24740 + Interview Questions in Mathematics Page 179 InterviewSolution

8901.	23.43¯ when expressed in the form pq(p, q are integers q ≠ 0), is(a) 232099(b) 2343100(c) 2343999(d) 2320199
Answer» $23 . \bar{43}$ when expressed in the form $\frac{p}{q}$ (p, q are integers q ≠ 0), is (a) $\frac{2320}{99}$ (b) $\frac{2343}{100}$ (c) $\frac{2343}{999}$ (d) $\frac{2320}{199}$

Discussion

8902.	The vertical angle of an isosceles triangle is 100°. Find its base angles.
Answer» The vertical angle of an isosceles triangle is 100°. Find its base angles.

Discussion

8903.	Use the given figure to find : (i) ∠ BAD. (ii) ∠ DQB.
Answer» Use the given figure to find : (i) $∠$ BAD. (ii) $∠$ DQB.

8903.

Use the given figure to find : (i) ∠ BAD. (ii) ∠ DQB.

Answer»

Use the given figure to find :

(i) $∠$ BAD.

(ii) $∠$ DQB.

Discussion

8904.	The value of 5+26 is(a) 3-2(b) 3+2(c) 5+6(d) none of these
Answer» The value of $\sqrt{5 + 2 \sqrt{6}}$ is (a) $\sqrt{3} - \sqrt{2}$ (b) $\sqrt{3} + \sqrt{2}$ (c) $\sqrt{5} + \sqrt{6}$ (d) none of these

Discussion

8905.	An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are(a) 48°, 60°, 72°(b) 50°, 60°, 70°(c) 52°, 56°, 72°(d) 42°, 60°, 76°
Answer» An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are (a) 48°, 60°, 72° (b) 50°, 60°, 70° (c) 52°, 56°, 72° (d) 42°, 60°, 76°

Discussion

8906.	If D is the mid-point of side BC of ∆ABC and AB→+AC→=k AD→ , then k = ______________.
Answer» If D is the mid-point of side BC of $∆ A B C and \vec{A B} + \vec{A C} = k \vec{A D}$ , then k = ______________.

Discussion

8907.	A rod of uniform thickness is placed along x axis with end point at origin.If length of rod is L and its linear mass density is proportional to x find dis†an ce of its centre of mass from origin
Answer» A rod of uniform thickness is placed along x axis with end point at origin.If length of rod is L and its linear mass density is proportional to x find dis†an ce of its centre of mass from origin

Discussion

8908.	Which of the following given lengths can be the sides of a triangle?
Answer» Which of the following given lengths can be the sides of a triangle?

Discussion

8909.	The area of an isosceles right triangle is 128 cm2. Find the length of its hypotenuse
Answer» The area of an isosceles right triangle is 128 cm2. Find the length of its hypotenuse

Discussion

8910.	Factorise:32x2+16x+10
Answer» Factorise: $\frac{3}{2} x^{2} + 16 x + 10$

Discussion

8911.	Area of parallelogram ABCD equals to 100 cm2. What is the area of Δ DEC?
Answer» Area of parallelogram ABCD equals to 100 $c m^{2}$ . What is the area of $Δ$ DEC?

Discussion

8912.	The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class 10.6. Then the upper class boundary of the highest class is(a) 35.6(b) 33.1(c) 30.6(d) 28.1
Answer» The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class 10.6. Then the upper class boundary of the highest class is (a) 35.6 (b) 33.1 (c) 30.6 (d) 28.1

Discussion

8913.	18. Find the area enclosed by the lines 3x²–5xy+y²=0 and y=6.
Answer» 18. Find the area enclosed by the lines 3x²–5xy+y²=0 and y=6.

Discussion

8914.	sketch a graph for \| y \| = \| 1- \|x - 1\|\|
Answer» sketch a graph for \| y \| = \| 1- \|x - 1\|\|

Discussion

8915.	Let P=⎡⎢⎣1004101641⎤⎥⎦ and I be the identity matrix of order 3. If Q=[qij] is a matrix such that P50−Q=I, then q31+q32q21 equals
Answer» $Let P = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 4 & 1 & 0 16 & 4 & 1 \end{matrix} ⎤ ⎥ ⎦$ and $I$ be the identity matrix of order $3.$ If $Q = [q_{i j}]$ is a matrix such that $P^{50} - Q = I,$ then $\frac{q_{31} + q_{32}}{q_{21}}$ equals

Discussion

8916.	A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30∘ to 45∘ in 12 minutes, find the time taken by the car now to reach the tower.
Answer» A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from $30^{\circ}$ to $45^{\circ}$ in 12 minutes, find the time taken by the car now to reach the tower.

Discussion

8917.	In figure AN and CP are perpendiculars to the diagonal BD of a parallelogram ABCD.Prove that:(1) △ADN≅△CBP (2) AN = CP
Answer» In figure AN and CP are perpendiculars to the diagonal BD of a parallelogram ABCD. Prove that: (1) $△ A D N ≅ △ C B P$ (2) AN = CP

Discussion

8918.	The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rhombus, if(a) ABCD is a Parallelogram(b) ABCD is rhombus(c) diagonals of ABCD are equal(4) diagonals of ABCD are perpendicular to each other.
Answer» The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rhombus, if (a) ABCD is a Parallelogram (b) ABCD is rhombus (c) diagonals of ABCD are equal (4) diagonals of ABCD are perpendicular to each other.

Discussion

8919.	If √13−x√10=√8+√5 then the value of x is
Answer» If $\sqrt{13 - x \sqrt{10}}$ = $\sqrt{8} + \sqrt{5}$ then the value of x is

Discussion

8920.	In the triangle ABC. the. Bisector of angel. B. and C intersect each other at the point Of proof that angle BOC =90-1/2 angel A
Answer» In the triangle ABC. the. Bisector of angel. B. and C intersect each other at the point Of proof that angle BOC =90-1/2 angel A

Discussion

8921.	In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa told Chameli, “I think ABCD is a square”. State whether Champa's statement is correct or not.
Answer» In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa told Chameli, “I think ABCD is a square”. State whether Champa's statement is correct or not.

Discussion

8922.	AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that(i) ΔDAP ≅ ΔEBP(ii) AD = BE
Answer» AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that (i) ΔDAP ≅ ΔEBP (ii) AD = BE

8922.

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that(i) ΔDAP ≅ ΔEBP(ii) AD = BE

Answer»

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that

(i) ΔDAP ≅ ΔEBP

(ii) AD = BE

Discussion

8923.	Calculate the mean and the median for the following continuous frequency distributions. Class0−1010−2020−3030−4040−5050−6060−70fi68202515104
Answer» Calculate the mean and the median for the following continuous frequency distributions. $\begin{matrix} C l a s s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 f_{i} & 6 & 8 & 20 & 25 & 15 & 10 & 4 \end{matrix}$

8923.

Calculate the mean and the median for the following continuous frequency distributions. Class0−1010−2020−3030−4040−5050−6060−70fi68202515104

Answer»

Calculate the mean and the median for the following continuous frequency distributions.

$\begin{matrix} C l a s s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 f_{i} & 6 & 8 & 20 & 25 & 15 & 10 & 4 \end{matrix}$

Discussion

8924.	The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is(a) (–5, 0)(b) (0, –5)(c) (5, 0)(d) (0, 5)
Answer» The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is (a) (–5, 0) (b) (0, –5) (c) (5, 0) (d) (0, 5)

Discussion

8925.	In the given figure, BA \|\| ED and BC \|\| EF. Show that ∠ABC=∠DEF.
Answer» In the given figure, BA \|\| ED and BC \|\| EF. Show that $∠ A B C = ∠ D E F$ .

8925.

In the given figure, BA || ED and BC || EF. Show that ∠ABC=∠DEF.

Answer»

In the given figure, BA || ED and BC || EF. Show that $∠ A B C = ∠ D E F$ .

Discussion

8926.	In a parallelogram ABCD, the bisector of ∠A also bisects BC at X. Find AB : AD.
Answer» In a parallelogram ABCD, the bisector of ∠A also bisects BC at X. Find AB : AD.

Discussion

8927.	2x4 − 7x3 − 13x2 + 63x − 45
Answer» 2x⁴ − 7x³ − 13x² + 63x − 45

Discussion

8928.	Insert commas suitably and write the names according to Indian System of Numeration:87595762
Answer» Insert commas suitably and write the names according to Indian System of Numeration: 87595762

Discussion

8929.	Question 140The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square equal in area to the sum of the first two squares.
Answer» Question 140 The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

8929.

Question 140The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Answer»

Question 140

The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Discussion

8930.	In a shop, 380 people buy socks, 150 people buy shoes, and 200 people buy belts. If there are a total of 580 people who bought either socks or shoes or belts and only 30 people bought all the three things? So, how many people bought exactly two things?
Answer» In a shop, $380$ people buy socks, $150$ people buy shoes, and $200$ people buy belts. If there are a total of $580$ people who bought either socks or shoes or belts and only $30$ people bought all the three things? So, how many people bought exactly two things?

Discussion

8931.	The curved surface area of a cylinder is 250 sq.cm. If the circumference of its base is 25cm, then its height is ____.
Answer» The curved surface area of a cylinder is 250 sq.cm. If the circumference of its base is 25cm, then its height is ____.

Discussion

8932.	Find the diameter of the circle (in feet) if the circumference of the circle is 3140 feet.[Use π = 3.14]1000
Answer» Find the diameter of the circle (in feet) if the circumference of the circle is 3140 feet. [Use π = 3.14] 1000

Discussion

8933.	One of the exterior angles of a triangle is 80∘ and the interior opposite angles are in the ratio 3 : 5. Find the angles of the triangle.
Answer» One of the exterior angles of a triangle is $80^{\circ}$ and the interior opposite angles are in the ratio 3 : 5. Find the angles of the triangle.

Discussion

8934.	Which of the following cannot be a part of a set of rational numbers?
Answer» Which of the following cannot be a part of a set of rational numbers?

Discussion

8935.	The following bar graph gives the marks scored by 3 students, Shubh, Aman and Anurag out of 100. Whose average score is highest in all the 3 subjects?
Answer» The following bar graph gives the marks scored by 3 students, Shubh, Aman and Anurag out of 100. Whose average score is highest in all the 3 subjects?

8935.

The following bar graph gives the marks scored by 3 students, Shubh, Aman and Anurag out of 100. Whose average score is highest in all the 3 subjects?

Answer»

The following bar graph gives the marks scored by 3 students, Shubh, Aman and Anurag out of 100. Whose average score is highest in all the 3 subjects?

Discussion

8936.	If x square +x+1=0 then find the value of summasion of x^r +1÷x^r
Answer» If x square +x+1=0 then find the value of summasion of x^r +1÷x^r

Discussion

8937.	In the figure, if ∠BAC=60o and ∠BCA=20o, find ∠ADC
Answer» In the figure, if $∠ B A C = 60^{o} a n d ∠ B C A = 20^{o}, f i n d ∠ A D C$

8937.

In the figure, if ∠BAC=60o and ∠BCA=20o, find ∠ADC

Answer»

In the figure, if $∠ B A C = 60^{o} a n d ∠ B C A = 20^{o}, f i n d ∠ A D C$

Discussion

8938.	ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Which of the following should be true?
Answer» ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Which of the following should be true?

Discussion

8939.	Question 119 (iii) Write a positive integer and a negative integer whose difference is a negative integer.
Answer» Question 119 (iii) Write a positive integer and a negative integer whose difference is a negative integer.

8939.

Question 119 (iii) Write a positive integer and a negative integer whose difference is a negative integer.

Answer»

Question 119 (iii)

Write a positive integer and a negative integer whose difference is a negative integer.

Discussion

8940.	The graph of the linear equation: 2x+3y=6, cuts the y-axis at the point:
Answer» The graph of the linear equation: 2x+3y=6, cuts the y-axis at the point:

Discussion

8941.	P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.
Answer» P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.

Discussion

8942.	How to find area of triangle?
Answer» How to find area of triangle?

Discussion

8943.	Find the area of shaded portion in the given figure. [2 MARKS]
Answer» Find the area of shaded portion in the given figure. [2 MARKS]

8943.

Find the area of shaded portion in the given figure. [2 MARKS]

Answer»

Find the area of shaded portion in the given figure. [2 MARKS]

Discussion

8944.	If √2=1.4142, then find the value of √2 −1√2 +1
Answer» If $\sqrt{2}$ =1.4142, then find the value of $\frac{\sqrt{2} - 1}{\sqrt{2} + 1}$

Discussion

8945.	In the figure given below, prove that BC < AC < CD.
Answer» In the figure given below, prove that BC < AC < CD.

Discussion

8946.	In the figure, p is a transversal to lines m and n, ∠2=1200 and ∠5=600. Prove that m\|\|n
Answer» In the figure, p is a transversal to lines m and n, $∠ 2 = 120^{0} a n d ∠ 5 = 60^{0}$ . Prove that m\|\|n

8946.

In the figure, p is a transversal to lines m and n, ∠2=1200 and ∠5=600. Prove that m||n

Answer»

In the figure, p is a transversal to lines m and n, $∠ 2 = 120^{0} a n d ∠ 5 = 60^{0}$ . Prove that m||n

Discussion

8947.	Question 2The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.
Answer» Question 2 The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

Discussion

8948.	Which of the following is a linear polynomial?
Answer» Which of the following is a linear polynomial?

Discussion

8949.	Kishan's father took a loan from the bank at 12.5% interest p.a. for 4 years. Calculate the total amount that he paid at the end of 4 years if the loan taken was 10000 times the interest rate.
Answer» Kishan's father took a loan from the bank at 12.5% interest p.a. for 4 years. Calculate the total amount that he paid at the end of 4 years if the loan taken was 10000 times the interest rate.

8949.

Kishan's father took a loan from the bank at 12.5% interest p.a. for 4 years. Calculate the total amount that he paid at the end of 4 years if the loan taken was 10000 times the interest rate.

Answer»

Kishan's father took a loan from the bank at 12.5% interest p.a. for 4 years.

Calculate the total amount that he paid at the end of 4 years if the loan taken was 10000 times the interest rate.

Discussion

8950.	How does AB the whole square =32 has changed into 4\sqrt2
Answer» How does AB the whole square =32 has changed into 4\sqrt2

Discussion

Explore topic-wise InterviewSolutions in .

23.43¯ when expressed in the form pq(p, q are integers q ≠ 0), is(a) 232099(b) 2343100(c) 2343999(d) 2320199

The vertical angle of an isosceles triangle is 100°. Find its base angles.

Use the given figure to find : (i) ∠ BAD. (ii) ∠ DQB.

The value of 5+26 is(a) 3-2(b) 3+2(c) 5+6(d) none of these

An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are(a) 48°, 60°, 72°(b) 50°, 60°, 70°(c) 52°, 56°, 72°(d) 42°, 60°, 76°

If D is the mid-point of side BC of ∆ABC and AB→+AC→=k AD→ , then k = ______________.

A rod of uniform thickness is placed along x axis with end point at origin.If length of rod is L and its linear mass density is proportional to x find dis†an ce of its centre of mass from origin

Which of the following given lengths can be the sides of a triangle?

The area of an isosceles right triangle is 128 cm2. Find the length of its hypotenuse

Factorise:32x2+16x+10

Area of parallelogram ABCD equals to 100 cm2. What is the area of Δ DEC?

The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class 10.6. Then the upper class boundary of the highest class is(a) 35.6(b) 33.1(c) 30.6(d) 28.1

18. Find the area enclosed by the lines 3x²–5xy+y²=0 and y=6.

sketch a graph for | y | = | 1- |x - 1||

Let P=⎡⎢⎣1004101641⎤⎥⎦ and I be the identity matrix of order 3. If Q=[qij] is a matrix such that P50−Q=I, then q31+q32q21 equals

A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30∘ to 45∘ in 12 minutes, find the time taken by the car now to reach the tower.

In figure AN and CP are perpendiculars to the diagonal BD of a parallelogram ABCD.Prove that:(1) △ADN≅△CBP (2) AN = CP

The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rhombus, if(a) ABCD is a Parallelogram(b) ABCD is rhombus(c) diagonals of ABCD are equal(4) diagonals of ABCD are perpendicular to each other.

If √13−x√10=√8+√5 then the value of x is

In the triangle ABC. the. Bisector of angel. B. and C intersect each other at the point Of proof that angle BOC =90-1/2 angel A

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa told Chameli, “I think ABCD is a square”. State whether Champa's statement is correct or not.

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that(i) ΔDAP ≅ ΔEBP(ii) AD = BE

Calculate the mean and the median for the following continuous frequency distributions. Class0−1010−2020−3030−4040−5050−6060−70fi68202515104

The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is(a) (–5, 0)(b) (0, –5)(c) (5, 0)(d) (0, 5)

In the given figure, BA || ED and BC || EF. Show that ∠ABC=∠DEF.

In a parallelogram ABCD, the bisector of ∠A also bisects BC at X. Find AB : AD.

2x4 − 7x3 − 13x2 + 63x − 45

Insert commas suitably and write the names according to Indian System of Numeration:87595762

Question 140The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

In a shop, 380 people buy socks, 150 people buy shoes, and 200 people buy belts. If there are a total of 580 people who bought either socks or shoes or belts and only 30 people bought all the three things? So, how many people bought exactly two things?

The curved surface area of a cylinder is 250 sq.cm. If the circumference of its base is 25cm, then its height is ____.

Find the diameter of the circle (in feet) if the circumference of the circle is 3140 feet.[Use π = 3.14]1000

One of the exterior angles of a triangle is 80∘ and the interior opposite angles are in the ratio 3 : 5. Find the angles of the triangle.

Which of the following cannot be a part of a set of rational numbers?

The following bar graph gives the marks scored by 3 students, Shubh, Aman and Anurag out of 100. Whose average score is highest in all the 3 subjects?

If x square +x+1=0 then find the value of summasion of x^r +1÷x^r

In the figure, if ∠BAC=60o and ∠BCA=20o, find ∠ADC

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Which of the following should be true?

Question 119 (iii) Write a positive integer and a negative integer whose difference is a negative integer.

The graph of the linear equation: 2x+3y=6, cuts the y-axis at the point:

P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.

How to find area of triangle?

Find the area of shaded portion in the given figure. [2 MARKS]

If √2=1.4142, then find the value of √2 −1√2 +1

In the figure given below, prove that BC < AC < CD.

In the figure, p is a transversal to lines m and n, ∠2=1200 and ∠5=600. Prove that m||n

Question 2The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

Which of the following is a linear polynomial?

Kishan's father took a loan from the bank at 12.5% interest p.a. for 4 years. Calculate the total amount that he paid at the end of 4 years if the loan taken was 10000 times the interest rate.

How does AB the whole square =32 has changed into 4\sqrt2