32581 + Interview Questions in Mathematics Page 66 InterviewSolution

3251.	Write the value of 1-sin2θsec2θ.
Answer» Write the value of $(1 - \sin^{2} θ) \sec^{2} θ$ .

Discussion

3252.	Draw an angle of measure 45∘ and bisect it.
Answer» Draw an angle of measure $45^{\circ}$ and bisect it.

Discussion

3253.

The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70. Class 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40 Frequency 12 a 12 15 b 6 6 4

Answer» The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70.

Class	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	12	a	12	15	b	6	6	4

Discussion

3254.	Three major powers that emerged in Southern India in the 7th century AD were: I.Cheras II.Cholas III.Chalukyas IV.Pallavas V.Pandyas
Answer» Three major powers that emerged in Southern India in the $7^{t h}$ century AD were: I.Cheras II.Cholas III.Chalukyas IV.Pallavas V.Pandyas

Discussion

3255.	A children’s park is of circular shape with radius 21 m. What is the length of fencing to be done at the boundary of the park?
Answer» A children’s park is of circular shape with radius 21 m. What is the length of fencing to be done at the boundary of the park?

Discussion

3256.	Three circle touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm
Answer» Three circle touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm

Discussion

3257.	Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. The area of aluminium sheet required to make the cone is (Use π=3.14)
Answer» Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are $10$ cm and $7$ cm respectively. The area of aluminium sheet required to make the cone is (Use $π = 3.14$ )

Discussion

3258.	The image of the line x−12=y+1−1=z−34 on the plane x+2y+z=6 is
Answer» The image of the line $\frac{x - 1}{2} = \frac{y + 1}{- 1} = \frac{z - 3}{4}$ on the plane $x + 2 y + z = 6$ is

Discussion

3259.	for A=460 degrees, show that 2sinA/2= -√(1+sin A)-√(1-sin A)
Answer» for A=460 degrees, show that 2sinA/2= -√(1+sin A)-√(1-sin A)

Discussion

3260.	tan 30° cosec 60° + tan 60° sec 30°
Answer» tan 30° cosec 60° + tan 60° sec 30°

Discussion

3261.	Mark the correct alternative in the following question:The initial count of bacteria is x and it becomes y times every day. The total count of bacteria after one week is(a) 7xy (b) x + 7y (c) xy7 (d) xy6
Answer» Mark the correct alternative in the following question: The initial count of bacteria is x and it becomes y times every day. The total count of bacteria after one week is (a) 7xy (b) x + 7y (c) xy⁷ (d) xy⁶

Discussion

3262.	There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is
Answer» There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

Discussion

3263.	5 chairs and 4 tables together cost ₹ 5,600, while 4 chairs and 3 tables together cost₹ 4,340. Find the cost of a chair and that of a table.
Answer» 5 chairs and 4 tables together cost ₹ 5,600, while 4 chairs and 3 tables together cost ₹ 4,340. Find the cost of a chair and that of a table.

Discussion

3264.	In an equilateral triangle ABC, D is a point on side BC such that BD = BC. Prove that 9 AD2 = 7 AB2.
Answer» In an equilateral triangle ABC, D is a point on side BC such that BD = BC. Prove that 9 AD² = 7 AB².

Discussion

3265.	The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.
Answer» The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

Discussion

3266.	The area of the region formed by the points P(x,y) where x≥4,y≥5, which are closer to the point (4,5) than to the line x=6, is
Answer» The area of the region formed by the points $P (x, y)$ where $x \geq 4, y \geq 5$ , which are closer to the point $(4, 5)$ than to the line $x = 6$ , is

Discussion

3267.	If 1 is a zero of the polynomial p(x) = ax2 − 3(a − 1) x − 1, then find the value of a.
Answer» If 1 is a zero of the polynomial p(x) = ax² − 3(a − 1) x − 1, then find the value of a.

Discussion

3268.	If the adjoint of a 3×3 matrix A is ⎡⎢⎣144217113⎤⎥⎦, then the possible value(s) of the determinant of A is(are)
Answer» If the adjoint of a $3 \times 3$ matrix $A$ is $⎡ ⎢ ⎣ \begin{matrix} 1 & 4 & 4 2 & 1 & 7 1 & 1 & 3 \end{matrix} ⎤ ⎥ ⎦$ , then the possible value(s) of the determinant of $A$ is(are)

Discussion

3269.	In the given figure, DE∥BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x
Answer» In the given figure, DE∥BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x

Discussion

3270.	If the diagram in Fig. 2.22 shows the graph of the polynomial f(x) = ax2 + bx + c, then(a) a > 0, b < 0 and c > 0(b) a < 0, b < 0 and c < 0(c) a < 0, b > 0 and c > 0(d) a < 0, b > 0 and c < 0
Answer» If the diagram in Fig. 2.22 shows the graph of the polynomial f(x) = ax² + bx + c, then (a) a > 0, b < 0 and c > 0 (b) a < 0, b < 0 and c < 0 (c) a < 0, b > 0 and c > 0 (d) a < 0, b > 0 and c < 0

Discussion

3271.	Study the adjoining figure. Write the ratio in relation to basic proportionality theorem and it corollary, in terms of a, b, c and d.
Answer» Study the adjoining figure. Write the ratio in relation to basic proportionality theorem and it corollary, in terms of a, b, c and d.

3271.

Study the adjoining figure. Write the ratio in relation to basic proportionality theorem and it corollary, in terms of a, b, c and d.

Answer»

Study the adjoining figure. Write the ratio in relation to basic proportionality theorem and it corollary, in terms of a, b, c and d.

Discussion

3272.	The areas of two similar triangles Δ ABC and Δ DEF are 144 cm2 and 81 cm2 respectively. If the longest side of larger Δ ABC be 36 cm, then the longest side of the smaller triangle Δ DEF is(a) 20 cm(b) 26 cm(c) 27 cm(d) 30 cm
Answer» The areas of two similar triangles $Δ A B C$ and $Δ D E F$ are $144 c m^{2}$ and $81 c m^{2}$ respectively. If the longest side of larger $Δ A B C$ be $36 c m$ , then the longest side of the smaller triangle $Δ D E F$ is (a) $20 c m$ (b) $26 c m$ (c) $27 c m$ (d) $30 c m$

Discussion

3273.

Following is the summary of cash transactions of the Royal Club for the year ended 31st March, 2018: RECEIPTS AND PAYMENTS ACCOUNT Dr. Cr. Receipts ₹ Payments ₹ To Balance b/d (cash) 31,900 By Rent 16,800 To Entrance Fees 25,500 By Wages 24,500 To Subscriptions 1,60,000 By Electricity Charges 7,200 To Donations 16,500 By Honorarium 43,500 To Life Membership Fees 25,000 By Books 21,300 To Profit on Entertainment 5,600 By Office Expenses 45,000 By 3% Fixed Deposit 80,000 (1st October, 2017) By Balance c/d (Cash at Bank) 24,200 By Balance c/d (Cash in Hand) 2,000 2,64,500 2,64,500 In the beginning of the year , the club possessed Books of ₹ 2,00,000 and Furniture of ₹ 85,000. Subscriptions in arrears in the beginning of the year amounted to ₹ 3,500 and at the end of the year ₹ 4,500 and six months Rent ₹ 6,000 was due both in the beginning of the year and at the end of the year.Prepare Income and Expenditure Account of the club for the year ended 31st March , 2018 and ist Balance Sheet as at that date after writing off ₹ 5,000 and ₹ 11,300 on Furniture and books respectively.

Answer» Following is the summary of cash transactions of the Royal Club for the year ended 31st March, 2018:

RECEIPTS AND PAYMENTS ACCOUNT
Dr.				Cr.
Receipts	₹	Payments	₹
To Balance b/d (cash)	31,900	By Rent	16,800
To Entrance Fees	25,500	By Wages	24,500
To Subscriptions	1,60,000	By Electricity Charges	7,200
To Donations	16,500	By Honorarium	43,500
To Life Membership Fees	25,000	By Books	21,300
To Profit on Entertainment	5,600	By Office Expenses	45,000
		By 3% Fixed Deposit	80,000
		(1st October, 2017)
		By Balance c/d (Cash at Bank)	24,200
		By Balance c/d (Cash in Hand)	2,000

	2,64,500		2,64,500

In the beginning of the year , the club possessed Books of ₹ 2,00,000 and Furniture of ₹ 85,000. Subscriptions in arrears in the beginning of the year amounted to ₹ 3,500 and at the end of the year ₹ 4,500 and six months Rent ₹ 6,000 was due both in the beginning of the year and at the end of the year.

Prepare Income and Expenditure Account of the club for the year ended 31st March , 2018 and ist Balance Sheet as at that date after writing off ₹ 5,000 and ₹ 11,300 on Furniture and books respectively.

Discussion

3274.	Question 1 (i)Find the sum of the following APs.(i) 2, 7, 12,…., to 10 terms
Answer» Question 1 (i) Find the sum of the following APs. (i) 2, 7, 12,…., to 10 terms

Discussion

3275.	If ∆ABC ~ ∆PQR, A (∆ABC) = 80, A (∆PQR) = 125, then fill in the blanks.A∆ABCA∆. . . .=80125 ∴ ABPQ=
Answer» If ∆ABC ~ ∆PQR, A (∆ABC) = 80, A (∆PQR) = 125, then fill in the blanks. $\frac{A (∆ ABC)}{A (∆ . . . .)} = \frac{80}{125} ∴ \frac{AB}{PQ} = \frac{}{}$

Discussion

3276.	The water level in a cylinder raises by 16 cm when three spheres are dropped in it. If the ratio of the radii of the spheres is 1:2:3 and the radius of the cylinder is 6 cm, what is the volume of the smallest sphere in cm3?
Answer» The water level in a cylinder raises by 16 cm when three spheres are dropped in it. If the ratio of the radii of the spheres is 1:2:3 and the radius of the cylinder is 6 cm, what is the volume of the smallest sphere in $c m^{3}$ ?

Discussion

3277.	If 1 is the root of the quadratic equations ax2+5x+3=0 and bx2+6x–3=0, then which of the following is always true?
Answer» If $1$ is the root of the quadratic equations $a x^{2} + 5 x + 3 = 0$ and $b x^{2} + 6 x - 3 = 0$ , then which of the following is always true?

Discussion

3278.	While aligning a road along a hill with a ruling gradient of 4.5%, a horizontal curve of radius 150 m is encountered. The compensated gradient in percentage is________4
Answer» While aligning a road along a hill with a ruling gradient of 4.5%, a horizontal curve of radius 150 m is encountered. The compensated gradient in percentage is________ 4

Discussion

3279.	If 1176=2a3b7c, find a, b and c.
Answer» If $1176 = 2^{a} 3^{b} 7^{c}$ , find a, b and c.

Discussion

3280.	One card is drawn at random from a well shuffled deck of 52 cards. What is the probability of getting an ace?
Answer» One card is drawn at random from a well shuffled deck of 52 cards. What is the probability of getting an ace?

Discussion

3281.	If 3 tan θ=4, find the value of 4 cos θ−sin θ2 cos θ+sin θ
Answer» If 3 tan $θ$ =4, find the value of $\frac{4 c o s θ - s i n θ}{2 c o s θ + s i n θ}$

Discussion

3282.	Find a quadratic polynomial whose one zero is 8 and product of the zero is -56
Answer» Find a quadratic polynomial whose one zero is 8 and product of the zero is -56

Discussion

3283.	Determine the number of consequtive zeroes in 2³×5⁴×3⁴×7
Answer» Determine the number of consequtive zeroes in 2³×5⁴×3⁴×7

Discussion

3284.	A point P in space is such that the sum of square of its distances from x−axis, y−axis and z−axis is 9 units more than the sum of square of its distances from xy−plane, yz−plane and zx−plane. Then the distance( in units) of point P from origin is equal to
Answer» A point $P$ in space is such that the sum of square of its distances from $x -$ axis, $y -$ axis and $z -$ axis is $9 units$ more than the sum of square of its distances from $x y -$ plane, $y z -$ plane and $z x -$ plane. Then the distance( in $units$ ) of point $P$ from origin is equal to

Discussion

3285.	A triangle has sides 5 cm, 12 cm and 13 cm. Find the length to one decimal place, of the perpendicular from the opposite vertex to the side whose length is 13 cm.
Answer» A triangle has sides 5 cm, 12 cm and 13 cm. Find the length to one decimal place, of the perpendicular from the opposite vertex to the side whose length is 13 cm.

Discussion

3286.	In the given figure, two circles (having centres O1 and O2) touch externally at point P. S1T1 and S2T2 are two tangents at points S1 and S2 respectively. If ∠O1PS1=20∘, find the measure of ∠PS2T2.
Answer» In the given figure, two circles (having centres $O_{1}$ and $O_{2}$ ) touch externally at point P. $S_{1} T_{1}$ and $S_{2} T_{2}$ are two tangents at points $S_{1}$ and $S_{2}$ respectively. If $∠ O_{1} P S_{1} = 20^{\circ}$ , find the measure of $∠ P S_{2} T_{2}$ .

Discussion

3287.	Using Cramer's Rule and Solve for the values of x and y.3x+5y=297x+3y=33.
Answer» Using Cramer's Rule and Solve for the values of x and y. $3 x + 5 y = 29$ $7 x + 3 y = 33$ .

Discussion

3288.	Write a pair of irrational numbers whose sum is irrational.
Answer» Write a pair of irrational numbers whose sum is irrational.

Discussion

3289.	In the given figure, if AC = 8 cm, DQ = 4 cm, and BP = 6 cm, find the area (cm2) of the quadrilateral ABCD. 40
Answer» In the given figure, if AC = 8 cm, DQ = 4 cm, and BP = 6 cm, find the area (cm $^{2}$ ) of the quadrilateral ABCD. 40

Discussion

3290.	Which is the side adjacent to the angle θ?
Answer» Which is the side adjacent to the angle $θ$ ?

3290.

Which is the side adjacent to the angle θ?

Answer»

Which is the side adjacent to the angle $θ$ ?

Discussion

3291.	If the distance between the points (5, -2) and (1, a) is 5, find the values of a.
Answer» If the distance between the points (5, -2) and (1, a) is 5, find the values of a.

Discussion

3292.	Question 8 (ii) The figure depicts a racing track. ADHE is a semicircular track of inner radius 30m and thickness 10m. FGBC is another semicircular track with the same inner radius and thickness as ADHE. The space between the two semicircular tracks are covered by straight tracks of length 106m and thickness 10m on either side. Calculate the area of the racing track.
Answer» Question 8 (ii) The figure depicts a racing track. ADHE is a semicircular track of inner radius 30m and thickness 10m. FGBC is another semicircular track with the same inner radius and thickness as ADHE. The space between the two semicircular tracks are covered by straight tracks of length 106m and thickness 10m on either side. Calculate the area of the racing track.

Discussion

3293.	Find the 5th term of an arithmetic sequence whose nth term is 3n - 2.
Answer» Find the 5th term of an arithmetic sequence whose nth term is 3n - 2.

Discussion

3294.	Question 3 Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Answer» Question 3 Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Discussion

3295.	In the assumed mean method, if A is the assumed mean, then deviation di is :
Answer» In the assumed mean method, if A is the assumed mean, then deviation $d_{i}$ is :

Discussion

3296.	Evaluate:(i) 3.21+2.34(ii) 0.0345+6.124(iii) 6.9+32.26
Answer» Evaluate: (i) $3.21 + 2.34$ (ii) $0.0345 + 6.124$ (iii) $6.9 + 32.26$

Discussion

3297.	The greatest four digit number which when divided by 18 and 12 leaves a remainder of 4 in each case is(a) 9976(b) 9940(c) 9904(d) 9868
Answer» The greatest four digit number which when divided by 18 and 12 leaves a remainder of 4 in each case is (a) 9976 (b) 9940 (c) 9904 (d) 9868

Discussion

3298.	All circles are ___.
Answer» All circles are ___.

Discussion

3299.

If -2 and 3 are the zeros of the quadratic polynomial x2+(a+1)x+b then (a) a= -2, b=6 (b) a= 2, b=-6 (c) a= -2, b=-6 (d) a= 2, b=6

Answer»

If -2 and 3 are the zeros of the quadratic polynomial $x^{2} + (a + 1) x + b$ then

(a) a= -2, b=6 (b) a= 2, b=-6

(c) a= -2, b=-6 (d) a= 2, b=6

Discussion

3300.	Using factor theorem, show that g(x) is a factor of p(x), whenp(x) = 2x3 + 9x2 – 11x – 30, g(x) = x + 5
Answer» Using factor theorem, show that g(x) is a factor of p(x), when p(x) = 2x³ + 9x² – 11x – 30, g(x) = x + 5

Discussion

Explore topic-wise InterviewSolutions in .

Write the value of 1-sin2θsec2θ.

Draw an angle of measure 45∘ and bisect it.

The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70. Class 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40 Frequency 12 a 12 15 b 6 6 4

Three major powers that emerged in Southern India in the 7th century AD were: I.Cheras II.Cholas III.Chalukyas IV.Pallavas V.Pandyas

A children’s park is of circular shape with radius 21 m. What is the length of fencing to be done at the boundary of the park?

Three circle touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. The area of aluminium sheet required to make the cone is (Use π=3.14)

The image of the line x−12=y+1−1=z−34 on the plane x+2y+z=6 is

for A=460 degrees, show that 2sinA/2= -√(1+sin A)-√(1-sin A)

tan 30° cosec 60° + tan 60° sec 30°

Mark the correct alternative in the following question:The initial count of bacteria is x and it becomes y times every day. The total count of bacteria after one week is(a) 7xy (b) x + 7y (c) xy7 (d) xy6

There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

5 chairs and 4 tables together cost ₹ 5,600, while 4 chairs and 3 tables together cost₹ 4,340. Find the cost of a chair and that of a table.

In an equilateral triangle ABC, D is a point on side BC such that BD = BC. Prove that 9 AD2 = 7 AB2.

The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

The area of the region formed by the points P(x,y) where x≥4,y≥5, which are closer to the point (4,5) than to the line x=6, is

If 1 is a zero of the polynomial p(x) = ax2 − 3(a − 1) x − 1, then find the value of a.

If the adjoint of a 3×3 matrix A is ⎡⎢⎣144217113⎤⎥⎦, then the possible value(s) of the determinant of A is(are)

In the given figure, DE∥BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x

If the diagram in Fig. 2.22 shows the graph of the polynomial f(x) = ax2 + bx + c, then(a) a > 0, b < 0 and c > 0(b) a < 0, b < 0 and c < 0(c) a < 0, b > 0 and c > 0(d) a < 0, b > 0 and c < 0

Study the adjoining figure. Write the ratio in relation to basic proportionality theorem and it corollary, in terms of a, b, c and d.

The areas of two similar triangles Δ ABC and Δ DEF are 144 cm2 and 81 cm2 respectively. If the longest side of larger Δ ABC be 36 cm, then the longest side of the smaller triangle Δ DEF is(a) 20 cm(b) 26 cm(c) 27 cm(d) 30 cm

Question 1 (i)Find the sum of the following APs.(i) 2, 7, 12,…., to 10 terms

If ∆ABC ~ ∆PQR, A (∆ABC) = 80, A (∆PQR) = 125, then fill in the blanks.A∆ABCA∆. . . .=80125 ∴ ABPQ=

The water level in a cylinder raises by 16 cm when three spheres are dropped in it. If the ratio of the radii of the spheres is 1:2:3 and the radius of the cylinder is 6 cm, what is the volume of the smallest sphere in cm3?

If 1 is the root of the quadratic equations ax2+5x+3=0 and bx2+6x–3=0, then which of the following is always true?

While aligning a road along a hill with a ruling gradient of 4.5%, a horizontal curve of radius 150 m is encountered. The compensated gradient in percentage is________4

If 1176=2a3b7c, find a, b and c.

One card is drawn at random from a well shuffled deck of 52 cards. What is the probability of getting an ace?

If 3 tan θ=4, find the value of 4 cos θ−sin θ2 cos θ+sin θ

Find a quadratic polynomial whose one zero is 8 and product of the zero is -56

Determine the number of consequtive zeroes in 2³×5⁴×3⁴×7

A point P in space is such that the sum of square of its distances from x−axis, y−axis and z−axis is 9 units more than the sum of square of its distances from xy−plane, yz−plane and zx−plane. Then the distance( in units) of point P from origin is equal to

A triangle has sides 5 cm, 12 cm and 13 cm. Find the length to one decimal place, of the perpendicular from the opposite vertex to the side whose length is 13 cm.

In the given figure, two circles (having centres O1 and O2) touch externally at point P. S1T1 and S2T2 are two tangents at points S1 and S2 respectively. If ∠O1PS1=20∘, find the measure of ∠PS2T2.

Using Cramer's Rule and Solve for the values of x and y.3x+5y=297x+3y=33.

Write a pair of irrational numbers whose sum is irrational.

In the given figure, if AC = 8 cm, DQ = 4 cm, and BP = 6 cm, find the area (cm2) of the quadrilateral ABCD. 40

Which is the side adjacent to the angle θ?

If the distance between the points (5, -2) and (1, a) is 5, find the values of a.

Find the 5th term of an arithmetic sequence whose nth term is 3n - 2.

Question 3 Give one example each of a binomial of degree 35, and of a monomial of degree 100.

In the assumed mean method, if A is the assumed mean, then deviation di is :

Evaluate:(i) 3.21+2.34(ii) 0.0345+6.124(iii) 6.9+32.26

The greatest four digit number which when divided by 18 and 12 leaves a remainder of 4 in each case is(a) 9976(b) 9940(c) 9904(d) 9868

All circles are ___.

If -2 and 3 are the zeros of the quadratic polynomial x2+(a+1)x+b then (a) a= -2, b=6 (b) a= 2, b=-6 (c) a= -2, b=-6 (d) a= 2, b=6

Using factor theorem, show that g(x) is a factor of p(x), whenp(x) = 2x3 + 9x2 – 11x – 30, g(x) = x + 5