (a) 3 (b) −7/2 (c) 6 (d) −3

Discussion

46.	The centre of the circle x=1+2cosθ, y=−3+2sinθ, is
Answer» The centre of the circle $x = 1 + 2 cos θ, y = - 3 + 2 sin θ,$ is

Discussion

47.	2 AP's have same common difference the difference between their 100th term is 100. What is the difference between their 1000th term
Answer» 2 AP's have same common difference the difference between their 100th term is 100. What is the difference between their 1000th term

Discussion

48.	What is the solution to the system of equations: 2x + 4y = 8 and 4x + 8y = 0?
Answer» What is the solution to the system of equations: 2x + 4y = 8 and 4x + 8y = 0?

Discussion

49.	At one end of a diameter PQ of a circle of radius 5 cm, tangent XPY is drawn to the circle. The length of chord AB parallel to XY and at a distance of 8 cm from P is(a) 5 cm(b) 6 cm(c) 7 cm(d) 8 cm
Answer» At one end of a diameter PQ of a circle of radius 5 cm, tangent XPY is drawn to the circle. The length of chord AB parallel to XY and at a distance of 8 cm from P is (a) 5 cm (b) 6 cm (c) 7 cm (d) 8 cm

Discussion

50.	118.From a point P,two tangents PA and PB are drawn to a circle with centre O. If OP=diameter of the circle,show that triangle APB is an equilateral triangle
Answer» 118.From a point P,two tangents PA and PB are drawn to a circle with centre O. If OP=diameter of the circle,show that triangle APB is an equilateral triangle

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Mode is(a) least frequency value(b) middle most value(c) most frequent value(d) None of these

Given that √2 is a zero of the cubic polynomial 6x3+√2x2−10x−4√2, find its other two zeroes.

Rohit takes 2 hours to reach the airport travelling at a speed of 40 km/h. At what speed should Rohit travel to reach the airport in 80 min?

A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and the base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder.

4)boat goes 24 km upstream and 28 km downstream in 6 hrs .It goes 30 km upstream and 21km downstream in hrs .Find the speed of the boat in still water and also speed of the stream

With the axes of coordinates chosen along two adjacent sides of a rectangle, two opposite vertices have coordinates (0, 0) and (4, 3). What are the coordinates of the other two vertices?

Find the roots of the quadratic equation √2x2+7x+5√2=0 using factorisation method.

cot θ tan 90°-θ-sec90°-θcosec θ+sin265°+sin225°+3 tan 5°tan 45°tan 85°

In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is(a) 9 cm(b) 15 cm(c) 353 cm(d) 25 cm

12. A sponge contain water of 60%of its volume.find approximately,how much water will be found in 20 such sponge shaped like cylinder with two hemispherical ends if completely lengths of each sponge is 5cm and diameter is 2.8cm?

If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, then a = _______ and b = _______.

If the y-coordinate of a point is zero then this point always lies(a) on the y-axis(b) on the x-axis(c) in the I quadrant(d) in the IV quadrant

Th sum of the first 30 terms of the arithmetic sequence 10, 18, 26... is ___.

If the centre of a circle is (2a, a-7), then the values of 'a', if the circle passes through the point (11,-9) and has diameter 10√2 units will be:

Find the sum of the following APs.(i) 2, 7, 12,…., to 10 terms(ii) − 37, − 33, − 29 ,…, to 12 terms

ABCD is a trapezium in which AB || CD. The diagonals AC and BD intersect at O. Prove that : (i) ∆AOB ∼ ∆COD (ii) If OA = 6 cm, OC = 8 cm,Find:(a) Area ∆AOBArea ∆COD(b) Area ∆AODArea ∆COD

An experiment succeeds thrice as often as it fails. Find the probability that in the next live trials, there will be at least 3 successes.

If cos 3θ=√32, 0° &lt; 3θ &lt; 90°, then find the value of θ.

Question 5 (ix) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (ix) (cosecA−sinA)(secA−cosA)=1(tanA+cotA) [Hint : Simplify L.H.S and R.H.S separately]

find the zero of 3x^2-1

Consider the following pattern.Choose the option that comes next in the pattern.

If A, B, C are the interior angles of a ΔABC, then which of the following is not true?

In the figure; P and Q are the points of intersection of two circles with centres O &amp; O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

The mean of first 10 whole numbers is:

Two circles intersect in points P and Q. A secant passing through P intersects the circles in A and B respectively. Tangents to the circles at A and B intersect at T. Prove that A, Q, B and T lie on a circle.

A 6 ft tall man finds that the angle of elevation of a 24 ft high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.

Two circles touch each other externally. The sum of their areas is 490 π cm2. Their centres are separated by 28 cm. The difference of their perimeters is ___________.

In a right angled triangle, the orthocenter lies on ______________.

Express 0.1¯23 as a rational number in simplest form.

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) x-2a x-2b=4ab(vii) 9a2b2x2-24abcdx+16c2d2=0, a≠0, b≠0(viii) 2a2+b2x2+2a+bx+1=0(ix) b+cx2-a+b+cx+a=0

Kevin hired a cab and followed the path as shown in the figure. Find the difference between the total distance and the displacement covered by him if all the distances in the figure are in kilometres? Ans - _

How can I draw a triangle of circum radius 3cm and two angles 32 1/2 degree and 37 1/2 degree

Pair the cards correctly.

Evaluate(I) (II) (III) cos 48° − sin 42°(IV)cosec 31° − sec 59°

Hypotenuse is the side opposite to the angle that measures __ degrees in a triangle.

Evaluate the following :(i) sin 20°cos 70°(ii) cos 19°sin 71°(iii) sin 21°cos 69°(iv) tan 10°cot 80°(v) sec 11°cosec 79°

Find the sum of the terms of the finite AP : 1, 3, 5, 7,…,199

For AP show that ap+ap+2q=2ap+q

In the given figure, O is the centre of the circle. Tap on the angle whose value will be 2x∘.

The volume of concrete required to build the terrace, ifI. the terrace consists of 20 steps each 100 units long.II. each step has a rise of 12m and a breadth of 12m.

How do we draw a triangle with two of the angle 40° and 120° and circumradius 3 centimetres?

There are 10 songs on a playlist, in which you started playing the first track. You've turned shuffle on. What is the probability that the second track will be played next?

Evaluate each of the following(cosec2 45° sec2 30°) (sin2 30° + 4 cot2 45° − sec2 60°)

If y = 1 is a common root of the equations ay2+ay+3=0 and y2+y+b=0, then ab equals(a) 3(b) −7/2(c) 6(d) −3

The centre of the circle x=1+2cosθ, y=−3+2sinθ, is

2 AP's have same common difference the difference between their 100th term is 100. What is the difference between their 1000th term

What is the solution to the system of equations: 2x + 4y = 8 and 4x + 8y = 0?

At one end of a diameter PQ of a circle of radius 5 cm, tangent XPY is drawn to the circle. The length of chord AB parallel to XY and at a distance of 8 cm from P is(a) 5 cm(b) 6 cm(c) 7 cm(d) 8 cm

118.From a point P,two tangents PA and PB are drawn to a circle with centre O. If OP=diameter of the circle,show that triangle APB is an equilateral triangle

If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, then a = _ and b = _.

If cos 3θ=√32, 0° < 3θ < 90°, then find the value of θ.

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?