24740 + Interview Questions in Mathematics Page 56 InterviewSolution

2751.	The total surface area of a cubical die is 24 cm2. Find the length of each edge?
Answer» The total surface area of a cubical die is 24 cm². Find the length of each edge?

Discussion

2752.	Let ¯a=2¯i−3¯j+^k,¯b=^i−^j+3^k and ¯c=^i+^j−^k Then the system of vectors ¯a,¯band¯c
Answer» Let $¯ a = 2 ¯ i - 3 ¯ j +^k, ¯ b =^i -^j + 3^k a n d ¯ c =^i +^j -^k$ Then the system of vectors $¯ a, ¯ b a n d ¯ c$

Discussion

2753.	Without using calculating devices, compute the following correct to two decimals.(i) (ii) (iii)
Answer» Without using calculating devices, compute the following correct to two decimals. (i) (ii) (iii)

2753.

Without using calculating devices, compute the following correct to two decimals.(i) (ii) (iii)

Answer»

Without using calculating devices, compute the following correct to two decimals.

(i)

(ii)

(iii)

Discussion

2754.	What is the proof of the equation of a chord passing through a (acos(x);bSin(x)) and (a cos(y);bsin(y)) In Ellipse??
Answer» What is the proof of the equation of a chord passing through a (acos(x);bSin(x)) and (a cos(y);bsin(y)) In Ellipse??

Discussion

2755.	Question 2 The perimeter of an equilateral triangle is 60m. The area is
Answer» Question 2 The perimeter of an equilateral triangle is 60m. The area is

Discussion

2756.	Factorize:64a3 + 125b3 + 240a2b + 300ab2
Answer» Factorize: 64a³ + 125b³ + 240a²b + 300ab²

Discussion

2757.	If x = 2 is a root of the polynomial f(x) = 2x2 − 3x + 7a, find the value of a.
Answer» If x = 2 is a root of the polynomial f(x) = 2x² − 3x + 7a, find the value of a.

Discussion

2758.	Which of the following rational numbers are equivalent to 94?
Answer» Which of the following rational numbers are equivalent to $\frac{9}{4}$ ?

Discussion

2759.	Which of the following statements hold true for a quadrilateral ABCD?
Answer» Which of the following statements hold true for a quadrilateral ABCD?

Discussion

2760.	If Fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such PQ = RQ. ∠ PQT = ∠ RQU and ∠ TQS = ∠ UQS. Prove that QT = QU. [4 MARKS]
Answer» If Fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such PQ = RQ. $∠$ PQT = $∠$ RQU and $∠$ TQS = $∠$ UQS. Prove that QT = QU. [4 MARKS]

Discussion

2761.	x - y = 0 is a line:
Answer» x - y = 0 is a line:

Discussion

2762.	In fig. ABC is an isosceles triangle in which AB=AC.CP\|\|AB and AP is the bisector of exterior ∠CAD of ΔABC. Prove that ∠PAC=∠BCA and ABCP is a parallelogram.
Answer» In fig. ABC is an isosceles triangle in which $A B = A C . C P \| \| A B a n d A P$ is the bisector of exterior ∠CAD of ΔABC. Prove that $∠ P A C = ∠ B C A$ and $A B C P$ is a parallelogram.

Discussion

2763.	Factorise:3x2 – 14x + 8
Answer» Factorise: 3x²– 14x + 8

Discussion

2764.	The zeros of the polynomial p(x)=x2−3x are (a) 0,0 (b) 0,3 (c) 0, -4 (d) 3, -3
Answer» The zeros of the polynomial $p (x) = x^{2} - 3 x$ are (a) 0,0 (b) 0,3 (c) 0, -4 (d) 3, -3

Discussion

2765.	The internal angular bisectors of angles of a ΔABC meets circumcircle of ΔABC at D,E,F respectively then Area ofΔleABCArea ofΔleDEF=
Answer» The internal angular bisectors of angles of a $Δ A B C$ meets circumcircle of $Δ A B C$ at $D, E, F$ respectively then $\frac{Area of Δ^{l e} ABC}{Area of Δ^{l e} DEF} =$

Discussion

2766.	Burst the bubble if the rational number is terminating.
Answer» Burst the bubble if the rational number is terminating.

Discussion

2767.	The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.
Answer» The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.

Discussion

2768.	prove that each of the four sides of a rhombus is of the same length
Answer» prove that each of the four sides of a rhombus is of the same length

Discussion

2769.	Consider the figure shown.Which of the following is true?
Answer» Consider the figure shown. Which of the following is true?

Discussion

2770.	Rationalise the denominator in 1√3
Answer» Rationalise the denominator in $\frac{1}{\sqrt{3}}$

Discussion

2771.	Simplify the following expressions:(i) 4+7) (3+2(ii) 3+3) (5-2(iii) 5-2) (3-5
Answer» Simplify the following expressions: (i) $(4 + \sqrt{7}) (3 + \sqrt{2})$ (ii) $(3 + \sqrt{3}) (5 - \sqrt{2})$ (iii) $(\sqrt{5} - 2) (\sqrt{3} - \sqrt{5})$

Discussion

2772.	If thitta is an angle between the diagonals of a parallelogram ABCD whose vertices are A(0,2) B(2,-1) C(4,0) and D(2,3).show that tan thitta =2
Answer» If thitta is an angle between the diagonals of a parallelogram ABCD whose vertices are A(0,2) B(2,-1) C(4,0) and D(2,3).show that tan thitta =2

Discussion

2773.	the factors of x3−7x+6 are
Answer» the factors of $x^{3} - 7 x + 6$ are

Discussion

2774.	What is the difference between natural numbers and whole numbers?
Answer» What is the difference between natural numbers and whole numbers?

Discussion

2775.	If lines l \|\| m are intersected by lines n \|\| o and ∠1=34∘ then what is ∠8′?146
Answer» If lines l \|\| m are intersected by lines n \|\| o and $∠ 1 = 34^{\circ}$ then what is $∠ 8^{'}$ ? 146

Discussion

2776.	Question 3The numerical expression 38+(−5)7=−1956 shows that:(a) rational numbers are closed under addition.(b) rational numbers are not closed under addition.(c) rational numbers are closed under multiplication.(d) addition of rational numbers is not commutative.
Answer» Question 3 The numerical expression $\frac{3}{8} + \frac{(- 5)}{7} = \frac{- 19}{56}$ shows that: (a) rational numbers are closed under addition. (b) rational numbers are not closed under addition. (c) rational numbers are closed under multiplication. (d) addition of rational numbers is not commutative.

Discussion

2777.	Find x satisfying each of the following equations:(i) (ii) (iii) (iv) (v) (vi)
Answer» Find x satisfying each of the following equations: (i) (ii) (iii) (iv) (v) (vi)

2777.

Find x satisfying each of the following equations:(i) (ii) (iii) (iv) (v) (vi)

Answer»

Find x satisfying each of the following equations:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Discussion

2778.	Question 14If each observation of the data is increased by 5, then their mean:A) Remains the sameB) Becomes 5 times the original meanC) Is decreased by 5D) Is increases by 5
Answer» Question 14 If each observation of the data is increased by 5, then their mean: A) Remains the same B) Becomes 5 times the original mean C) Is decreased by 5 D) Is increases by 5

Discussion

2779.	If a,b, c are in continued proportion,then the value of a2+ab+b2b2+bc+c2 is equal to:[2 marks]
Answer» $If a,b, c are in continued proportion,$ $then the value of \frac{a^{2} + a b + b^{2}}{b^{2} + b c + c^{2}} is equal to:$ [2 marks]

Discussion

2780.	The measure of an angle is four times the measure of its supplementary angle. Then the angles are :-
Answer» The measure of an angle is four times the measure of its supplementary angle. Then the angles are :-

Discussion

2781.	Median is defined as:
Answer» Median is defined as:

Discussion

2782.	Equivalent ratio of 4:3 is :
Answer» Equivalent ratio of 4:3 is :

Discussion

2783.	Identify the equations with a positive constant of proportionality from the following options.
Answer» Identify the equations with a positive constant of proportionality from the following options.

Discussion

2784.	Find the quotient when f(x) = x3 + 3x2 + 3x + 5 is divided by g(x) = x + 2. Also, find the remainder.
Answer» Find the quotient when f(x) = x³ + 3x² + 3x + 5 is divided by g(x) = x + 2. Also, find the remainder.

Discussion

2785.	Find the sum of the number of angle bisector(s) and perpendicular bisector(s) drawn to construct a triangle ABC in which BC=8 cm, ∠B=45∘ and AB−AC=3.5 cm.
Answer» Find the sum of the number of angle bisector(s) and perpendicular bisector(s) drawn to construct a triangle ABC in which $B C = 8 c m, ∠ B = 45^{\circ} a n d A B - A C = 3.5 c m$ .

Discussion

2786.	Question 99 What portion of a 'Saree' can Rehana paint in 1 hour, if it requires 5 hours to paint the whole Saree? In 435 hours? In 312hours?
Answer» Question 99 What portion of a 'Saree' can Rehana paint in 1 hour, if it requires 5 hours to paint the whole Saree? In 4 $\frac{3}{5}$ hours? In 3 $\frac{1}{2} h o u r s$ ?

2786.

Question 99 What portion of a 'Saree' can Rehana paint in 1 hour, if it requires 5 hours to paint the whole Saree? In 435 hours? In 312hours?

Answer»

Question 99

What portion of a 'Saree' can Rehana paint in 1 hour, if it requires 5 hours to paint the whole Saree? In 4 $\frac{3}{5}$ hours? In 3 $\frac{1}{2} h o u r s$ ?

Discussion

2787.	Which of the following linear equations does not pass through the origin?
Answer» Which of the following linear equations does not pass through the origin?

Discussion

2788.	In a right triangle ABC, In which angle C=90° and CD perpendicular AB . If BC= aAB= c and CA= P, then A.1/p^2 not equal to 1/a^2+ 1/b^2B. A.1/p^2 equal to 1/a^2+ 1/b^2C.A.1/p^2 < 1/a^2+ 1/b^2D.A.1/p^2 > 1/a^2+ 1/b^2
Answer» In a right triangle ABC, In which angle C=90° and CD perpendicular AB . If BC= a AB= c and CA= P, then A.1/p^2 not equal to 1/a^2+ 1/b^2 B. A.1/p^2 equal to 1/a^2+ 1/b^2 C.A.1/p^2 < 1/a^2+ 1/b^2 D.A.1/p^2 > 1/a^2+ 1/b^2

Discussion

2789.	Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.
Answer» Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Discussion

2790.	Question 5 The next number in the pattern -62, -37, -12 is ___. (a) 25 (b) 13 (c) 0 (d) -13
Answer» Question 5 The next number in the pattern -62, -37, -12 is ___. (a) 25 (b) 13 (c) 0 (d) -13

2790.

Question 5 The next number in the pattern -62, -37, -12 is ___. (a) 25 (b) 13 (c) 0 (d) -13

Answer»

Question 5

The next number in the pattern -62, -37, -12 is ___.

(a) 25
(b) 13
(c) 0
(d) -13

Discussion

2791.	8. Plot the graph of \|x\| + \|y\|
Answer» 8. Plot the graph of \|x\| + \|y\|<=5 on a graph paper and find the area of the common solution region so obtained.

Discussion

2792.	If the sum of three numbers be 9 the sum of their squares be 29 and their sum of cubes be 99 then find the product
Answer» If the sum of three numbers be 9 the sum of their squares be 29 and their sum of cubes be 99 then find the product

Discussion

2793.	Cost of spare parts of a car is 10% of the cost of the car.Then, if the car cost $5000, the cost for the spare parts will be _______
Answer» Cost of spare parts of a car is $10 %$ of the cost of the car. Then, if the car cost $$ 5000$ , the cost for the spare parts will be _______

Discussion

2794.	How many parallelograms are there in the figure given below?
Answer» How many parallelograms are there in the figure given below?

Discussion

2795.	Find √27
Answer» Find √27

Discussion

2796.	Question 10A company packages its milk powder in a cylindrical container whose base has a diameter of 14 cm and height 20 cm. The company places a label on the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?
Answer» Question 10 A company packages its milk powder in a cylindrical container whose base has a diameter of 14 cm and height 20 cm. The company places a label on the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?

Discussion

2797.	Where does the othocentre lie in an obtuse angled triangle?
Answer» Where does the othocentre lie in an obtuse angled triangle?

Discussion

2798.	Question 5Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm
Answer» Question 5 Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm

Discussion

2799.	Evaluate : cos48∘−sin42∘=___
Answer» Evaluate : $c o s 48^{\circ} - s i n 42^{\circ} =$ ___

Discussion

2800.	If √2=1.414, then the value of √6−√3 upto three places of decimal is ______ .
Answer» If $\sqrt{2} = 1.414,$ then the value of $\sqrt{6} - \sqrt{3}$ upto three places of decimal is ______ .

Discussion

Explore topic-wise InterviewSolutions in .

The total surface area of a cubical die is 24 cm2. Find the length of each edge?

Let ¯a=2¯i−3¯j+^k,¯b=^i−^j+3^k and ¯c=^i+^j−^k Then the system of vectors ¯a,¯band¯c

Without using calculating devices, compute the following correct to two decimals.(i) (ii) (iii)

What is the proof of the equation of a chord passing through a (acos(x);bSin(x)) and (a cos(y);bsin(y)) In Ellipse??

Question 2 The perimeter of an equilateral triangle is 60m. The area is

Factorize:64a3 + 125b3 + 240a2b + 300ab2

If x = 2 is a root of the polynomial f(x) = 2x2 − 3x + 7a, find the value of a.

Which of the following rational numbers are equivalent to 94?

Which of the following statements hold true for a quadrilateral ABCD?

If Fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such PQ = RQ. ∠ PQT = ∠ RQU and ∠ TQS = ∠ UQS. Prove that QT = QU. [4 MARKS]

x - y = 0 is a line:

In fig. ABC is an isosceles triangle in which AB=AC.CP||AB and AP is the bisector of exterior ∠CAD of ΔABC. Prove that ∠PAC=∠BCA and ABCP is a parallelogram.

Factorise:3x2 – 14x + 8

The zeros of the polynomial p(x)=x2−3x are (a) 0,0 (b) 0,3 (c) 0, -4 (d) 3, -3

The internal angular bisectors of angles of a ΔABC meets circumcircle of ΔABC at D,E,F respectively then Area ofΔleABCArea ofΔleDEF=

Burst the bubble if the rational number is terminating.

The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.

prove that each of the four sides of a rhombus is of the same length

Consider the figure shown.Which of the following is true?

Rationalise the denominator in 1√3

Simplify the following expressions:(i) 4+7) (3+2(ii) 3+3) (5-2(iii) 5-2) (3-5

If thitta is an angle between the diagonals of a parallelogram ABCD whose vertices are A(0,2) B(2,-1) C(4,0) and D(2,3).show that tan thitta =2

the factors of x3−7x+6 are

What is the difference between natural numbers and whole numbers?

If lines l || m are intersected by lines n || o and ∠1=34∘ then what is ∠8′?146

Question 3The numerical expression 38+(−5)7=−1956 shows that:(a) rational numbers are closed under addition.(b) rational numbers are not closed under addition.(c) rational numbers are closed under multiplication.(d) addition of rational numbers is not commutative.

Find x satisfying each of the following equations:(i) (ii) (iii) (iv) (v) (vi)

Question 14If each observation of the data is increased by 5, then their mean:A) Remains the sameB) Becomes 5 times the original meanC) Is decreased by 5D) Is increases by 5

If a,b, c are in continued proportion,then the value of a2+ab+b2b2+bc+c2 is equal to:[2 marks]

The measure of an angle is four times the measure of its supplementary angle. Then the angles are :-

Median is defined as:

Equivalent ratio of 4:3 is :

Identify the equations with a positive constant of proportionality from the following options.

Find the quotient when f(x) = x3 + 3x2 + 3x + 5 is divided by g(x) = x + 2. Also, find the remainder.

Find the sum of the number of angle bisector(s) and perpendicular bisector(s) drawn to construct a triangle ABC in which BC=8 cm, ∠B=45∘ and AB−AC=3.5 cm.

Question 99 What portion of a 'Saree' can Rehana paint in 1 hour, if it requires 5 hours to paint the whole Saree? In 435 hours? In 312hours?

Which of the following linear equations does not pass through the origin?

In a right triangle ABC, In which angle C=90° and CD perpendicular AB . If BC= aAB= c and CA= P, then A.1/p^2 not equal to 1/a^2+ 1/b^2B. A.1/p^2 equal to 1/a^2+ 1/b^2C.A.1/p^2 < 1/a^2+ 1/b^2D.A.1/p^2 > 1/a^2+ 1/b^2

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Question 5 The next number in the pattern -62, -37, -12 is ___. (a) 25 (b) 13 (c) 0 (d) -13

8. Plot the graph of |x| + |y|

If the sum of three numbers be 9 the sum of their squares be 29 and their sum of cubes be 99 then find the product

Cost of spare parts of a car is 10% of the cost of the car.Then, if the car cost $5000, the cost for the spare parts will be _______

How many parallelograms are there in the figure given below?

Find √27

Question 10A company packages its milk powder in a cylindrical container whose base has a diameter of 14 cm and height 20 cm. The company places a label on the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?

Where does the othocentre lie in an obtuse angled triangle?

Question 5Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm

Evaluate : cos48∘−sin42∘=___

If √2=1.414, then the value of √6−√3 upto three places of decimal is ______ .