24740 + Interview Questions in Mathematics Page 143 InterviewSolution

7101.	In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, then find x.
Answer» In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, then find x.

Discussion

7102.	If k and 2k are zeros of f(x)=x3+4x2+9kx=90, find k and all three zeros of f(x).
Answer» If k and 2k are zeros of $f (x) = x^{3} + 4 x^{2} + 9 k x = 90$ , find k and all three zeros of f(x).

Discussion

7103.	Question 1If one of the zeroes of the quadratic polynomial (k–1)x2+kx+1 is -3, then the value of k is(A)43(B)−43(C)23(D)−23
Answer» Question 1 If one of the zeroes of the quadratic polynomial $(k - 1) x^{2} + k x + 1$ is -3, then the value of k is $(A) \frac{4}{3}$ $(B) \frac{- 4}{3}$ $(C) \frac{2}{3}$ $(D) \frac{- 2}{3}$

Discussion

7104.	In a bag there are 44 identical cards with figure of circle or square on them. There are 24 circles, of which 9 arc blue and rest are green and 20 squares of which 11 are blue and rest are green. One card is drawn from the bag at random. Find the probability that it has the figure of (i) square (ii) green colour, (iii) blue circle and (iv) green square.
Answer» In a bag there are 44 identical cards with figure of circle or square on them. There are 24 circles, of which 9 arc blue and rest are green and 20 squares of which 11 are blue and rest are green. One card is drawn from the bag at random. Find the probability that it has the figure of (i) square (ii) green colour, (iii) blue circle and (iv) green square.

Discussion

7105.	Observe the given figure and choose the correct statement
Answer» Observe the given figure and choose the correct statement

7105.

Observe the given figure and choose the correct statement

Answer»

Observe the given figure and choose the correct statement

Discussion

7106.	How to find irrational numbers between any two irrational or a rational number
Answer» How to find irrational numbers between any two irrational or a rational number

Discussion

7107.	State whether the following statements are true or false. Give reasons for your answer. (i) Every natural number is a whole number. (ii) Every whole number is a natural number. (iii) Every integer is a whole number. (iv) Every integer is a rational number. (v) Every rational number is an integer. (vi) Every rational number is a whole number.
Answer» State whether the following statements are true or false. Give reasons for your answer. (i) Every natural number is a whole number. (ii) Every whole number is a natural number. (iii) Every integer is a whole number. (iv) Every integer is a rational number. (v) Every rational number is an integer. (vi) Every rational number is a whole number.

7107.

State whether the following statements are true or false. Give reasons for your answer. (i) Every natural number is a whole number. (ii) Every whole number is a natural number. (iii) Every integer is a whole number. (iv) Every integer is a rational number. (v) Every rational number is an integer. (vi) Every rational number is a whole number.

Answer»

State whether the following statements are true or false. Give reasons for your answer.

(i) Every natural number is a whole number.

(ii) Every whole number is a natural number.

(iii) Every integer is a whole number.

(iv) Every integer is a rational number.

(v) Every rational number is an integer.

(vi) Every rational number is a whole number.

Discussion

7108.	Question 1In the given figure, sides QP and RQ of ΔPQR are produced to point S and T respectively, If ∠SPR=135∘ and ∠PQT=110∘, find ∠PRQ.
Answer» Question 1 In the given figure, sides QP and RQ of $Δ P Q R$ are produced to point S and T respectively, If $∠ S P R = 135^{\circ} a n d ∠ P Q T = 110^{\circ}$ , find $∠ P R Q .$

Discussion

7109.	A parallelogram and a triangle are on equal base and between the same parallel lines. The ratio of their areas is ______.
Answer» A parallelogram and a triangle are on equal base and between the same parallel lines. The ratio of their areas is ______.

Discussion

7110.	If A=[1347], then the value of adj(5A) is:
Answer» If $A = [\begin{matrix} 1 & 3 4 & 7 \end{matrix}]$ , then the value of $adj (5 A)$ is:

Discussion

7111.	Question 2 (ii)Find the measure of each exterior angle of a regular polygon of:(ii) 15 sides
Answer» Question 2 (ii) Find the measure of each exterior angle of a regular polygon of: (ii) 15 sides

Discussion

7112.	Trade amounts for the following countries are: India: $56 millionUSA: $84 millionChina: $120 millionGermany: $44 millionWhat is the average trade done by these countries?
Answer» Trade amounts for the following countries are: India: $56 million USA: $84 million China: $120 million Germany: $44 million What is the average trade done by these countries?

7112.

Trade amounts for the following countries are: India: $56 millionUSA: $84 millionChina: $120 millionGermany: $44 millionWhat is the average trade done by these countries?

Answer»

Trade amounts for the following countries are:

India: $56 million

USA: $84 million

China: $120 million

Germany: $44 million

What is the average trade done by these countries?

Discussion

7113.	Draw two intersecting lines to include an angle of 30∘. Use ruler and compass to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such point/points exist(s)?
Answer» Draw two intersecting lines to include an angle of 30 $^{\circ}$ . Use ruler and compass to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such point/points exist(s)?

Discussion

7114.	Question 11The students of Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? [Assume π=227]
Answer» Question 11 The students of Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? $[A s s u m e π = \frac{22}{7}]$

Discussion

7115.	In ΔABC, if AD is a median, which of the following relations holds good?
Answer» In $Δ A B C,$ if AD is a median, which of the following relations holds good?

Discussion

7116.	In triangle ABC points L M and N lie on BC AC and AB respectivelyabd AL BM and CN are concurrent Find numerical value of PL/AL+PM/BM+PN/CN
Answer» In triangle ABC points L M and N lie on BC AC and AB respectivelyabd AL BM and CN are concurrent Find numerical value of PL/AL+PM/BM+PN/CN

Discussion

7117.	A kite in the shape of a square with a diagonal 32cm and an isosceles triangles of base 8cm and sides 6cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?
Answer» A kite in the shape of a square with a diagonal 32cm and an isosceles triangles of base 8cm and sides 6cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?

Discussion

7118.	If k and 2k are zeros of f(x)=x3+4x2+9kx=90, find k and all three zeros of f(x).
Answer» If k and 2k are zeros of $f (x) = x^{3} + 4 x^{2} + 9 k x = 90$ , find k and all three zeros of f(x).

Discussion

7119.	If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB. [CBSE 2014]
Answer» If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB. [CBSE 2014]

Discussion

7120.	Question 2For which value(s) of k will the pair of equations kx + 3y = k – 3, 12x + ky = khas no solution?
Answer» Question 2 For which value(s) of k will the pair of equations kx + 3y = k – 3, 12x + ky = k has no solution?

Discussion

7121.	In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is ________.
Answer» In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is ________.

Discussion

7122.	If 4mn+16m2n balloons are to be distributed among 4mn children, how many balloons does each child get, if m=2?
Answer» If $4 m n + 16 m^{2} n$ balloons are to be distributed among $4 m n$ children, how many balloons does each child get, if $m = 2$ ?

Discussion

7123.	Simplify:(i) (16-1/5)5/2(ii) 32-35(iii) (343)-23(iv) (0.001)1/3(v) (25)3/2×(243)3/5(16)5/4×(8)4/3(vi) 258 ÷ 2513(vii) 5-1×7252×7-47/2 × 5-2×7353×7-5-5/2
Answer» Simplify: (i) $(16^{- 1 / 5})^{5 / 2}$ (ii) $\sqrt[5]{{(32)}^{- 3}}$ (iii) $\sqrt[3]{(343)^{- 2}}$ (iv) $(0.001)^{1 / 3}$ (v) $\frac{(25)^{3 / 2} \times (243)^{3 / 5}}{(16)^{5 / 4} \times (8)^{4 / 3}}$ (vi) ${(\frac{\sqrt{2}}{5})}^{8} \div {(\frac{\sqrt{2}}{5})}^{13}$ (vii) ${(\frac{5^{- 1} \times 7^{2}}{5^{2} \times 7^{- 4}})}^{7 / 2} \times {(\frac{5^{- 2} \times 7^{3}}{5^{3} \times 7^{- 5}})}^{- 5 / 2}$

Discussion

7124.	In the given fig., the measure of ∠ABC is:
Answer» In the given fig., the measure of ∠ABC is:

7124.

In the given fig., the measure of ∠ABC is:

Answer»

In the given fig., the measure of ∠ABC is:

Discussion

7125.	If α,β and γ are the zeroes of the cubic polynomial ax3+bx2+cx+d,then α+β+γ is equal to
Answer» If $α, β$ and $γ$ are the zeroes of the cubic polynomial $a x^{3} + b x^{2} + c x + d$ , then $α + β + γ$ is equal to

Discussion

7126.	Find the equation of a line whose slope = -3 and y-intercept =-1.
Answer» Find the equation of a line whose slope = -3 and y-intercept =-1.

Discussion

7127.	1. If X=cosy , find dy/dx in terms of y alone
Answer» 1. If X=cosy , find dy/dx in terms of y alone

Discussion

7128.	In the figure given below, state which lines are parallel and why?
Answer» In the figure given below, state which lines are parallel and why?

Discussion

7129.	in the figure AD IS THE MEDIAN OF A TRIANGLE ABC AND AM perpendicularTO BC. prove that AC square + AB SQUARE = 2AD SQUARE + .5BC SQUARE
Answer» in the figure AD IS THE MEDIAN OF A TRIANGLE ABC AND AM perpendicularTO BC. prove that AC square + AB SQUARE = 2AD SQUARE + .5BC SQUARE

Discussion

7130.	Question 94 State whether the statements are True or False. All kites are squares.
Answer» Question 94 State whether the statements are True or False. All kites are squares.

Discussion

7131.	The decimal expansion of 178 will terminate after _______ places of decimal.
Answer» The decimal expansion of $\frac{17}{8}$ will terminate after _______ places of decimal.

Discussion

7132.	If perpendiculars from any point within an angle on its arms are congruent, prove tht it lies on the bisector of that angle.
Answer» If perpendiculars from any point within an angle on its arms are congruent, prove tht it lies on the bisector of that angle.

Discussion

7133.	Through any point in the bisector of an angle, a straight line is drawn parallel to either arm of the angle. Prove that the triangle so formed is isosceles.
Answer» Through any point in the bisector of an angle, a straight line is drawn parallel to either arm of the angle. Prove that the triangle so formed is isosceles.

Discussion

7134.	Simplify each of the following as a single polynomial.(i) (3x + 3) (3x + 2)(ii) (3x − 4) (4x − 3)(iii) (iv) (v) (vi) (vii)
Answer» Simplify each of the following as a single polynomial. (i) (3x + 3) (3x + 2) (ii) (3x − 4) (4x − 3) (iii) (iv) (v) (vi) (vii)

7134.

Simplify each of the following as a single polynomial.(i) (3x + 3) (3x + 2)(ii) (3x − 4) (4x − 3)(iii) (iv) (v) (vi) (vii)

Answer»

Simplify each of the following as a single polynomial.

(i) (3x + 3) (3x + 2)

(ii) (3x − 4) (4x − 3)

(iii)

(iv)

(v)

(vi)

(vii)

Discussion

7135.	An angle is equal to its supplement. Determine its measure.
Answer» An angle is equal to its supplement. Determine its measure.

Discussion

7136.	If S is the circumcentre of a △ ABC and D,E,F are the feet of the altitudes of △ ABC then prove that SB is perpendicular to DF
Answer» If S is the circumcentre of a △ ABC and D,E,F are the feet of the altitudes of △ ABC then prove that SB is perpendicular to DF

Discussion

7137.	Which of these shows an obtuse angled triangle?
Answer» Which of these shows an obtuse angled triangle?

Discussion

7138.	Find the value of 1√10. If √10 =3.162
Answer» Find the value of $\frac{1}{\sqrt{10}}$ . If $\sqrt{10}$ =3.162

Discussion

7139.	The value of k for which x − 1 is a factor of 4x3 + 3x2 − 4x + k, is(a) 3(b) 1(c) −2(d) −3
Answer» The value of k for which x − 1 is a factor of 4x³ + 3x² − 4x + k, is (a) 3 (b) 1 (c) −2 (d) −3

Discussion

7140.	Which of the following point lies on the y-axis?
Answer» Which of the following point lies on the y-axis?

Discussion

7141.	In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.
Answer» In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.

7141.

In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.

Answer»

In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.

Discussion

7142.	If a cylindrical vessel has a hemispherical bottom with radius 4 cm and height 15 cm, then its volume is .
Answer» If a cylindrical vessel has a hemispherical bottom with radius 4 cm and height 15 cm, then its volume is .

Discussion

7143.	At an event, a sum of $1200 was collected from the participants.The correct equation representing the number of participants at the growth talk is
Answer» At an event, a sum of $$$ 1200 was collected from the participants.The correct equation representing the number of participants at the growth talk is

Discussion

7144.	A right angled triangle ABC is constructed with BC = 3 cm and AB + AC = 9 cm. If B is the right angled, then find the length of AC (in cm).5
Answer» A right angled triangle ABC is constructed with BC = 3 $cm$ and AB + AC = 9 $cm$ . If B is the right angled, then find the length of AC (in cm). 5

Discussion

7145.	A copper wire of diameter 6mm is evenly wrapped on a cylinder of length 15cm and diameter 49cm to cover its whole surface. Find the length and volume of the wire. If the specific gravity of copper is 9 grams per cubic cm. Find the weight of the wire
Answer» A copper wire of diameter $6 m m$ is evenly wrapped on a cylinder of length $15 c m$ and diameter $49 c m$ to cover its whole surface. Find the length and volume of the wire. If the specific gravity of copper is $9$ grams per cubic cm. Find the weight of the wire

Discussion

7146.	In the given figure, EFGH is a parallelogram, altitudes FK and FI are 8 cm and 4 cm, respectively. If EF = 10 cm, then the area of EFGH is
Answer» In the given figure, EFGH is a parallelogram, altitudes FK and FI are 8 cm and 4 cm, respectively. If EF = 10 cm, then the area of EFGH is

Discussion

7147.	How many cubic metres of earth must be dugout to sink a well 21 m deep and 6 m diameter? Find the cost of plastering the inner surface of the well at Rs 9.50 per m2.
Answer» How many cubic metres of earth must be dugout to sink a well 21 m deep and 6 m diameter? Find the cost of plastering the inner surface of the well at Rs 9.50 per m².

Discussion

7148.	Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?
Answer» Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

7148.

Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

Answer»

Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

Discussion

7149.	Show that 3√6 is not a rational number.
Answer» Show that $\sqrt[3]{6}$ is not a rational number.

Discussion

7150.	An irrational number between 5/7 and 7/9 is?
Answer» An irrational number between 5/7 and 7/9 is?

Discussion

Explore topic-wise InterviewSolutions in .

In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, then find x.

If k and 2k are zeros of f(x)=x3+4x2+9kx=90, find k and all three zeros of f(x).

Question 1If one of the zeroes of the quadratic polynomial (k–1)x2+kx+1 is -3, then the value of k is(A)43(B)−43(C)23(D)−23

Observe the given figure and choose the correct statement

How to find irrational numbers between any two irrational or a rational number

Question 1In the given figure, sides QP and RQ of ΔPQR are produced to point S and T respectively, If ∠SPR=135∘ and ∠PQT=110∘, find ∠PRQ.

A parallelogram and a triangle are on equal base and between the same parallel lines. The ratio of their areas is ______.

If A=[1347], then the value of adj(5A) is:

Question 2 (ii)Find the measure of each exterior angle of a regular polygon of:​(ii) 15 sides

Trade amounts for the following countries are: India: $56 millionUSA: $84 millionChina: $120 millionGermany: $44 millionWhat is the average trade done by these countries?

Draw two intersecting lines to include an angle of 30∘. Use ruler and compass to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such point/points exist(s)?

In ΔABC, if AD is a median, which of the following relations holds good?

In triangle ABC points L M and N lie on BC AC and AB respectivelyabd AL BM and CN are concurrent Find numerical value of PL/AL+PM/BM+PN/CN

A kite in the shape of a square with a diagonal 32cm and an isosceles triangles of base 8cm and sides 6cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?

If k and 2k are zeros of f(x)=x3+4x2+9kx=90, find k and all three zeros of f(x).

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB. [CBSE 2014]

Question 2For which value(s) of k will the pair of equations kx + 3y = k – 3, 12x + ky = khas no solution?

In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is ________.

If 4mn+16m2n balloons are to be distributed among 4mn children, how many balloons does each child get, if m=2?

Simplify:(i) (16-1/5)5/2(ii) 32-35(iii) (343)-23(iv) (0.001)1/3(v) (25)3/2×(243)3/5(16)5/4×(8)4/3(vi) 258 ÷ 2513(vii) 5-1×7252×7-47/2 × 5-2×7353×7-5-5/2

In the given fig., the measure of ∠ABC is:

If α,β and γ are the zeroes of the cubic polynomial ax3+bx2+cx+d,then α+β+γ is equal to

Find the equation of a line whose slope = -3 and y-intercept =-1.

1. If X=cosy , find dy/dx in terms of y alone

In the figure given below, state which lines are parallel and why?

in the figure AD IS THE MEDIAN OF A TRIANGLE ABC AND AM perpendicularTO BC. prove that AC square + AB SQUARE = 2AD SQUARE + .5BC SQUARE

Question 94 State whether the statements are True or False. All kites are squares.

The decimal expansion of 178 will terminate after _______ places of decimal.

If perpendiculars from any point within an angle on its arms are congruent, prove tht it lies on the bisector of that angle.

Through any point in the bisector of an angle, a straight line is drawn parallel to either arm of the angle. Prove that the triangle so formed is isosceles.

Simplify each of the following as a single polynomial.(i) (3x + 3) (3x + 2)(ii) (3x − 4) (4x − 3)(iii) (iv) (v) (vi) (vii)

An angle is equal to its supplement. Determine its measure.

If S is the circumcentre of a △ ABC and D,E,F are the feet of the altitudes of △ ABC then prove that SB is perpendicular to DF

Which of these shows an obtuse angled triangle?

Find the value of 1√10. If √10 =3.162

The value of k for which x − 1 is a factor of 4x3 + 3x2 − 4x + k, is(a) 3(b) 1(c) −2(d) −3

Which of the following point lies on the y-axis?

In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.

If a cylindrical vessel has a hemispherical bottom with radius 4 cm and height 15 cm, then its volume is .

At an event, a sum of $1200 was collected from the participants.The correct equation representing the number of participants at the growth talk is

A right angled triangle ABC is constructed with BC = 3 cm and AB + AC = 9 cm. If B is the right angled, then find the length of AC (in cm).5

A copper wire of diameter 6mm is evenly wrapped on a cylinder of length 15cm and diameter 49cm to cover its whole surface. Find the length and volume of the wire. If the specific gravity of copper is 9 grams per cubic cm. Find the weight of the wire

In the given figure, EFGH is a parallelogram, altitudes FK and FI are 8 cm and 4 cm, respectively. If EF = 10 cm, then the area of EFGH is

How many cubic metres of earth must be dugout to sink a well 21 m deep and 6 m diameter? Find the cost of plastering the inner surface of the well at Rs 9.50 per m2.

Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

Show that 3√6 is not a rational number.

An irrational number between 5/7 and 7/9 is?

Question 2 (ii)Find the measure of each exterior angle of a regular polygon of:(ii) 15 sides