24740 + Interview Questions in Mathematics Page 73 InterviewSolution

3601.	The the given figure, EAD ⊥ BCD. Ray FAC cuts ray EAD at a point A such that ∠EAF = 30°. Also, in ∆BAC, ∠BAC = x° and ∠ABC = (x + 10)°. Then, the value of x is(a) 20(b) 25(c) 30(d) 35
Answer» The the given figure, EAD ⊥ BCD. Ray FAC cuts ray EAD at a point A such that ∠EAF = 30°. Also, in ∆BAC, ∠BAC = x° and ∠ABC = (x + 10)°. Then, the value of x is (a) 20 (b) 25 (c) 30 (d) 35

Discussion

3602.	In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then, the percentage of the population traveling by car or bus is
Answer» In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then, the percentage of the population traveling by car or bus is

Discussion

3603.

The time required for students to do a science experiment and the number of students is shown in the following grouped frequency distribution table. Show the information by a histogram and also by a frequency polygon. Time required for experiment (minutes) 20 - 22 22 - 24 24 - 26 26 - 28 28 - 30 30 - 32 No. of students 8 16 22 18 14 12

Answer» The time required for students to do a science experiment and the number of students is shown in the following grouped frequency distribution table. Show the information by a histogram and also by a frequency polygon.

Time required for experiment (minutes)	20 - 22	22 - 24	24 - 26	26 - 28	28 - 30	30 - 32
No. of students	8	16	22	18	14	12

Discussion

3604.	For what values of a and b the intercepts cut off on the coordinate axes by the line ax+by+8=0 are equal in length but opposite in signs to those cut off by the line 2x-3y+6=0 on the axes
Answer» For what values of a and b the intercepts cut off on the coordinate axes by the line ax+by+8=0 are equal in length but opposite in signs to those cut off by the line 2x-3y+6=0 on the axes

Discussion

3605.	12+34=?
Answer» $\frac{1}{2} + \frac{3}{4} = ?$

Discussion

3606.	Question 10Prove that √3+√5 is irrational.
Answer» Question 10 Prove that $\sqrt{3} + \sqrt{5}$ is irrational.

Discussion

3607.	There are two identical circles with same inside design as shown in the figure. The identical triangular leaves are to be painted red and the remaining area green. Find the total area to be painted red.
Answer» There are two identical circles with same inside design as shown in the figure. The identical triangular leaves are to be painted red and the remaining area green. Find the total area to be painted red.

Discussion

3608.	ΔABC is an isosceles triangle in which AB = AC. Show that ∠B = ∠C.
Answer» ΔABC is an isosceles triangle in which AB = AC. Show that ∠B = ∠C.

Discussion

3609.	In the given figure, ABCD is a parallelogram. AB is extended to a point E and DE intersects BC at H. FGCD is a parallelogram and the extended GF passes through the point H as shown in the figure. If area (ABCD) = 22 cm2 and area (FGCD) = 10 cm2, then what is the area of the shaded region?
Answer» In the given figure, ABCD is a parallelogram. AB is extended to a point E and DE intersects BC at H. FGCD is a parallelogram and the extended GF passes through the point H as shown in the figure. If area (ABCD) = 22 cm2 and area (FGCD) = 10 cm2, then what is the area of the shaded region?

3609.

In the given figure, ABCD is a parallelogram. AB is extended to a point E and DE intersects BC at H. FGCD is a parallelogram and the extended GF passes through the point H as shown in the figure. If area (ABCD) = 22 cm2 and area (FGCD) = 10 cm2, then what is the area of the shaded region?

Answer»

In the given figure, ABCD is a parallelogram. AB is extended to a point E and DE intersects BC at H.

FGCD is a parallelogram and the extended GF passes through the point H as shown in the figure.

If area (ABCD) = 22 cm2 and area (FGCD) = 10 cm2, then what is the area of the shaded region?

Discussion

3610.	In the given figure, what is the angle subtended by chord AB at the point C on the circle?
Answer» In the given figure, what is the angle subtended by chord AB at the point C on the circle?

Discussion

3611.	Prove that every rectangle is a parallelogram.
Answer» Prove that every rectangle is a parallelogram.

Discussion

3612.	Calculate the C.I. to be paid when a sum of ₹20,000 is taken for one year at 10% per annum compounded semi annually.
Answer» Calculate the C.I. to be paid when a sum of ₹20,000 is taken for one year at 10% per annum compounded semi annually.

Discussion

3613.	The difference between the sides at right angles a right angled triangle is14cm .The area of the triangle is 120cm squared . Calculate the perimeter of the triangle
Answer» The difference between the sides at right angles a right angled triangle is14cm .The area of the triangle is 120cm squared . Calculate the perimeter of the triangle

Discussion

3614.	In the given figure, if AB \|\| CD, ∠APQ = 50º and ∠PRD = 127º, find x and y.
Answer» In the given figure, if AB \|\| CD, ∠APQ = 50º and ∠PRD = 127º, find x and y.

3614.

In the given figure, if AB || CD, ∠APQ = 50º and ∠PRD = 127º, find x and y.

Answer»

In the given figure, if AB || CD, ∠APQ = 50º and ∠PRD = 127º, find x and y.

Discussion

3615.	The Equation y = - 5, in two variables can be written in the form of ax + by + c = 0 as
Answer» The Equation y = - 5, in two variables can be written in the form of ax + by + c = 0 as

Discussion

3616.	Draw a hexagon with all sides equal, but not all angles equal.
Answer» Draw a hexagon with all sides equal, but not all angles equal.

Discussion

3617.	Which of the following equations have a constant of proportionality equal to 2?
Answer» Which of the following equations have a constant of proportionality equal to 2?

Discussion

3618.	The remainder when the polynomial (x^32 + 1)x + (3x^2 + x)^99 + (3x^2 + x)^3 is divided by 27x^6 + 27x^5 + x^3(9x + 1) + x is equal to
Answer» The remainder when the polynomial (x^32 + 1)x + (3x^2 + x)^99 + (3x^2 + x)^3 is divided by 27x^6 + 27x^5 + x^3(9x + 1) + x is equal to

Discussion

3619.	Identify the following figure.
Answer» Identify the following figure.

3619.

Identify the following figure.

Answer»

Identify the following figure.

Discussion

3620.	In the given figure, BE and CF are two equal altitudes of ΔABC.Show that (i) ΔABE ≅ ΔACF, (ii) AB = AC.
Answer» In the given figure, BE and CF are two equal altitudes of ΔABC. Show that (i) ΔABE ≅ ΔACF, (ii) AB = AC.

Discussion

3621.	Question 16 D, E and F are respectively the mid-points of the sides AB, BC and CA of a ΔABC. Prove that by joining these mid-points D, E and F, the ΔABC is divided into four congruent triangles.
Answer» Question 16 D, E and F are respectively the mid-points of the sides AB, BC and CA of a $Δ A B C$ . Prove that by joining these mid-points D, E and F, the $Δ A B C$ is divided into four congruent triangles.

Discussion

3622.	Prove that the medians of an equilateral triangle are equal.
Answer» Prove that the medians of an equilateral triangle are equal.

Discussion

3623.	If sec θ + tan θ = x, then sec θ =(a) x2+1x(b) x2+12x(c) x2-12x(d) x2-1x
Answer» If sec θ + tan θ = x, then sec θ = (a) $\frac{x^{2} + 1}{x}$ (b) $\frac{x^{2} + 1}{2 x}$ (c) $\frac{x^{2} - 1}{2 x}$ (d) $\frac{x^{2} - 1}{x}$

Discussion

3624.	The numerical factor of a term is known as
Answer» The numerical factor of a term is known as

Discussion

3625.	Pick the option which matches the two columns.
Answer» Pick the option which matches the two columns.

Discussion

3626.	In the figure, △EFA is a right-angled triangle with ∠EFA=90∘ and △FGB is an equilateral triangle, find y–2x.
Answer» In the figure, $△ E F A$ is a right-angled triangle with $∠ E F A = 90^{\circ}$ and $△ F G B$ is an equilateral triangle, find $y - 2 x$ .

Discussion

3627.	Question 5In figure, if ABIIDC and AC, PQ intersect each other at the point O. Prove that OA.CQ = OC.AP.
Answer» Question 5 In figure, if ABIIDC and AC, PQ intersect each other at the point O. Prove that OA.CQ = OC.AP.

Discussion

3628.	If the distance between the points (t, 2/t ) and ( 1/t, -2t ) is 3, where t is a natural number, then (t^2+1/t^2) is.
Answer» If the distance between the points (t, 2/t ) and ( 1/t, -2t ) is 3, where t is a natural number, then (t^2+1/t^2) is.

Discussion

3629.	Which of the following is the empirical relation between mean, mode and median?
Answer» Which of the following is the empirical relation between mean, mode and median?

Discussion

3630.	Question 4(iv)Factorisex4−(x−z)4
Answer» Question 4(iv) Factorise $x^{4} - (x - z)^{4}$

Discussion

3631.	Question 11 Eleven bags of wheat flour, each marked 5kg, actually contained the following weights of flour (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04,5.07, 5.00 Find the probability that any of these bags chosen at random contains more than 5 Kg of flour.
Answer» Question 11 Eleven bags of wheat flour, each marked 5kg, actually contained the following weights of flour (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04,5.07, 5.00 Find the probability that any of these bags chosen at random contains more than 5 Kg of flour.

Discussion

3632.	PQRS is a trapezium such that PQ \|\| RS and PQ = 10 cm, QR = 5 cm, RS = 8 cm and PS = 5 cm, then area of PQRS is
Answer» PQRS is a trapezium such that PQ \|\| RS and PQ = 10 cm, QR = 5 cm, RS = 8 cm and PS = 5 cm, then area of PQRS is

Discussion

3633.	In the figure below, if AC>AB and D is point on AC such that AB = AD, then the relation between BC and CD is .
Answer» In the figure below, if AC $>$ AB and D is point on AC such that AB = AD, then the relation between BC and CD is .

Discussion

3634.	The minimum number of triangles that can be kept together to construct a quadrilateral is _
Answer» The minimum number of triangles that can be kept together to construct a quadrilateral is _

Discussion

3635.	If 1 and -3 are the zeroes of a polynomial p(x) = x^3 - ax^2 - 13x + b , find the values of a and b.
Answer» If 1 and -3 are the zeroes of a polynomial p(x) = x^3 - ax^2 - 13x + b , find the values of a and b.

3635.

If 1 and -3 are the zeroes of a polynomial p(x) = x^3 - ax^2 - 13x + b , find the values of a and b.

Answer»

If 1 and -3 are the zeroes of a polynomial p(x) = x^3 - ax^2 - 13x + b ,

find the values of a and b.

Discussion

3636.	Two adjacent angles of a rhombus are 3x−40∘ and 2x+20∘. Find the measurement of the greater angle in degrees.100
Answer» $Two adjacent angles of a rhombus are 3 x - 40^{\circ} and 2 x + 20^{\circ} . Find the measurement of the greater angle in degrees.$ 100

Discussion

3637.	In the following figure, what can be concluded from the below given conditions. Given: AB = CD and AC = DE.
Answer» In the following figure, what can be concluded from the below given conditions. Given: AB = CD and AC = DE.

3637.

In the following figure, what can be concluded from the below given conditions. Given: AB = CD and AC = DE.

Answer»

In the following figure, what can be concluded from the below given conditions.

Given: AB = CD and AC = DE.

Discussion

3638.	the sides KI and TE of a quadrilateral KITE are extended to points A a angle EKI equals to
Answer» the sides KI and TE of a quadrilateral KITE are extended to points A a angle EKI equals to

Discussion

3639.	If measures opposite angles of a parallelogram are (60 − x)° and (3x − 4)°, then find the measures of angles of the parallelogram.
Answer» If measures opposite angles of a parallelogram are (60 − x)° and (3x − 4)°, then find the measures of angles of the parallelogram.

Discussion

3640.	Question 88 (x)Factorise the following expression.24x2yz3−6xy3z2+15x2y2z−5xyz
Answer» Question 88 (x) Factorise the following expression. $24 x^{2} y z^{3} - 6 x y^{3} z^{2} + 15 x^{2} y^{2} z - 5 x y z$

Discussion

3641.	In the figure given alongside, ABCD is a square and EF is parallel to diagonal BD. If EM = FM, prove that DF = BE.
Answer» In the figure given alongside, ABCD is a square and EF is parallel to diagonal BD. If EM = FM, prove that DF = BE.

Discussion

3642.	Two numbers which have exactly three factors are
Answer» Two numbers which have exactly three factors are

Discussion

3643.	The sum of a rational number and an irrational number is ________ number.
Answer» The sum of a rational number and an irrational number is ________ number.

Discussion

3644.	Find the zeros of the polynomial 2s2-(1+2√2)s+√2 and verify the relationship between the zeros and coefficient of the polynomial.
Answer» Find the zeros of the polynomial 2s2-(1+2√2)s+√2 and verify the relationship between the zeros and coefficient of the polynomial.

Discussion

3645.	In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that ∠DBC=60∘ and ∠BAC=40∘. Find (i) ∠BCD, (ii) ∠CAD.
Answer» In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that $∠ D B C = 60^{\circ} a n d ∠ B A C = 40^{\circ} . Find (i) ∠ B C D, (i i) ∠ C A D$ .

3645.

In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that ∠DBC=60∘ and ∠BAC=40∘. Find (i) ∠BCD, (ii) ∠CAD.

Answer»

In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that $∠ D B C = 60^{\circ} a n d ∠ B A C = 40^{\circ} . Find (i) ∠ B C D, (i i) ∠ C A D$ .

Discussion

3646.	Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:(i) p(x) = 2x3 + x2 − 2x − 1, g(x) = x + 1(ii) p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2(iii) p(x) = x3 − 4 x2 + x + 6, g(x) = x − 3
Answer» Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x³ + x² − 2x − 1, g(x) = x + 1 (ii) p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2 (iii) p(x) = x³ − 4 x² + x + 6, g(x) = x − 3

3646.

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:(i) p(x) = 2x3 + x2 − 2x − 1, g(x) = x + 1(ii) p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2(iii) p(x) = x3 − 4 x2 + x + 6, g(x) = x − 3

Answer»

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:

(i) p(x) = 2x³ + x² − 2x − 1, g(x) = x + 1

(ii) p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2

(iii) p(x) = x³ − 4 x² + x + 6, g(x) = x − 3

Discussion

3647.	A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. What is the radius of the sphere?
Answer» A cone is $8.4 cm$ high and the radius of its base is $2.1 cm$ . It is melted and recast into a sphere. What is the radius of the sphere?

Discussion

3648.	Which of the following point(s) have same projection on z− axis as of point P(−2,−1,−3) does ?
Answer» Which of the following point(s) have same projection on $z -$ axis as of point $P (- 2, - 1, - 3)$ does ?

Discussion

3649.	of the following rational numbers is a non-terminating and repeating decimal.
Answer» of the following rational numbers is a non-terminating and repeating decimal.

Discussion

3650.

An irrational number is marked on the number line (D) as shown in the figure below. Then the value of D is ________.

Answer»

An irrational number is marked on the number line (D) as shown in the figure below. Then the value of D is ________.

Discussion

Explore topic-wise InterviewSolutions in .

The the given figure, EAD ⊥ BCD. Ray FAC cuts ray EAD at a point A such that ∠EAF = 30°. Also, in ∆BAC, ∠BAC = x° and ∠ABC = (x + 10)°. Then, the value of x is(a) 20(b) 25(c) 30(d) 35

In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then, the percentage of the population traveling by car or bus is

For what values of a and b the intercepts cut off on the coordinate axes by the line ax+by+8=0 are equal in length but opposite in signs to those cut off by the line 2x-3y+6=0 on the axes

12+34=?

Question 10Prove that √3+√5 is irrational.

There are two identical circles with same inside design as shown in the figure. The identical triangular leaves are to be painted red and the remaining area green. Find the total area to be painted red.

ΔABC is an isosceles triangle in which AB = AC. Show that ∠B = ∠C.

In the given figure, ABCD is a parallelogram. AB is extended to a point E and DE intersects BC at H. FGCD is a parallelogram and the extended GF passes through the point H as shown in the figure. If area (ABCD) = 22 cm2 and area (FGCD) = 10 cm2, then what is the area of the shaded region?

In the given figure, what is the angle subtended by chord AB at the point C on the circle?

Prove that every rectangle is a parallelogram.

Calculate the C.I. to be paid when a sum of ₹20,000 is taken for one year at 10% per annum compounded semi annually.

The difference between the sides at right angles a right angled triangle is14cm .The area of the triangle is 120cm squared . Calculate the perimeter of the triangle

In the given figure, if AB || CD, ∠APQ = 50º and ∠PRD = 127º, find x and y.

The Equation y = - 5, in two variables can be written in the form of ax + by + c = 0 as

Draw a hexagon with all sides equal, but not all angles equal.

Which of the following equations have a constant of proportionality equal to 2?

The remainder when the polynomial (x^32 + 1)x + (3x^2 + x)^99 + (3x^2 + x)^3 is divided by 27x^6 + 27x^5 + x^3(9x + 1) + x is equal to

Identify the following figure.

In the given figure, BE and CF are two equal altitudes of ΔABC.Show that (i) ΔABE ≅ ΔACF, (ii) AB = AC.

Question 16 D, E and F are respectively the mid-points of the sides AB, BC and CA of a ΔABC. Prove that by joining these mid-points D, E and F, the ΔABC is divided into four congruent triangles.

Prove that the medians of an equilateral triangle are equal.

If sec θ + tan θ = x, then sec θ =(a) x2+1x(b) x2+12x(c) x2-12x(d) x2-1x

The numerical factor of a term is known as

Pick the option which matches the two columns.

In the figure, △EFA is a right-angled triangle with ∠EFA=90∘ and △FGB is an equilateral triangle, find y–2x.

Question 5In figure, if ABIIDC and AC, PQ intersect each other at the point O. Prove that OA.CQ = OC.AP.

If the distance between the points (t, 2/t ) and ( 1/t, -2t ) is 3, where t is a natural number, then (t^2+1/t^2) is.

Which of the following is the empirical relation between mean, mode and median?

Question 4(iv)Factorisex4−(x−z)4

Question 11 Eleven bags of wheat flour, each marked 5kg, actually contained the following weights of flour (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04,5.07, 5.00 Find the probability that any of these bags chosen at random contains more than 5 Kg of flour.

PQRS is a trapezium such that PQ || RS and PQ = 10 cm, QR = 5 cm, RS = 8 cm and PS = 5 cm, then area of PQRS is

In the figure below, if AC&gt;AB and D is point on AC such that AB = AD, then the relation between BC and CD is .

The minimum number of triangles that can be kept together to construct a quadrilateral is _

If 1 and -3 are the zeroes of a polynomial p(x) = x^3 - ax^2 - 13x + b , find the values of a and b.

Two adjacent angles of a rhombus are 3x−40∘ and 2x+20∘. Find the measurement of the greater angle in degrees.100

In the following figure, what can be concluded from the below given conditions. Given: AB = CD and AC = DE.

the sides KI and TE of a quadrilateral KITE are extended to points A a angle EKI equals to

If measures opposite angles of a parallelogram are (60 − x)° and (3x − 4)°, then find the measures of angles of the parallelogram.

Question 88 (x)Factorise the following expression.24x2yz3−6xy3z2+15x2y2z−5xyz

In the figure given alongside, ABCD is a square and EF is parallel to diagonal BD. If EM = FM, prove that DF = BE.

Two numbers which have exactly three factors are

The sum of a rational number and an irrational number is ________ number.

Find the zeros of the polynomial 2s2-(1+2√2)s+√2 and verify the relationship between the zeros and coefficient of the polynomial.

In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that ∠DBC=60∘ and ∠BAC=40∘. Find (i) ∠BCD, (ii) ∠CAD.

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:(i) p(x) = 2x3 + x2 − 2x − 1, g(x) = x + 1(ii) p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2(iii) p(x) = x3 − 4 x2 + x + 6, g(x) = x − 3

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. What is the radius of the sphere?

Which of the following point(s) have same projection on z− axis as of point P(−2,−1,−3) does ?

of the following rational numbers is a non-terminating and repeating decimal.

An irrational number is marked on the number line (D) as shown in the figure below. Then the value of D is ________.

In the figure below, if AC>AB and D is point on AC such that AB = AD, then the relation between BC and CD is .