24740 + Interview Questions in Mathematics Page 122 InterviewSolution

6051.	What is Emerson's enhancement effect and Red drop effect?
Answer» What is Emerson's enhancement effect and Red drop effect?

Discussion

6052.	Prove that √3+√5 is irrational.
Answer» Prove that $\sqrt{3} + \sqrt{5}$ is irrational.

Discussion

6053.	If the distance of a point P(x, y) from the origin(0,0) is constant, then the point P lies on a _______.
Answer» If the distance of a point P(x, y) from the origin(0,0) is constant, then the point P lies on a _______.

Discussion

6054.	On 1st January, 2019, A draws a bill on B for ₹ 1,000 payable after 3 months. Immediately after its acceptance, A sends the bill to his bank for collection. On the due date, the bill was dishonoured. Record the transactions in the Journals of A and B.
Answer» On 1st January, 2019, A draws a bill on B for ₹ 1,000 payable after 3 months. Immediately after its acceptance, A sends the bill to his bank for collection. On the due date, the bill was dishonoured. Record the transactions in the Journals of A and B.

Discussion

6055.	BC is a chord with centre O. A is a point on an arc BC as shown in the figure. Prove that: (i) ∠BAC+∠OBC=90∘, if A is the point on the major arc (ii) ∠BAC−∠OBC=90∘, if A is the point on the minor arc.
Answer» BC is a chord with centre O. A is a point on an arc BC as shown in the figure. Prove that: (i) $∠ B A C + ∠ O B C = 90^{\circ}$ , if A is the point on the major arc (ii) $∠ B A C - ∠ O B C = 90^{\circ}$ , if A is the point on the minor arc.

6055.

BC is a chord with centre O. A is a point on an arc BC as shown in the figure. Prove that: (i) ∠BAC+∠OBC=90∘, if A is the point on the major arc (ii) ∠BAC−∠OBC=90∘, if A is the point on the minor arc.

Answer»

BC is a chord with centre O. A is a point on an arc BC as shown in the figure. Prove that:

(i) $∠ B A C + ∠ O B C = 90^{\circ}$ , if A is the point on the major arc

(ii) $∠ B A C - ∠ O B C = 90^{\circ}$ , if A is the point on the minor arc.

Discussion

6056.	The area surrounded by a conical tent is 4526 m2. If the cost of canvas is Rs. 17 per square meter, then find the total cost of canvas.
Answer» The area surrounded by a conical tent is 4526 m². If the cost of canvas is Rs. 17 per square meter, then find the total cost of canvas.

Discussion

6057.	An oil tin in the shape of a cuboid having dimensions, 26 cm × 26 cm × 45 cm . If 1 sq. m sheet costs ₹10 , then find the total cost for making 20 such tins.
Answer» An oil tin in the shape of a cuboid having dimensions, 26 cm $\times$ 26 cm $\times$ 45 cm . If 1 sq. m sheet costs ₹10 , then find the total cost for making 20 such tins.

Discussion

6058.	In a right triangle, the hypotenuse is the __side
Answer» In a right triangle, the hypotenuse is the __side

Discussion

6059.	What is theory of relativity
Answer» What is theory of relativity

Discussion

6060.	(5 tan-1)-2
Answer» (5 tan^-1)^-2

Discussion

6061.	4p³ -12p²- 37p -15 ÷2p+1
Answer» 4p³ -12p²- 37p -15 ÷2p+1

Discussion

6062.	The capital invested by A is triple the capital invested by B. The capital invested by B is four times the capital invested by C. Then the ratio of their profit split is ______.
Answer» The capital invested by A is triple the capital invested by B. The capital invested by B is four times the capital invested by C. Then the ratio of their profit split is ______.

Discussion

6063.	32. Xsquare - 2ax + asquare-bsquarw solve for x by factorisation method
Answer» 32. Xsquare - 2ax + asquare-bsquarw solve for x by factorisation method

Discussion

6064.	Solve the following pair of equations and choose the correct answer. 2x + y = 7 3x + 2y = 12
Answer» Solve the following pair of equations and choose the correct answer. 2x + y = 7 3x + 2y = 12

Discussion

6065.	A caution sign is shown in the given figure. Find the area to be painted in red (shaded in figure), in order to warn the people about the danger ahead. [Use √3=1.732]
Answer» A caution sign is shown in the given figure. Find the area to be painted in red (shaded in figure), in order to warn the people about the danger ahead. [Use $\sqrt{3} = 1.732$ ]

Discussion

6066.	Which of the following collections are sets ? Justify your answer :(i) A collection of all natural numbers less than 50.(ii) The collection of good hockey players in India.(iii) The collection of all girls in your class.
Answer» Which of the following collections are sets ? Justify your answer : (i) A collection of all natural numbers less than 50. (ii) The collection of good hockey players in India. (iii) The collection of all girls in your class.

6066.

Which of the following collections are sets ? Justify your answer :(i) A collection of all natural numbers less than 50.(ii) The collection of good hockey players in India.(iii) The collection of all girls in your class.

Answer»

Which of the following collections are sets ? Justify your answer :

(i) A collection of all natural numbers less than 50.

(ii) The collection of good hockey players in India.

(iii) The collection of all girls in your class.

Discussion

6067.	The value of c for which the conclusion of Lagrange's Theorem holds for the function f(x)=√a2−x2,a>1 on the interval [1,a]
Answer» The value of $c$ for which the conclusion of Lagrange's Theorem holds for the function $f (x) = \sqrt{a^{2} - x^{2}}, a > 1$ on the interval $[1, a]$

Discussion

6068.	21. Prove that - tan15^°+cot 15^°=4
Answer» 21. Prove that - tan15^°+cot 15^°=4

Discussion

6069.	1+sin θ1-sin θ is equal to(a) sec θ + tan θ(b) sec θ − tan θ(c) sec2 θ + tan2 θ(d) sec2 θ − tan2 θ
Answer» $\sqrt{\frac{1 + \sin θ}{1 - \sin θ}}$ is equal to (a) sec θ + tan θ (b) sec θ − tan θ (c) sec² θ + tan² θ (d) sec² θ − tan² θ

Discussion

6070.	3. Two identical circles intersect at (0,5) and (0,-5). Each circle passes through the centre of the other circle. Find the area of either circle.
Answer» 3. Two identical circles intersect at (0,5) and (0,-5). Each circle passes through the centre of the other circle. Find the area of either circle.

Discussion

6071.	Question 5 ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ ABD=∠ ACD.
Answer» Question 5 ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that $∠ A B D = ∠ A C D .$

Discussion

6072.	Question 19The point of the term (a, -a) always lies on the line:A) x = aB) y = -aC) y = xD) x + y = 0
Answer» Question 19 The point of the term (a, -a) always lies on the line: A) x = a B) y = -a C) y = x D) x + y = 0

Discussion

6073.	If X is the mean of n values x1, x2, ......,xn of variable X, then ∑i=1n(xi-X) is always equal to _____________.
Answer» If $X$ is the mean of n values x₁, x₂, ......,x_n of variable X, then $\sum_{i = 1}^{n} (x_{i} - X)$ is always equal to _____________.

Discussion

6074.	Abscissa of a point is positive in
Answer» Abscissa of a point is positive in

Discussion

6075.	For the set of numbers 2, 2, 4, 5 and 12, which of the following statements is true?(a) Mean = Median(b) Mean > Mode(c) Mean > Mode(d) Mode = Median
Answer» For the set of numbers 2, 2, 4, 5 and 12, which of the following statements is true? (a) Mean = Median (b) Mean > Mode (c) Mean > Mode (d) Mode = Median

Discussion

6076.	Let there be a polynomial P(x) and any real number ‘a’. When the polynomial P(x) is divided by (x – a) the remainder obtained is P(a). The above statement is often concluded as
Answer» Let there be a polynomial P(x) and any real number ‘a’. When the polynomial P(x) is divided by (x – a) the remainder obtained is P(a). The above statement is often concluded as

Discussion

6077.	By using elementary operations, find the inverse of the matrix A=[122−1]
Answer» By using elementary operations, find the inverse of the matrix $A = [\begin{matrix} 1 & 2 2 & - 1 \end{matrix}]$

Discussion

6078.	Factorise:x2-22x-30
Answer» Factorise: $x^{2} - 2 \sqrt{2} x - 30$

Discussion

6079.	Express 0.4¯7 in the form pq, where p and q are integers and q≠0.
Answer» Express $0.4 ¯ 7$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

Discussion

6080.	Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a rhombus.
Answer» Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a rhombus.

Discussion

6081.	Why any number power 0 =1?
Answer» Why any number power 0 =1?

Discussion

6082.	The pair of lines and 2x−7y−5=0 are consistent.
Answer» The pair of lines and $2 x - 7 y - 5 = 0$ are consistent.

Discussion

6083.	96.Find the number of words that can be formed by selecting 5 letters of the word INDEPENDENT
Answer» 96.Find the number of words that can be formed by selecting 5 letters of the word INDEPENDENT

Discussion

6084.	The curved surface area of a cone is 4070 cm2 and its diameter is 70 cm. What is its slant height? (Use π = 22/7).
Answer» The curved surface area of a cone is 4070 cm² and its diameter is 70 cm. What is its slant height? (Use $π$ = 22/7).

Discussion

6085.	What is the result when we convert 0.625 into a fraction in its simplest form?
Answer» What is the result when we convert 0.625 into a fraction in its simplest form?

Discussion

6086.	In a triangle, P, Q and R are the mid points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, the perimeter of the quadrilateral ARPQ is
Answer» In a triangle, P, Q and R are the mid points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, the perimeter of the quadrilateral ARPQ is

6086.

In a triangle, P, Q and R are the mid points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, the perimeter of the quadrilateral ARPQ is

Answer»

In a triangle, P, Q and R are the mid points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, the perimeter of the quadrilateral ARPQ is

Discussion

6087.	Work out the surface area of the following shape.
Answer» Work out the surface area of the following shape.

Discussion

6088.	The pillars of an apartment are in a cylindrical shape. If each pillar has a circular base of radius 40 cm and height 20 m, then how much concrete would be required to build 7 such pillars?
Answer» The pillars of an apartment are in a cylindrical shape. If each pillar has a circular base of radius 40 cm and height 20 m, then how much concrete would be required to build 7 such pillars?

Discussion

6089.	In the given figure, L and M are the mid- points of AB and BC respectively.(i) If AB = BC, prove that AL = MC.(ii) If BL = BM, prove that AB = BC.Hint(i) AB=BC⇒12AB=12BC⇒AL=MC.(ii) BL=BM⇒2BL=2BM⇒AB=BC.
Answer» In the given figure, L and M are the mid- points of AB and BC respectively. (i) If AB = BC, prove that AL = MC. (ii) If BL = BM, prove that AB = BC. Hint (i) $A B = B C \Rightarrow \frac{1}{2} A B = \frac{1}{2} B C \Rightarrow A L = M C$ . (ii) $B L = B M \Rightarrow 2 B L = 2 B M \Rightarrow A B = B C$ .

Discussion

6090.	From the following figure, prove that θ+ϕ=90∘. Also prove that there are two other right angled triangle. Find sinα,cosβ and tanϕ.
Answer» From the following figure, prove that $θ + ϕ = 90^{\circ}$ . Also prove that there are two other right angled triangle. Find $sin α, cos β a n d tan ϕ .$

Discussion

6091.	Read the figure. On the basis of this figure match the Column-I with Column-II. Column-IColumn-II(A) Co-ordinates of point C is(p) −5(B) The abscissa of point E is(q) (0,0)(C) The ordinate of the point F is(r) 0(D) Co-ordinates of point O is(s) (−5,3) Choose the correct option:
Answer» Read the figure. On the basis of this figure match the Column-I with Column-II. $\begin{matrix} Column-I & Column-II (A) Co-ordinates of point C is & (p) - 5 (B) The abscissa of point E is & (q) (0, 0) (C) The ordinate of the point F is & (r) 0 (D) Co-ordinates of point O is & (s) (- 5, 3) \end{matrix}$ Choose the correct option:

Discussion

6092.	Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is
Answer» Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is

6092.

Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is

Answer»

Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is

Discussion

6093.	In the given figure, AB∥DC, BO = 6 cm and DO = 8 cm; find BP×DO
Answer» In the given figure, $A B ∥ D C$ , BO = 6 cm and DO = 8 cm; find $B P \times D O$

6093.

In the given figure, AB∥DC, BO = 6 cm and DO = 8 cm; find BP×DO

Answer»

In the given figure, $A B ∥ D C$ , BO = 6 cm and DO = 8 cm; find $B P \times D O$

Discussion

6094.	D is a point on the side BC of ΔABC such that ∠ADC=∠BAC. Prove that CACD=CBCA or, CA2=CB×CD. [2 MARKS]
Answer» D is a point on the side BC of $Δ A B C$ such that $∠ A D C = ∠ B A C$ . Prove that $\frac{C A}{C D} = \frac{C B}{C A}$ or, $C A^{2} = C B \times C D$ . [2 MARKS]

Discussion

6095.	In the given figure, AE is the diameter of the circle. Write down the numerical value of ∠ ABC + ∠ CDE. Give reasons for your answer.
Answer» In the given figure, AE is the diameter of the circle. Write down the numerical value of $∠$ ABC + $∠$ CDE. Give reasons for your answer.

6095.

In the given figure, AE is the diameter of the circle. Write down the numerical value of ∠ ABC + ∠ CDE. Give reasons for your answer.

Answer»

In the given figure, AE is the diameter of the circle. Write down the numerical value of $∠$ ABC + $∠$ CDE. Give reasons for your answer.

Discussion

6096.	The length of a cuboid is twice its breadth. The breadth is twice its height. Then, the ratio of LSA to TSA is .
Answer» The length of a cuboid is twice its breadth. The breadth is twice its height. Then, the ratio of LSA to TSA is .

Discussion

6097.	Question 1 (i)Classify 2−√5 as rational or irrational.
Answer» Question 1 (i) Classify $2 - \sqrt{5}$ as rational or irrational.

Discussion

6098.	Question 92 (xvi) Factorise the following using the identity a2−b2=(a+b)(a−b). 1331x3y−11y3x
Answer» Question 92 (xvi) Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$ $1331 x^{3} y - 11 y^{3} x$

6098.

Question 92 (xvi) Factorise the following using the identity a2−b2=(a+b)(a−b). 1331x3y−11y3x

Answer»

Question 92 (xvi)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$1331 x^{3} y - 11 y^{3} x$

Discussion

6099.	Find the reference angle for 220 degree
Answer» Find the reference angle for 220 degree

Discussion

6100.	74. Draw the graph of linear equation x=4 and y=5.Find the area formed by the two graphs and the axis
Answer» 74. Draw the graph of linear equation x=4 and y=5.Find the area formed by the two graphs and the axis

Discussion

Explore topic-wise InterviewSolutions in .

What is Emerson's enhancement effect and Red drop effect?

Prove that √3+√5 is irrational.

If the distance of a point P(x, y) from the origin(0,0) is constant, then the point P lies on a _______.

On 1st January, 2019, A draws a bill on B for ₹ 1,000 payable after 3 months. Immediately after its acceptance, A sends the bill to his bank for collection. On the due date, the bill was dishonoured. Record the transactions in the Journals of A and B.

BC is a chord with centre O. A is a point on an arc BC as shown in the figure. Prove that: ​ (i) ∠BAC+∠OBC=90∘, if A is the point on the major arc (ii) ∠BAC−∠OBC=90∘, if A is the point on the minor arc.

The area surrounded by a conical tent is 4526 m2. If the cost of canvas is Rs. 17 per square meter, then find the total cost of canvas.

An oil tin in the shape of a cuboid having dimensions, 26 cm × 26 cm × 45 cm . If 1 sq. m sheet costs ₹10 , then find the total cost for making 20 such tins.

In a right triangle, the hypotenuse is the __side

What is theory of relativity

(5 tan-1)-2

4p³ -12p²- 37p -15 ÷2p+1

The capital invested by A is triple the capital invested by B. The capital invested by B is four times the capital invested by C. Then the ratio of their profit split is ______.

32. Xsquare - 2ax + asquare-bsquarw solve for x by factorisation method

Solve the following pair of equations and choose the correct answer. 2x + y = 7 3x + 2y = 12

A caution sign is shown in the given figure. Find the area to be painted in red (shaded in figure), in order to warn the people about the danger ahead. [Use √3=1.732]

Which of the following collections are sets ? Justify your answer :(i) A collection of all natural numbers less than 50.(ii) The collection of good hockey players in India.(iii) The collection of all girls in your class.

The value of c for which the conclusion of Lagrange's Theorem holds for the function f(x)=√a2−x2,a&gt;1 on the interval [1,a]

21. Prove that - tan15^°+cot 15^°=4

1+sin θ1-sin θ is equal to(a) sec θ + tan θ(b) sec θ − tan θ(c) sec2 θ + tan2 θ(d) sec2 θ − tan2 θ

3. Two identical circles intersect at (0,5) and (0,-5). Each circle passes through the centre of the other circle. Find the area of either circle.

Question 5 ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ ABD=∠ ACD.

Question 19The point of the term (a, -a) always lies on the line:A) x = aB) y = -aC) y = x​​​​​​​D) x + y = 0​​​​​​​

If X is the mean of n values x1, x2, ......,xn of variable X, then ∑i=1n(xi-X) is always equal to _____________.

Abscissa of a point is positive in

For the set of numbers 2, 2, 4, 5 and 12, which of the following statements is true?(a) Mean = Median(b) Mean > Mode(c) Mean > Mode(d) Mode = Median

Let there be a polynomial P(x) and any real number ‘a’. When the polynomial P(x) is divided by (x – a) the remainder obtained is P(a). The above statement is often concluded as

By using elementary operations, find the inverse of the matrix A=[122−1]

Factorise:x2-22x-30

Express 0.4¯7 in the form pq, where p and q are integers and q≠0.

Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a rhombus.

Why any number power 0 =1?

The pair of lines and 2x−7y−5=0 are consistent.

96.Find the number of words that can be formed by selecting 5 letters of the word INDEPENDENT

The curved surface area of a cone is 4070 cm2 and its diameter is 70 cm. What is its slant height? (Use π = 22/7).

What is the result when we convert 0.625 into a fraction in its simplest form?

In a triangle, P, Q and R are the mid points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, the perimeter of the quadrilateral ARPQ is

Work out the surface area of the following shape.

The pillars of an apartment are in a cylindrical shape. If each pillar has a circular base of radius 40 cm and height 20 m, then how much concrete would be required to build 7 such pillars?

In the given figure, L and M are the mid- points of AB and BC respectively.(i) If AB = BC, prove that AL = MC.(ii) If BL = BM, prove that AB = BC.Hint(i) AB=BC⇒12AB=12BC⇒AL=MC.(ii) BL=BM⇒2BL=2BM⇒AB=BC.

From the following figure, prove that θ+ϕ=90∘. Also prove that there are two other right angled triangle. Find sinα,cosβ and tanϕ.

Read the figure. On the basis of this figure match the Column-I with Column-II. Column-IColumn-II(A) Co-ordinates of point C is(p) −5(B) The abscissa of point E is(q) (0,0)(C) The ordinate of the point F is(r) 0(D) Co-ordinates of point O is(s) (−5,3) Choose the correct option:

Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is

In the given figure, AB∥DC, BO = 6 cm and DO = 8 cm; find BP×DO

D is a point on the side BC of ΔABC such that ∠ADC=∠BAC. Prove that CACD=CBCA or, CA2=CB×CD. [2 MARKS]

In the given figure, AE is the diameter of the circle. Write down the numerical value of ∠ ABC + ∠ CDE. Give reasons for your answer.

The length of a cuboid is twice its breadth. The breadth is twice its height. Then, the ratio of LSA to TSA is .

Question 1 (i)Classify 2−√5 as rational or irrational.

Question 92 (xvi) Factorise the following using the identity a2−b2=(a+b)(a−b). 1331x3y−11y3x

Find the reference angle for 220 degree

74. Draw the graph of linear equation x=4 and y=5.Find the area formed by the two graphs and the axis

BC is a chord with centre O. A is a point on an arc BC as shown in the figure. Prove that: (i) ∠BAC+∠OBC=90∘, if A is the point on the major arc (ii) ∠BAC−∠OBC=90∘, if A is the point on the minor arc.

The value of c for which the conclusion of Lagrange's Theorem holds for the function f(x)=√a2−x2,a>1 on the interval [1,a]

Question 19The point of the term (a, -a) always lies on the line:A) x = aB) y = -aC) y = xD) x + y = 0