32581 + Interview Questions in Mathematics Page 55 InterviewSolution

2701.	s =(3t3+7t2+14t+8)m t=1s on the objrct axclaration is. 1. 10m /s 2. 32m/s 3. 23m/s 4. 16 m/
Answer» s =(3t3+7t2+14t+8)m t=1s on the objrct axclaration is. 1. 10m /s 2. 32m/s 3. 23m/s 4. 16 m/

Discussion

2702.	Question 4Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.
Answer» Question 4 Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.

Discussion

2703.	What is the curved surface area of a cone of base diameter 30 centimetres and height 40 centimetres?
Answer» What is the curved surface area of a cone of base diameter 30 centimetres and height 40 centimetres?

Discussion

2704.	Which of these methods gives the highest value of mean?
Answer» Which of these methods gives the highest value of mean?

Discussion

2705.	Prove the following trigonometric identities.tan2θ cos2θ = 1 − cos2θ
Answer» Prove the following trigonometric identities. tan²θ cos²θ = 1 − cos²θ

Discussion

2706.	Solve XCIV - XLVII
Answer» Solve XCIV - XLVII

Discussion

2707.	Find the side (in cm) of a cube whose surface area is 294 cm2.7
Answer» Find the side (in cm) of a cube whose surface area is 294 ${cm}^{2}$ . 7

Discussion

2708.	The polynomial x4 - 2x3 + 3x2 - ax + b when divided by (x+1) and (x-1) gives remainders 19 and 5 respectively. Find the remainder when the polynomial is divided by (x-3).
Answer» The polynomial $x^{4}$ - 2 $x^{3}$ + 3 $x^{2}$ - ax + b when divided by (x+1) and (x-1) gives remainders 19 and 5 respectively. Find the remainder when the polynomial is divided by (x-3).

Discussion

2709.	Diagonals AC and BD of a trapezium ABCD with AB \|\| DC intersect each other at the point O. Using similarity criterion for two triangles, show that OAOC=OBOD.
Answer» Diagonals AC and BD of a trapezium ABCD with AB \|\| DC intersect each other at the point O. Using similarity criterion for two triangles, show that $\frac{OA}{OC} = \frac{OB}{OD}$ .

Discussion

2710.	In the two similar triangles, __ and BC are the hypotenuse of the larger and smaller triangles respectively.
Answer» In the two similar triangles, __ and BC are the hypotenuse of the larger and smaller triangles respectively.

Discussion

2711.

If the mean of the following frequency distribution is 188, find the missing frequencies x and y, if the sum of all frequencies is 100. Class0–8080–160160–240240–320320–400Frequency2025xy10

Answer»

If the mean of the following frequency distribution is $188,$ find the missing frequencies x and y, if the sum of all frequencies is $100.$

Class	$0 - 80$	$80 - 160$	$160 - 240$	$240 - 320$	$320 - 400$
Frequency	$20$	$25$	$x$	$y$	$10$

Discussion

2712.	If 3cotθ=4, then write the value of 2cosθ+sinθ4cosθ-sinθ.
Answer» $If 3 \cot θ = 4, then write the value of \frac{(2 \cos θ + \sin θ)}{(4 \cos θ - \sin θ)} .$

Discussion

2713.	How to express all T Ratios in terms of Sin A
Answer» How to express all T Ratios in terms of Sin A

Discussion

2714.	a and b are two co-primes. Which of the following is/are true?(a) LCM (a, b) = a × b(b) HCF (a, b) = 1(c) Both (a) and (b)(d) Neither (a) nor (b)
Answer» a and b are two co-primes. Which of the following is/are true? (a) LCM (a, b) = a × b (b) HCF (a, b) = 1 (c) Both (a) and (b) (d) Neither (a) nor (b)

Discussion

2715.	value of 1/4pieEpcillumnot
Answer» value of 1/4pieEpcillumnot

Discussion

2716.	13. Find the value of sin150, cos150, tan150, cosec150, sec150, cot150.
Answer» 13. Find the value of sin150, cos150, tan150, cosec150, sec150, cot150.

Discussion

2717.	36.Find the area of the circle with positive x–axis & x^2+y^2=a^2.
Answer» 36.Find the area of the circle with positive x–axis & x^2+y^2=a^2.

Discussion

2718.	In the given figure if AB = 5cm and BC = 12 cm then the radius of the circle is ___
Answer» In the given figure if AB = 5cm and BC = 12 cm then the radius of the circle is ___

2718.

In the given figure if AB = 5cm and BC = 12 cm then the radius of the circle is ___

Answer»

In the given figure if AB = 5cm and BC = 12 cm then the radius of the circle is ___

Discussion

2719.	What number should be added to 3x3−5x2+6x so that when resulting polynomial is divided by x - 3, the remainder is 8
Answer» What number should be added to $3 x^{3} - 5 x^{2} + 6 x$ so that when resulting polynomial is divided by x - 3, the remainder is 8

Discussion

2720.	The outer circumference of a circular race-track is 528m . The track is everywhere 14m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre . Use π=227
Answer» The outer circumference of a circular race-track is $528 m$ . The track is everywhere $14 m$ wide. Calculate the cost of levelling the track at the rate of $50$ paise per square metre . Use $π = \frac{22}{7}$

Discussion

2721.	The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is
Answer» The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

Discussion

2722.	A shopkeeper sells an article at its marked price of ₹ 7500 and charges sales-tax at the rate of 12% from the customer. If the shopkeeper pays a VAT of ₹ 180, calculate the price inclusive of tax paid by the shopkeeper.
Answer» A shopkeeper sells an article at its marked price of ₹ 7500 and charges sales-tax at the rate of 12% from the customer. If the shopkeeper pays a VAT of ₹ 180, calculate the price inclusive of tax paid by the shopkeeper.

Discussion

2723.	A binomial is a polynomial with __terms
Answer» A binomial is a polynomial with __terms

Discussion

2724.	If [0, 1], then sin–1x + cot–1x + cos–1x + tan–1x is equal to
Answer» If [0, 1], then sin–1x + cot–1x + cos–1x + tan–1x is equal to

Discussion

2725.	The length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre is = ___ cm.
Answer» The length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre is = ___ cm.

Discussion

2726.	An army contingent of 616 members is to march behnind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
Answer» An army contingent of 616 members is to march behnind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Discussion

2727.	Length of the altitude on the hypotenuse of a right angled triangle with area A cm2 and one of the sides equal to b cm is __ cm.
Answer» Length of the altitude on the hypotenuse of a right angled triangle with area $A {cm}^{2}$ and one of the sides equal to $b cm$ is __ cm.

Discussion

2728.	Question 13 (i)A dice is thrown once. Find the probability of getting a prime number.
Answer» Question 13 (i) A dice is thrown once. Find the probability of getting a prime number.

Discussion

2729.	Find the area of the major sector of a circle with radius 42 cm and of angle 30°.(Use π = 227 5082
Answer» Find the area of the major sector of a circle with radius 42 cm and of angle 30°. (Use π = $\frac{22}{7}$ 5082

Discussion

2730.	Q. Find the 7th term of an AP whose sum of n terms is 3n^2+5n.Q. If the sum of the first p, q and r terms of an AP are x, y and z respectively, then prove that x/p (q-r) + y/q (r-p) + z/r (p-q) = 0.
Answer» Q. Find the 7th term of an AP whose sum of n terms is 3n^2+5n. Q. If the sum of the first p, q and r terms of an AP are x, y and z respectively, then prove that x/p (q-r) + y/q (r-p) + z/r (p-q) = 0.

Discussion

2731.	In figure below P, Q, R are the points where the incircle of ΔABC touches the sides. Find ∠AQR.
Answer» In figure below P, Q, R are the points where the incircle of $Δ A B C$ touches the sides. Find $∠ A Q R .$

2731.

In figure below P, Q, R are the points where the incircle of ΔABC touches the sides. Find ∠AQR.

Answer»

In figure below P, Q, R are the points where the incircle of $Δ A B C$ touches the sides. Find $∠ A Q R .$

Discussion

2732.	Find the discriminant for the quadratic equation represented by px2+√pqx+q=0 and determine the nature of roots. (p and q have same sign)
Answer» Find the discriminant for the quadratic equation represented by $p x^{2} + \sqrt{p q} x + q = 0$ and determine the nature of roots. (p and q have same sign)

Discussion

2733.	In the given figure, O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If ∠ TPQ = 70o, find ∠ TRQ.
Answer» In the given figure, O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If $∠$ TPQ = $70^{o}$ , find $∠$ TRQ.

Discussion

2734.	Find the median of the following data. Class interval0−100100−200200−300300−400400−500Frequency7111598
Answer» Find the median of the following data. $\begin{matrix} C l a s s i n t e r v a l & 0 - 100 & 100 - 200 & 200 - 300 & 300 - 400 & 400 - 500 F r e q u e n c y & 7 & 11 & 15 & 9 & 8 \end{matrix}$

2734.

Find the median of the following data. Class interval0−100100−200200−300300−400400−500Frequency7111598

Answer»

Find the median of the following data.

$\begin{matrix} C l a s s i n t e r v a l & 0 - 100 & 100 - 200 & 200 - 300 & 300 - 400 & 400 - 500 F r e q u e n c y & 7 & 11 & 15 & 9 & 8 \end{matrix}$

Discussion

2735.	The value of the middle term of the A.P. –11, –7, –3, ...., 49, 53 is ________.
Answer» The value of the middle term of the A.P. –11, –7, –3, ...., 49, 53 is ________.

Discussion

2736.	A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.
Answer» A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.

Discussion

2737.	If A = B = 60°, verify that(i) cos (A − B) = cos A cos B + sin A sin B(ii) sin (A − B) = sin A cos B − cos A sin B(iii) tan A-B=tan A-tan B1+tan A tan B
Answer» If A = B = 60°, verify that (i) cos (A − B) = cos A cos B + sin A sin B (ii) sin (A − B) = sin A cos B − cos A sin B (iii) $\tan (A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$

Discussion

2738.	If the sides of a triangle are 4cm, 5cm , 6cm, then ratio of the cosine of the least and the greatest angles is
Answer» If the sides of a triangle are $4$ cm, $5$ cm , $6$ cm, then ratio of the cosine of the least and the greatest angles is

Discussion

2739.

From the following prepare Single Column Cash Book of Suresh, Chennai and post them into ledger accounts: 2018 ₹ April 1 Cash in Hand 6,400 April 3 Received Cash from Anupama 1,00,000 April 4 Paid into Bank 80,000 April 5 Received from Bhumika as commission ₹ 6,000 plus CGST and SGST 6% each April 6 Paid Wages 30,000 April 7 Withdrawn from Bank for expenses 30,000 April 8 Purchased goods from Ashok on credit of ₹ 10,000 plus CGST ans SGST 6% each April 9 Cash sales of ₹ 10,000 charged CGST and SGST 6% each April 11 Drew Cash for domestic purposes 10,000 April 12 Purchased furniture for ₹ 4,000 plus CGST and SGST 6% each April 13 Paid to Ruma 1,200 April 14 Paid to Ganguly Brothers for office fan ₹ 1,500 plus CGST and SGST 6% each April 15 Paid own life insurance premium from office cash 800 April 16 Purchased stationery ₹ 1,000 plus CGST and SGST 6% each April 17 Paid office expenses 500 April 18 Remitted to Raman 900 April 19 Paid electricity charges 100 April 20 Received interest from Gupta &Co. 500 April 30 Deposited all cash into bank in excess of 2,000

Answer» From the following prepare Single Column Cash Book of Suresh, Chennai and post them into ledger accounts:


2018		₹
April 1	Cash in Hand	6,400
April 3	Received Cash from Anupama	1,00,000
April 4	Paid into Bank	80,000
April 5	Received from Bhumika as commission ₹ 6,000 plus CGST and SGST 6% each
April 6	Paid Wages	30,000
April 7	Withdrawn from Bank for expenses	30,000
April 8	Purchased goods from Ashok on credit of ₹ 10,000 plus CGST ans SGST 6% each
April 9	Cash sales of ₹ 10,000 charged CGST and SGST 6% each
April 11	Drew Cash for domestic purposes	10,000
April 12	Purchased furniture for ₹ 4,000 plus CGST and SGST 6% each
April 13	Paid to Ruma	1,200
April 14	Paid to Ganguly Brothers for office fan ₹ 1,500 plus CGST and SGST 6% each
April 15	Paid own life insurance premium from office cash	800
April 16	Purchased stationery ₹ 1,000 plus CGST and SGST 6% each
April 17	Paid office expenses	500
April 18	Remitted to Raman	900
April 19	Paid electricity charges	100
April 20	Received interest from Gupta &Co.	500
April 30	Deposited all cash into bank in excess of	2,000

Discussion

2740.	What is the volume of the figure given below?
Answer» What is the volume of the figure given below?

2740.

What is the volume of the figure given below?

Answer»

What is the volume of the figure given below?

Discussion

2741.	In the given figure the value of DC is ___ .
Answer» In the given figure the value of DC is ___ .

2741.

In the given figure the value of DC is ___ .

Answer»

In the given figure the value of DC is ___ .

Discussion

2742.	In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10cm. What is the length of the tangent PC?
Answer» In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10cm. What is the length of the tangent PC?

Discussion

2743.	Without using trigonometric tables, prove that:(i) cos 81° − sin 9° = 0(ii) tan 71° − cot 19° = 0(iii) cosec 60° − sec 30° = 0(iv) cot 34° − tan 56° = 0(v) sin248° + sin242° = 1(vi) cos272° + cos218° = 1
Answer» Without using trigonometric tables, prove that: (i) cos 81° − sin 9° = 0 (ii) tan 71° − cot 19° = 0 (iii) cosec 60° − sec 30° = 0 (iv) cot 34° − tan56° = 0 (v) sin²48° + sin²42° = 1 (vi) cos²72° + cos²18° = 1

Discussion

2744.	Find the sum of all even intergers between 101 and 999.
Answer» Find the sum of all even intergers between 101 and 999.

Discussion

2745.	If,show that
Answer» If, show that

Discussion

2746.	Represent 0.98333333… in a rational form. After obtaining the rational form, flip the numerator and denominator. Is it still a recurring fraction? [4 MARKS]
Answer» Represent 0.98333333… in a rational form. After obtaining the rational form, flip the numerator and denominator. Is it still a recurring fraction? [4 MARKS]

Discussion

2747.	Write the value of sin2θ cos2θ1+tan2θ1+cot2θ.
Answer» Write the value of $\sin^{2} θ \cos^{2} θ (1 + \tan^{2} θ) (1 + \cot^{2} θ)$ .

Discussion

2748.	If A,B and C are the interior angles of a triangle ABC, then the value of sin(B+C2)×cot(A+B−C2) is equal to
Answer» If A,B and C are the interior angles of a triangle ABC, then the value of $s i n (\frac{B + C}{2}) \times c o t (\frac{A + B - C}{2})$ is equal to

Discussion

2749.	In ∆ABC, D and E are points on sides AB and AC respectively such that AD ✕ EC = AE ✕ DB. Prove that DE \|\| BC.
Answer» In ∆ABC, D and E are points on sides AB and AC respectively such that AD ✕ EC = AE ✕ DB. Prove that DE \|\| BC.

Discussion

2750.	If α and β are the zeros of the quadratic polynomial 2x² + 5x + 2, then find the value of α4+β4
Answer» If $α$ and $β$ are the zeros of the quadratic polynomial 2x² + 5x + 2, then find the value of $α^{4} + β^{4}$

Discussion

Explore topic-wise InterviewSolutions in .

s =(3t3+7t2+14t+8)m t=1s on the objrct axclaration is. 1. 10m /s 2. 32m/s 3. 23m/s 4. 16 m/

Question 4Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.

What is the curved surface area of a cone of base diameter 30 centimetres and height 40 centimetres?

Which of these methods gives the highest value of mean?

Prove the following trigonometric identities.tan2θ cos2θ = 1 − cos2θ

Solve XCIV - XLVII

Find the side (in cm) of a cube whose surface area is 294 cm2.7

The polynomial x4 - 2x3 + 3x2 - ax + b when divided by (x+1) and (x-1) gives remainders 19 and 5 respectively. Find the remainder when the polynomial is divided by (x-3).

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using similarity criterion for two triangles, show that OAOC=OBOD.

In the two similar triangles, __ and BC are the hypotenuse of the larger and smaller triangles respectively.

If the mean of the following frequency distribution is 188, find the missing frequencies x and y, if the sum of all frequencies is 100. Class0–8080–160160–240240–320320–400Frequency2025xy10

If 3cotθ=4, then write the value of 2cosθ+sinθ4cosθ-sinθ.

How to express all T Ratios in terms of Sin A

a and b are two co-primes. Which of the following is/are true?(a) LCM (a, b) = a × b(b) HCF (a, b) = 1(c) Both (a) and (b)(d) Neither (a) nor (b)

value of 1/4pieEpcillumnot

13. Find the value of sin150, cos150, tan150, cosec150, sec150, cot150.

36.Find the area of the circle with positive x–axis & x^2+y^2=a^2.

In the given figure if AB = 5cm and BC = 12 cm then the radius of the circle is ___

What number should be added to 3x3−5x2+6x so that when resulting polynomial is divided by x - 3, the remainder is 8

The outer circumference of a circular race-track is 528m . The track is everywhere 14m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre . Use π=227

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

A shopkeeper sells an article at its marked price of ₹ 7500 and charges sales-tax at the rate of 12% from the customer. If the shopkeeper pays a VAT of ₹ 180, calculate the price inclusive of tax paid by the shopkeeper.

A binomial is a polynomial with __terms

If [0, 1], then sin–1x + cot–1x + cos–1x + tan–1x is equal to

The length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre is = ___ cm.

An army contingent of 616 members is to march behnind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Length of the altitude on the hypotenuse of a right angled triangle with area A cm2 and one of the sides equal to b cm is __ cm.

Question 13 (i)A dice is thrown once. Find the probability of getting a prime number.

Find the area of the major sector of a circle with radius 42 cm and of angle 30°.(Use π = 227 5082

Q. Find the 7th term of an AP whose sum of n terms is 3n^2+5n.Q. If the sum of the first p, q and r terms of an AP are x, y and z respectively, then prove that x/p (q-r) + y/q (r-p) + z/r (p-q) = 0.

In figure below P, Q, R are the points where the incircle of ΔABC touches the sides. Find ∠AQR.

Find the discriminant for the quadratic equation represented by px2+√pqx+q=0 and determine the nature of roots. (p and q have same sign)

In the given figure, O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If ∠ TPQ = 70o, find ∠ TRQ.

Find the median of the following data. Class interval0−100100−200200−300300−400400−500Frequency7111598

The value of the middle term of the A.P. –11, –7, –3, ...., 49, 53 is ________.

A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.

If A = B = 60°, verify that(i) cos (A − B) = cos A cos B + sin A sin B(ii) sin (A − B) = sin A cos B − cos A sin B(iii) tan A-B=tan A-tan B1+tan A tan B

If the sides of a triangle are 4cm, 5cm , 6cm, then ratio of the cosine of the least and the greatest angles is

What is the volume of the figure given below?

In the given figure the value of DC is ___ .

In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10cm. What is the length of the tangent PC?

Without using trigonometric tables, prove that:(i) cos 81° − sin 9° = 0(ii) tan 71° − cot 19° = 0(iii) cosec 60° − sec 30° = 0(iv) cot 34° − tan 56° = 0(v) sin248° + sin242° = 1(vi) cos272° + cos218° = 1

Find the sum of all even intergers between 101 and 999.

If,show that

Represent 0.98333333… in a rational form. After obtaining the rational form, flip the numerator and denominator. Is it still a recurring fraction? [4 MARKS]

Write the value of sin2θ cos2θ1+tan2θ1+cot2θ.

If A,B and C are the interior angles of a triangle ABC, then the value of sin(B+C2)×cot(A+B−C2) is equal to

In ∆ABC, D and E are points on sides AB and AC respectively such that AD ✕ EC = AE ✕ DB. Prove that DE || BC.

If α and β are the zeros of the quadratic polynomial 2x² + 5x + 2, then find the value of α4+β4