24740 + Interview Questions in Mathematics Page 201 InterviewSolution

10001.	What is the factorised form of w(x + y) - z(x + y)?
Answer» What is the factorised form of w(x + y) - z(x + y)?

Discussion

10002.	When the square of a number is decreased by 15, it is equal to twice the original number. Find the possible values of the number.
Answer» When the square of a number is decreased by 15, it is equal to twice the original number. Find the possible values of the number.

Discussion

10003.	21. Write the volume of hemisphere in terms of surface area of a sphere.
Answer» 21. Write the volume of hemisphere in terms of surface area of a sphere.

Discussion

10004.	Find the value of x if x:36::8:48.
Answer» Find the value of $x$ if $x : 36 :: 8 : 48$ .

Discussion

10005.	Find the value of−163÷−43.
Answer» Find the value of $- \frac{16}{3} \div - \frac{4}{3} .$

Discussion

10006.	The value of tan(90−A)cot(90−A) is
Answer» The value of $\frac{t a n (90 - A)}{c o t (90 - A)}$ is

Discussion

10007.	In a trapezium ABCD, AB \|\| DC, AB = a cm, and DC = b cm. If M and N are the midpoints of the nonparallel sides, AD and BC respectively then find the ratio of ar(DCNM) and ar(MNBA).
Answer» In a trapezium ABCD, AB \|\| DC, AB = a cm, and DC = b cm. If M and N are the midpoints of the nonparallel sides, AD and BC respectively then find the ratio of ar(DCNM) and ar(MNBA).

Discussion

10008.	Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes is
Answer» Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes is

Discussion

10009.	The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.
Answer» The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.

Discussion

10010.	Draw a circle of radius 3.2 cm
Answer» Draw a circle of radius 3.2 cm

Discussion

10011.	Classify the following polynomials as linear, quadratic and cubic polynomial. (i) 2x2 + 3 x + 1 (ii) 5p (iii) 2y - 12 (iv) m3 + 7m2 + 52m - 7 (v) a2 (vi) 3r3
Answer» Classify the following polynomials as linear, quadratic and cubic polynomial. (i) 2x² + 3 x + 1 (ii) $5 p$ (iii) $\sqrt{2} y - \frac{1}{2}$ (iv) $m^{3} + 7 m^{2} + \frac{5}{2} m - \sqrt{7}$ (v) $a^{2}$ (vi) $3 r^{3}$

Discussion

10012.	Question 1 (ii)Evaluate :tan26∘cot64∘
Answer» Question 1 (ii) Evaluate : $\frac{t a n 26^{\circ}}{c o t 64^{\circ}}$

Discussion

10013.	In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC+∠BOD=2∠AEC. [4 MARKS]
Answer» In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that $∠ A O C + ∠ B O D = 2 ∠ A E C$ . [4 MARKS]

10013.

In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC+∠BOD=2∠AEC. [4 MARKS]

Answer»

In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that $∠ A O C + ∠ B O D = 2 ∠ A E C$ .

[4 MARKS]

Discussion

10014.	In figure, arc AB is congruent to arc AC and O is the centre of the circle. Prove that OA is the perpendicular bisector of BC. [4 MARKS]
Answer» In figure, arc AB is congruent to arc AC and O is the centre of the circle. Prove that OA is the perpendicular bisector of BC. [4 MARKS]

Discussion

10015.	Rakesh lent out Rs 8000 for 5 years at 15% per annum and borrowed Rs 6000 for 3 years at 12% per annum. How much did he gain or lose?
Answer» Rakesh lent out Rs 8000 for 5 years at 15% per annum and borrowed Rs 6000 for 3 years at 12% per annum. How much did he gain or lose?

Discussion

10016.	Factorise a−a3+b3−b is _______
Answer» Factorise $a - a^{3} + b^{3} - b$ is _______

Discussion

10017.	The three angles of a quadrilateral are 75∘, 90∘ and 75∘. What is the fouth angle?
Answer» The three angles of a quadrilateral are $75^{\circ}$ , $90^{\circ}$ and $75^{\circ}$ . What is the fouth angle?

Discussion

10018.	In the given figure, O is the centre of the sector. ∠ROQ = ∠MON = 60° . OR = 7 cm, and OM = 21 cm. Find the lengths of arc RXQ and arc MYN. ( π=227)
Answer» In the given figure, O is the centre of the sector. $∠$ ROQ = $∠$ MON = 60^° . OR = 7 cm, and OM = 21 cm. Find the lengths of arc RXQ and arc MYN. ( $π = \frac{22}{7}$ )

Discussion

10019.	In ΔPQR, S is any point on the side QR. Show that PQ + QR + RP > 2 PS
Answer» In ΔPQR, S is any point on the side QR. Show that PQ + QR + RP $>$ 2 PS

Discussion

10020.	If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be
Answer» If radius of the sphere is (5.3 $\pm$ 0.1)cm. Then percentage error in its volume will be

Discussion

10021.	A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are α and β respectively. Prove that the height of the tower is h tan αtan β−tan α
Answer» A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are $α$ and $β$ respectively. Prove that the height of the tower is $\frac{h t a n α}{t a n β - t a n α}$

Discussion

10022.	In a2x2+ax, if 'a' is constant and 'x' is a variable, this expression would become a polynomial in ___ variable(s). (Write in words)
Answer» In $a^{2} x^{2} + a x$ , if 'a' is constant and 'x' is a variable, this expression would become a polynomial in ___ variable(s). (Write in words)

Discussion

10023.	Question 88 (viii)Factorise the following expression.2a3−3a2b+5ab2−ab
Answer» Question 88 (viii) Factorise the following expression. $2 a^{3} - 3 a^{2} b + 5 a b^{2} - a b$

Discussion

10024.	Prove that:(i) 11+xa-b+11+xb-a=1(ii) 11+xb-a+xc-a+11+xa-b+xc-b+11+xb-c+xa-c=1
Answer» Prove that: (i) $\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$ (ii) $\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1$

Discussion

10025.	If two towers of height h1 and h2 subtend angles 45∘ and 30∘ respectively at the midpoint of the line joining their feet, then find the ratio of h1:h2.
Answer» If two towers of height $h_{1} a n d h_{2}$ subtend angles $45^{\circ} a n d 30^{\circ}$ respectively at the midpoint of the line joining their feet, then find the ratio of $h_{1} : h_{2} .$

10025.

If two towers of height h1 and h2 subtend angles 45∘ and 30∘ respectively at the midpoint of the line joining their feet, then find the ratio of h1:h2.

Answer»

If two towers of height $h_{1} a n d h_{2}$ subtend angles $45^{\circ} a n d 30^{\circ}$ respectively at the midpoint of the line joining their feet, then find the ratio of

$h_{1} : h_{2} .$

Discussion

10026.	The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find its diameter of its base.
Answer» The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find its diameter of its base.

Discussion

10027.	Rewrite the following statements by using symbols wherever needed.(a) a exceeds b by 10(b) Twice the product of p and q divided by r.(c) x is not equal to two times y.(d) Four times m is greater than seven. (e) The excess of 15 over 10 is 5.
Answer» Rewrite the following statements by using symbols wherever needed. $(a) a exceeds b by 10$ $(b) Twice the product of p and q divided by r .$ $(c) x is not equal to two times y .$ $(d) Four times m is greater than seven.$ $(e) The excess of 15 over 10 is 5.$

Discussion

10028.	Draw any polygon and divide it into triangular parts as shown here. Thus work out the sum of the measures of the angles of the polygon.
Answer» Draw any polygon and divide it into triangular parts as shown here. Thus work out the sum of the measures of the angles of the polygon.

Discussion

10029.	If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p. [CBSE 2015]
Answer» If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p. [CBSE 2015]

Discussion

10030.	find the maximum wavelength in \overset oA for Li^{+2 }ion in paschen series of emission spectrum
Answer» find the maximum wavelength in \overset oA for Li^{+2 }ion in paschen series of emission spectrum

Discussion

10031.	A jeweller makes 3-strand pearl necklace. Each strand has 75 pearls. How many packets of 100 pearls will be needed for 12500 such necklaces
Answer» A jeweller makes 3-strand pearl necklace. Each strand has 75 pearls. How many packets of 100 pearls will be needed for 12500 such necklaces

Discussion

10032.	An equilateral triangle ABC is inscribed in a circle centered at O, as shown below. OE is a radius such that it is perpendicular to BC and cuts BC at point D. If OD = 7 cm, then the radius of this circle is
Answer» An equilateral triangle ABC is inscribed in a circle centered at O, as shown below. OE is a radius such that it is perpendicular to BC and cuts BC at point D. If OD = 7 cm, then the radius of this circle is

10032.

An equilateral triangle ABC is inscribed in a circle centered at O, as shown below. OE is a radius such that it is perpendicular to BC and cuts BC at point D. If OD = 7 cm, then the radius of this circle is

Answer»

An equilateral triangle ABC is inscribed in a circle centered at O, as shown below. OE is a radius such that it is perpendicular to BC and cuts BC at point D. If OD = 7 cm, then the radius of this circle is

Discussion

10033.	Two opposite angles of a parallelogram are (3x−2)∘ and(50−x)∘. Find the measure of each angle of the parallelogram.
Answer» Two opposite angles of a parallelogram are $(3 x - 2)^{\circ} a n d (50 - x)^{\circ} .$ Find the measure of each angle of the parallelogram.

Discussion

10034.	Find the amount on Rs. 24000 compounded semi- annually for one and half years at the rate of 10% per annum.
Answer» Find the amount on Rs. 24000 compounded semi- annually for one and half years at the rate of $10 %$ per annum.

Discussion

10035.	In a right triangle ΔABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. If AC = 2AB, what is the area of Δ ABD, given, area of Δ ABC = 5 sq units.
Answer» In a right triangle $Δ$ ABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. If AC = 2AB, what is the area of $Δ$ ABD, given, area of $Δ$ ABC = 5 sq units.

Discussion

10036.	Find the distance between the following pair of points:(a) (−6, 7) and (−1, −5)(b) (a+b, b+c) and (a−b, c−b)(c) (asinα, −bcosα) and (−acos α, bsin α)(d) (a, 0) and (0, b)
Answer» Find the distance between the following pair of points: (a) (−6, 7) and (−1, −5) (b) (a+b, b+c) and (a−b, c−b) (c) (asinα, −bcosα) and (−acos α, bsin α) (d) (a, 0) and (0, b)

Discussion

10037.	Question 2 Write four solutions for each of the following equations: (i)2x+y=7 (ii)πx+y=9 (iii)x=4y
Answer» Question 2 Write four solutions for each of the following equations: $(i) 2 x + y = 7 (i i) π x + y = 9 (i i i) x = 4 y$

Discussion

10038.	If x=-12 is a zero of the polynomial p(x) = 8x3 − ax2−x + 2, find the value of a.
Answer» If $x = - \frac{1}{2}$ is a zero of the polynomial p(x) = 8x³ − ax²−x + 2, find the value of a.

Discussion

10039.	In what time will Rs 64000 amount to Rs 68921 at 5% per annum, interest being compounded half - yearly?
Answer» In what time will Rs 64000 amount to Rs 68921 at $5 %$ per annum, interest being compounded half - yearly?

Discussion

10040.	In right ΔABC, CF is the median drawn to hypotenuse AB, CE is the bisector of ∠ACB and CD is the altitude to AB. If ∠DCE = 36°, then find the measure of ∠ECF in degree.
Answer» In right ΔABC, CF is the median drawn to hypotenuse AB, CE is the bisector of ∠ACB and CD is the altitude to AB. If ∠DCE = 36°, then find the measure of ∠ECF in degree.

Discussion

10041.	18. angle CAB = 30 ,angle ACB = 90 . ACFG and BCDE are the squares of side AC and BC respectively. Segment BG and Segment AE intersect AC and BG at K
Answer» 18. angle CAB = 30 ,angle ACB = 90 . ACFG and BCDE are the squares of side AC and BC respectively. Segment BG and Segment AE intersect AC and BG at K

Discussion

10042.	If the sides of a TRIANGLE are doubled find the percent increase in area
Answer» If the sides of a TRIANGLE are doubled find the percent increase in area

Discussion

10043.	Construct a triangle ABC in which BC is 4 cm, angle B is 45∘ and AB − AC = 1.75 cm.
Answer» Construct a triangle ABC in which BC is 4 cm, angle B is $45^{\circ}$ and AB − AC = 1.75 cm.

Discussion

10044.	Calculate 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50.
Answer» Calculate 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50.

Discussion

10045.	ntwhat is Mean, Median, and Mode ?n
Answer» ntwhat is Mean, Median, and Mode ?n

Discussion

10046.	Factorize:a2 + 2ab +b2 − c2
Answer» Factorize: a² + 2ab +b² − c²

Discussion

10047.	Study the information in the following pie charts to answer these questions: DETAILS OF 1500 EMPLOYEES WORKING IN AN ORGANISATION ON VARIOUS SCALES Break-up of 1500 Employees Across the Scales Break-up of 800 Male Employees Across the Scales What is the ratio between male and female employees respectively working in Scale V?
Answer» Study the information in the following pie charts to answer these questions: DETAILS OF 1500 EMPLOYEES WORKING IN AN ORGANISATION ON VARIOUS SCALES Break-up of 1500 Employees Across the Scales Break-up of 800 Male Employees Across the Scales What is the ratio between male and female employees respectively working in Scale V?

Discussion

10048.	In a triangle ABC this statement will always be true.
Answer» In a triangle ABC this statement will always be true.

Discussion

10049.	Find x if log2 (x−5)>3
Answer» Find $x$ if ${log}_{2} (x - 5) > 3$

Discussion

10050.	In the given figure, if the altitude and the base of parallelogram are 12 cm and 6 cm respectively, then the area of triangle BEC is:
Answer» In the given figure, if the altitude and the base of parallelogram are 12 cm and 6 cm respectively, then the area of triangle BEC is:

10050.

In the given figure, if the altitude and the base of parallelogram are 12 cm and 6 cm respectively, then the area of triangle BEC is:

Answer»

In the given figure, if the altitude and the base of parallelogram are 12 cm and 6 cm respectively, then the area of triangle BEC is:

Discussion

Explore topic-wise InterviewSolutions in .

What is the factorised form of w(x + y) - z(x + y)?

When the square of a number is decreased by 15, it is equal to twice the original number. Find the possible values of the number.

21. Write the volume of hemisphere in terms of surface area of a sphere.

Find the value of x if x:36::8:48.

Find the value of−163÷−43.

The value of tan(90−A)cot(90−A) is

In a trapezium ABCD, AB || DC, AB = a cm, and DC = b cm. If M and N are the midpoints of the nonparallel sides, AD and BC respectively then find the ratio of ar(DCNM) and ar(MNBA).

Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes is

The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.

Draw a circle of radius 3.2 cm

Classify the following polynomials as linear, quadratic and cubic polynomial. (i) 2x2 + 3 x + 1 (ii) 5p (iii) 2y - 12 (iv) m3 + 7m2 + 52m - 7 (v) a2 (vi) 3r3

Question 1 (ii)Evaluate :tan26∘cot64∘

In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC+∠BOD=2∠AEC. [4 MARKS]​

In figure, arc AB is congruent to arc AC and O is the centre of the circle. Prove that OA is the perpendicular bisector of BC. [4 MARKS]

Rakesh lent out Rs 8000 for 5 years at 15% per annum and borrowed Rs 6000 for 3 years at 12% per annum. How much did he gain or lose?

Factorise a−a3+b3−b is _______

The three angles of a quadrilateral are 75∘, 90∘ and 75∘. What is the fouth angle?

In the given figure, O is the centre of the sector. ∠ROQ = ∠MON = 60° . OR = 7 cm, and OM = 21 cm. Find the lengths of arc RXQ and arc MYN. ( π=227)

In ΔPQR, S is any point on the side QR. Show that PQ + QR + RP &gt; 2 PS

If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are α and β respectively. Prove that the height of the tower is h tan αtan β−tan α

In a2x2+ax, if 'a' is constant and 'x' is a variable, this expression would become a polynomial in ___ variable(s). (Write in words)

Question 88 (viii)Factorise the following expression.2a3−3a2b+5ab2−ab

Prove that:(i) 11+xa-b+11+xb-a=1(ii) 11+xb-a+xc-a+11+xa-b+xc-b+11+xb-c+xa-c=1

If two towers of height h1 and h2 subtend angles 45∘ and 30∘ respectively at the midpoint of the line joining their feet, then find the ratio of h1:h2.

The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find its diameter of its base.

Rewrite the following statements by using symbols wherever needed.(a) a exceeds b by 10(b) Twice the product of p and q divided by r.(c) x is not equal to two times y.(d) Four times m is greater than seven. (e) The excess of 15 over 10 is 5.

Draw any polygon and divide it into triangular parts as shown here. Thus work out the sum of the measures of the angles of the polygon.

If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p. [CBSE 2015]

find the maximum wavelength in \overset oA for Li^{+2 }ion in paschen series of emission spectrum

A jeweller makes 3-strand pearl necklace. Each strand has 75 pearls. How many packets of 100 pearls will be needed for 12500 such necklaces

An equilateral triangle ABC is inscribed in a circle centered at O, as shown below. OE is a radius such that it is perpendicular to BC and cuts BC at point D. If OD = 7 cm, then the radius of this circle is

Two opposite angles of a parallelogram are (3x−2)∘ and(50−x)∘. Find the measure of each angle of the parallelogram.

Find the amount on Rs. 24000 compounded semi- annually for one and half years at the rate of 10% per annum.

In a right triangle ΔABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. If AC = 2AB, what is the area of Δ ABD, given, area of Δ ABC = 5 sq units.

Find the distance between the following pair of points:(a) (−6, 7) and (−1, −5)(b) (a+b, b+c) and (a−b, c−b)(c) (asinα, −bcosα) and (−acos α, bsin α)(d) (a, 0) and (0, b)

Question 2 Write four solutions for each of the following equations: (i)2x+y=7 (ii)πx+y=9 (iii)x=4y

If x=-12 is a zero of the polynomial p(x) = 8x3 − ax2−x + 2, find the value of a.

In what time will Rs 64000 amount to Rs 68921 at 5% per annum, interest being compounded half - yearly?

In right ΔABC, CF is the median drawn to hypotenuse AB, CE is the bisector of ∠ACB and CD is the altitude to AB. If ∠DCE = 36°, then find the measure of ∠ECF in degree.

18. angle CAB = 30 ,angle ACB = 90 . ACFG and BCDE are the squares of side AC and BC respectively. Segment BG and Segment AE intersect AC and BG at K

If the sides of a TRIANGLE are doubled find the percent increase in area

Construct a triangle ABC in which BC is 4 cm, angle B is 45∘ and AB − AC = 1.75 cm.

Calculate 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50.

ntwhat is Mean, Median, and Mode ?n

Factorize:a2 + 2ab +b2 − c2

In a triangle ABC this statement will always be true.

Find x if log2 (x−5)&gt;3

In the given figure, if the altitude and the base of parallelogram are 12 cm and 6 cm respectively, then the area of triangle BEC is:

In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC+∠BOD=2∠AEC. [4 MARKS]

In ΔPQR, S is any point on the side QR. Show that PQ + QR + RP > 2 PS

Find x if log2 (x−5)>3