32581 + Interview Questions in Mathematics Page 85 InterviewSolution

4201.	Trapizium PQRS PQ\\RS PQ=2RS. PQandRS intersects at O areaof triangle POQ=64 cm. Find area of triangle SOR
Answer» Trapizium PQRS PQ\\RS PQ=2RS. PQandRS intersects at O areaof triangle POQ=64 cm. Find area of triangle SOR

Discussion

4202.	A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a plateform of 22 m by 14 m. Find the height of the plateform.
Answer» A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a plateform of 22 m by 14 m. Find the height of the plateform.

Discussion

4203.	Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
Answer» Find the sum of the first 25 terms of an A.P. whose nth term is given by a_n = 2 − 3n.

Discussion

4204.	Choose the correct answer in each of the following questions:The sum of first n terms of an AP is (5n − n2). The nth term of the AP is (a) (5 − 2n) (b) (6 − 2n) (c) (2n − 5) (d) (2n − 6)
Answer» Choose the correct answer in each of the following questions: The sum of first n terms of an AP is (5n − n²). The nth term of the AP is (a) (5 − 2n) (b) (6 − 2n) (c) (2n − 5) (d) (2n − 6)

Discussion

4205.	A dividend of 13 % was declared on ₹ 100 shares selling at a certain price. If the rate of return is 6.5 % ,calculate (i) the market value of the shares (ii) the amount to be invested to obtain an annual dividend of ₹ 3900
Answer» A dividend of 13 % was declared on ₹ 100 shares selling at a certain price. If the rate of return is 6.5 % ,calculate (i) the market value of the shares (ii) the amount to be invested to obtain an annual dividend of ₹ 3900

4205.

A dividend of 13 % was declared on ₹ 100 shares selling at a certain price. If the rate of return is 6.5 % ,calculate (i) the market value of the shares (ii) the amount to be invested to obtain an annual dividend of ₹ 3900

Answer»

A dividend of 13 % was declared on ₹ 100 shares selling at a certain price. If the rate of return is 6.5 % ,calculate

(i) the market value of the shares

(ii) the amount to be invested to obtain an annual dividend of ₹ 3900

Discussion

4206.	The empirical relation between mean, mode and median is(a) Mode = 3 Median − 2 Mean(b) Mode = 2 Median − 3 Mean(c) Median = 3 Mode − 2 Mean(d) Mean = 3 Median − 2 Mode
Answer» The empirical relation between mean, mode and median is (a) Mode = 3 Median − 2 Mean (b) Mode = 2 Median − 3 Mean (c) Median = 3 Mode − 2 Mean (d) Mean = 3 Median − 2 Mode

Discussion

4207.	\|2x - 1\| + \|x - 2\| >= 5 Solve for x
Answer» \|2x - 1\| + \|x - 2\| >= 5 Solve for x

Discussion

4208.	The following observations are arranged in ascending order. The median of the data is 25. Find the value of x. 17,x,24,x+7,35,36,46
Answer» The following observations are arranged in ascending order. The median of the data is $25.$ Find the value of $x .$ $17, x, 24, x + 7, 35, 36, 46$

4208.

The following observations are arranged in ascending order. The median of the data is 25. Find the value of x. 17,x,24,x+7,35,36,46

Answer»

The following observations are arranged in ascending order. The median of the data is $25.$ Find the value of $x .$

$17, x, 24, x + 7, 35, 36, 46$

Discussion

4209.	In the given frequency distribution, which is/are the median term(s)?Age in yearsNumber of people15316817101810195204
Answer» In the given frequency distribution, which is/are the median term(s)? $\begin{matrix} A g e i n y e a r s & N u m b e r o f p e o p l e 15 & 3 16 & 8 17 & 10 18 & 10 19 & 5 20 & 4 \end{matrix}$

Discussion

4210.	Question 18Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?
Answer» Question 18 Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?

Discussion

4211.	Find the missing operation for the arithmetical expression. 39−(6×5)
Answer» Find the missing operation for the arithmetical expression. $39 - (6 \times 5)$

Discussion

4212.	In a class of 35, students are numbered from 1 to 35. The ratio of boys and girls is 4 : 3. The roll numbers of students begin with boys and end with girls. Find the probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number.
Answer» In a class of 35, students are numbered from 1 to 35. The ratio of boys and girls is 4 : 3. The roll numbers of students begin with boys and end with girls. Find the probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number.

Discussion

4213.	In a right angle triangle ΔABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of ΔABD and ΔBCD?
Answer» In a right angle triangle $Δ A B C$ , a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of $Δ A B D$ and $Δ B C D$ ?

Discussion

4214.	What is the surface are of a pyramid with a square base length of 3 cm and a slant height of 4 cm?
Answer» What is the surface are of a pyramid with a square base length of 3 cm and a slant height of 4 cm?

Discussion

4215.	The angle between the bisectors of the two acute angles of a right angled triangle is:
Answer» The angle between the bisectors of the two acute angles of a right angled triangle is:

Discussion

4216.	Pair of linear equations x + 2y + 5 = 0 and 3x + 6y -1 = 0 have
Answer» Pair of linear equations x + 2y + 5 = 0 and 3x + 6y -1 = 0 have

Discussion

4217.	18. Find the indicated term an=4n-3;a17,a24
Answer» 18. Find the indicated term an=4n-3;a17,a24

Discussion

4218.	Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.
Answer» Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.

4218.

Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.

Answer»

Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.

Discussion

4219.	Question 8Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12.
Answer» Question 8 Find the $20^{t h}$ term of the AP whose $7^{t h}$ term is 24 less than the $11^{t h}$ term, first term being 12.

Discussion

4220.	Show that(I) tan 48° tan 23° tan 42° tan 67° = 1(II)cos 38° cos 52° − sin 38° sin 52° = 0
Answer» Show that (I) tan 48° tan 23° tan 42° tan 67° = 1 (II)cos 38° cos 52° − sin 38° sin 52° = 0

4220.

Show that(I) tan 48° tan 23° tan 42° tan 67° = 1(II)cos 38° cos 52° − sin 38° sin 52° = 0

Answer»

Show that

(I) tan 48° tan 23° tan 42° tan 67° = 1

(II)cos 38° cos 52° − sin 38° sin 52° = 0

Discussion

4221.	In the given figure, AB = 15 cm, BC = 20 cm and CD = 7 cm. If ∠ABC = ∠ADC=90∘, then AD =____________cm
Answer» In the given figure, AB = 15 cm, BC = 20 cm and CD = 7 cm. If $∠ A B C$ = $∠ A D C = 90^{\circ}$ , then AD =____________cm

4221.

In the given figure, AB = 15 cm, BC = 20 cm and CD = 7 cm. If ∠ABC = ∠ADC=90∘, then AD =____________cm

Answer»

In the given figure, AB = 15 cm, BC = 20 cm and CD = 7 cm. If $∠ A B C$ = $∠ A D C = 90^{\circ}$ , then AD =____________cm

Discussion

4222.	If [322−3][xy]=[15], then x+y is equal to
Answer» If $[\begin{matrix} 3 & 2 2 & - 3 \end{matrix}] [\begin{matrix} x y \end{matrix}] = [\begin{matrix} 15 \end{matrix}],$ then $x + y$ is equal to

Discussion

4223.	If the focus and vertex of the parabola are (p,0) and (q,0), respectively, then its equations when p>q and q>p are: If the focus and vertex of the parabola are (0,p) and (0,q), respectively, then its equations when p>q and q>p are
Answer» If the focus and vertex of the parabola are (p,0) and (q,0), respectively, then its equations when p>q and q>p are: If the focus and vertex of the parabola are (0,p) and (0,q), respectively, then its equations when p>q and q>p are

Discussion

4224.	From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.
Answer» From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.

Discussion

4225.	The following figure represents a __.
Answer» The following figure represents a __.

4225.

The following figure represents a __.

Answer»

The following figure represents a __.

Discussion

4226.	A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied into a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel. [CBSE 2012]
Answer» A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied into a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel. [CBSE 2012]

Discussion

4227.	A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and minor arc respectively .
Answer» A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and minor arc respectively .

Discussion

4228.	If x=4√6√2+√3. find the value of x+2√2x−2√2+x+2√3x−2√3, using the properties of proportion.
Answer» If $x = \frac{4 \sqrt{6}}{\sqrt{2} + \sqrt{3}}$ . find the value of $\frac{x + 2 \sqrt{2}}{x - 2 \sqrt{2}} + \frac{x + 2 \sqrt{3}}{x - 2 \sqrt{3}}$ , using the properties of proportion.

Discussion

4229.	On dividing 55390 by 299, the remainder is 75. Find the quotient using division algorithm.
Answer» On dividing 55390 by 299, the remainder is 75. Find the quotient using division algorithm.

Discussion

4230.	If x1, x2, x3, are the roots of the cubic equation x³ + 2x + 6 = 0, prove that S7 = 2(S4 - S6). [Sn = (x1)^n + (x2)^n + (x3)^n]
Answer» If x1, x2, x3, are the roots of the cubic equation x³ + 2x + 6 = 0, prove that S7 = 2(S4 - S6). [Sn = (x1)^n + (x2)^n + (x3)^n]

Discussion

4231.	If the number 1.2.22.23.24...........220.3.32.33.34........310is written in power of '6' then the highestpower of '6' is _____.
Answer» $If the number {1.2.2}^{2} {.2}^{3} {.2}^{4} . . . . . . . . . . {.2}^{20} . {3.3}^{2} {.3}^{3} {.3}^{4} . . . . . . . {.3}^{10}$ $is written in power of '6' then the highest$ $power of '6' is _____.$

Discussion

4232.	why remainder is always less than divisor ? prove it using euclids division lemma.
Answer» why remainder is always less than divisor ? prove it using euclids division lemma.

Discussion

4233.	write the first 5 terms of the sequence whose nth term is n-2/3
Answer» write the first 5 terms of the sequence whose nth term is n-2/3

Discussion

4234.	Six bells commence tolling together and toll at intervals of 2,4,6,8,10,12 min. respectively. In 30 hours,how many times do they toll together. Please explain every step..
Answer» Six bells commence tolling together and toll at intervals of 2,4,6,8,10,12 min. respectively. In 30 hours,how many times do they toll together. Please explain every step..

Discussion

4235.	What is the H.C.F of x2+2x−8,x3−4x2+4x,x2−4
Answer» What is the H.C.F of $x^{2} + 2 x - 8, x^{3} - 4 x^{2} + 4 x, x^{2} - 4$

Discussion

4236.	Solve each of the following quadratic equations:x2-4ax-b2+4a2=0 [CBSE 2012]
Answer» Solve each of the following quadratic equations: $x^{2} - 4 a x - b^{2} + 4 a^{2} = 0$ [CBSE 2012]

Discussion

4237.	43. Find the inclination of the line \sqrt{}3x-3y+6=0.
Answer» 43. Find the inclination of the line \sqrt{}3x-3y+6=0.

Discussion

4238.	Given below are the sides of a triangle. In which cases are the triangles right angled?(i) 8, 15, 17 (ii) 9, 10, 14 (iii) 7, 24, 25
Answer» Given below are the sides of a triangle. In which cases are the triangles right angled? (i) 8, 15, 17 (ii) 9, 10, 14 (iii) 7, 24, 25

4238.

Given below are the sides of a triangle. In which cases are the triangles right angled?(i) 8, 15, 17 (ii) 9, 10, 14 (iii) 7, 24, 25

Answer»

Given below are the sides of a triangle. In which cases are the triangles right angled?

(i) 8, 15, 17 (ii) 9, 10, 14 (iii) 7, 24, 25

Discussion

4239.	Find the number of balls each of radius 1cm . Can be made from a solid sphere of lead of radius 6cm
Answer» Find the number of balls each of radius 1cm . Can be made from a solid sphere of lead of radius 6cm

Discussion

4240.	Which term of the AP 53, 48, 43,....................... is the first negative term.?
Answer» Which term of the AP 53, 48, 43,....................... is the first negative term.?

Discussion

4241.	Question 10In the figure, if ∠AOB=90∘ and ∠ABC=30∘, then ∠CAO is equal to(A) 30∘ (B) 45∘ (C) 90∘ (D) 60∘
Answer» Question 10 In the figure, if $∠ A O B = 90^{\circ} a n d ∠ A B C = 30^{\circ}, t h e n ∠ C A O$ is equal to (A) $30^{\circ}$ (B) $45^{\circ}$ (C) $90^{\circ}$ (D) $60^{\circ}$

Discussion

4242.	In the given right angled isosceles triangle ABC, if AC = 10 cm then determine the area of triangle in square cm. 25
Answer» In the given right angled isosceles triangle ABC, if AC = 10 cm then determine the area of triangle in square cm. 25

Discussion

4243.	If the sum of the zeros of the quadratic polynomial f(x) = kx2 − 3x + 5 is 1, write the value of k.
Answer» If the sum of the zeros of the quadratic polynomial f(x) = kx² − 3x + 5 is 1, write the value of k.

Discussion

4244.	Choose the correct answer in each of the following questions:The sum of first 40 positive integers divisible by 6 is [CBSE 2014](a) 2460 (b) 3640 (c) 4920 (d) 4860
Answer» Choose the correct answer in each of the following questions: The sum of first 40 positive integers divisible by 6 is [CBSE 2014] (a) 2460 (b) 3640 (c) 4920 (d) 4860

Discussion

4245.	Very-Short and Short-Answer QuestionsIf the numbers (2n − 1), (3n + 2) and (6n − 1) are in AP, find the value of n and the numbers. [CBSE 2013C]
Answer» Very-Short and Short-Answer Questions If the numbers (2n − 1), (3n + 2) and (6n − 1) are in AP, find the value of n and the numbers. [CBSE 2013C]

Discussion

4246.	If r1=9 cm and r2=5 cm, then find the area of the shaded region. (Use π=227)176
Answer» If $r_{1} = 9 c m$ and $r_{2} = 5 c m$ , then find the area of the shaded region. (Use $π = \frac{22}{7}$ ) 176

Discussion

4247.	What are the arguments put forward by Decius Brutus to convince Caesar to go to the Capitol?
Answer» What are the arguments put forward by Decius Brutus to convince Caesar to go to the Capitol?

Discussion

4248.	Find one of the roots of the quadratic equation 2x2−7x+3=0 by the method of completion of the square. Also, what is the equation obtained after completion of the square?
Answer» Find one of the roots of the quadratic equation ${2 x}^{2} - 7 x + 3 = 0$ by the method of completion of the square. Also, what is the equation obtained after completion of the square?

Discussion

4249.	Question 4In the given figure, is PQRS is a parallelogram and ABIIPS, then prove that OCIISR.
Answer» Question 4 In the given figure, is PQRS is a parallelogram and ABIIPS, then prove that OCIISR.

Discussion

4250.	Consider the sequence of numbers2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, ..Identify 5th,8th & 12th term in the above sequence.
Answer» Consider the sequence of numbers 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, .. Identify $5^{t h}$ , $8^{t h}$ & $12^{t h}$ term in the above sequence.

4250.

Consider the sequence of numbers2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, ..Identify 5th,8th & 12th term in the above sequence.

Answer»

Consider the sequence of numbers

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, ..

Identify $5^{t h}$ , $8^{t h}$ & $12^{t h}$ term in the above sequence.

Discussion

Explore topic-wise InterviewSolutions in .

Trapizium PQRS PQ\\RS PQ=2RS. PQandRS intersects at O areaof triangle POQ=64 cm. Find area of triangle SOR

A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a plateform of 22 m by 14 m. Find the height of the plateform.

Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.

Choose the correct answer in each of the following questions:The sum of first n terms of an AP is (5n − n2). The nth term of the AP is (a) (5 − 2n) (b) (6 − 2n) (c) (2n − 5) (d) (2n − 6)

A dividend of 13 % was declared on ₹ 100 shares selling at a certain price. If the rate of return is 6.5 % ,calculate (i) the market value of the shares (ii) the amount to be invested to obtain an annual dividend of ₹ 3900

The empirical relation between mean, mode and median is(a) Mode = 3 Median − 2 Mean(b) Mode = 2 Median − 3 Mean(c) Median = 3 Mode − 2 Mean(d) Mean = 3 Median − 2 Mode

|2x - 1| + |x - 2| >= 5 Solve for x

The following observations are arranged in ascending order. The median of the data is 25. Find the value of x. 17,x,24,x+7,35,36,46

In the given frequency distribution, which is/are the median term(s)?Age in yearsNumber of people15316817101810195204

Question 18Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?

Find the missing operation for the arithmetical expression. 39−(6×5)

In a right angle triangle ΔABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of ΔABD and ΔBCD?

What is the surface are of a pyramid with a square base length of 3 cm and a slant height of 4 cm?

The angle between the bisectors of the two acute angles of a right angled triangle is:

Pair of linear equations x + 2y + 5 = 0 and 3x + 6y -1 = 0 have

18. Find the indicated term an=4n-3;a17,a24

Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.

Question 8Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12.

Show that(I) tan 48° tan 23° tan 42° tan 67° = 1(II)cos 38° cos 52° − sin 38° sin 52° = 0

In the given figure, AB = 15 cm, BC = 20 cm and CD = 7 cm. If ∠ABC = ∠ADC=90∘, then AD =____________cm

If [322−3][xy]=[15], then x+y is equal to

If the focus and vertex of the parabola are (p,0) and (q,0), respectively, then its equations when p>q and q>p are: If the focus and vertex of the parabola are (0,p) and (0,q), respectively, then its equations when p>q and q>p are

From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.

The following figure represents a __.

A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied into a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel. [CBSE 2012]

A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and minor arc respectively .

If x=4√6√2+√3. find the value of x+2√2x−2√2+x+2√3x−2√3, using the properties of proportion.

On dividing 55390 by 299, the remainder is 75. Find the quotient using division algorithm.

If x1, x2, x3, are the roots of the cubic equation x³ + 2x + 6 = 0, prove that S7 = 2(S4 - S6). [Sn = (x1)^n + (x2)^n + (x3)^n]

If the number 1.2.22.23.24...........220.3.32.33.34........310is written in power of '6' then the highestpower of '6' is _____.

why remainder is always less than divisor ? prove it using euclids division lemma.

write the first 5 terms of the sequence whose nth term is n-2/3

Six bells commence tolling together and toll at intervals of 2,4,6,8,10,12 min. respectively. In 30 hours,how many times do they toll together. Please explain every step..

What is the H.C.F of x2+2x−8,x3−4x2+4x,x2−4

Solve each of the following quadratic equations:x2-4ax-b2+4a2=0 [CBSE 2012]

43. Find the inclination of the line \sqrt{}3x-3y+6=0.

Given below are the sides of a triangle. In which cases are the triangles right angled?(i) 8, 15, 17 (ii) 9, 10, 14 (iii) 7, 24, 25

Find the number of balls each of radius 1cm . Can be made from a solid sphere of lead of radius 6cm

Which term of the AP 53, 48, 43,....................... is the first negative term.?

Question 10In the figure, if ∠AOB=90∘ and ∠ABC=30∘, then ∠CAO is equal to(A) 30∘ (B) 45∘ (C) 90∘ (D) 60∘

In the given right angled isosceles triangle ABC, if AC = 10 cm then determine the area of triangle in square cm. 25

If the sum of the zeros of the quadratic polynomial f(x) = kx2 − 3x + 5 is 1, write the value of k.

Choose the correct answer in each of the following questions:The sum of first 40 positive integers divisible by 6 is [CBSE 2014](a) 2460 (b) 3640 (c) 4920 (d) 4860

Very-Short and Short-Answer QuestionsIf the numbers (2n − 1), (3n + 2) and (6n − 1) are in AP, find the value of n and the numbers. [CBSE 2013C]

If r1=9 cm and r2=5 cm, then find the area of the shaded region. (Use π=227)176

What are the arguments put forward by Decius Brutus to convince Caesar to go to the Capitol?

Find one of the roots of the quadratic equation 2x2−7x+3=0 by the method of completion of the square. Also, what is the equation obtained after completion of the square?

Question 4In the given figure, is PQRS is a parallelogram and ABIIPS, then prove that OCIISR.

Consider the sequence of numbers2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, ..Identify 5th,8th &amp; 12th term in the above sequence.

Consider the sequence of numbers2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, ..Identify 5th,8th & 12th term in the above sequence.