24740 + Interview Questions in Mathematics Page 72 InterviewSolution

3551.	In a parallelogram ABCD, if ∠D = 115°, then write the measure of ∠A.
Answer» In a parallelogram ABCD, if ∠D = 115°, then write the measure of ∠A.

Discussion

3552.	In a Δ ABC, the internal bisectors of ∠B and ∠C meet at P and the external bisectors of ∠B and ∠C meet at Q, Prove that ∠BPC + ∠BQC = 180°.
Answer» In a Δ ABC, the internal bisectors of ∠B and ∠C meet at P and the external bisectors of ∠B and ∠C meet at Q, Prove that ∠BPC + ∠BQC = 180°.

Discussion

3553.	Manu is 4 years younger than Mridula. 4 years back, Mridula’s age was one and a half times Manu’s age. What are their ages now?
Answer» Manu is 4 years younger than Mridula. 4 years back, Mridula’s age was one and a half times Manu’s age. What are their ages now?

Discussion

3554.	Draw the graph of each of the following linear equations in two variables:(i) x + y = 4(ii) x − y = 0(iii) −x + y = 6(iv) y = 2x(v) 3x + 5y = 15(vi) x2-y3=2(vii) x-23= y-3(viii) 2y = −x + 1
Answer» Draw the graph of each of the following linear equations in two variables: (i) x + y = 4 (ii) x − y = 0 (iii) −x + y = 6 (iv) y = 2x (v) 3x + 5y = 15 (vi) $\frac{x}{2} - \frac{y}{3} = 2$ (vii) $\frac{x - 2}{3} = y - 3$ (viii) 2y = −x + 1

Discussion

3555.	What is the perpendicular distance of the point Q (5,7) from y-axis?
Answer» What is the perpendicular distance of the point Q (5,7) from y-axis?

Discussion

3556.	What does a geometry box consist of? What are the main instruments used for construction? [1 MARK]
Answer» What does a geometry box consist of? What are the main instruments used for construction? [1 MARK]

Discussion

3557.	What can you say about the sum of a rational number and an irrational number?
Answer» What can you say about the sum of a rational number and an irrational number?

Discussion

3558.	Question 3 (iv)Simplify:712.812
Answer» Question 3 (iv) Simplify: $7^{\frac{1}{2}} {.8}^{\frac{1}{2}}$

3558.

Question 3 (iv)Simplify:712.812

Answer»

Question 3 (iv)

Simplify:

$7^{\frac{1}{2}} {.8}^{\frac{1}{2}}$

Discussion

3559.	A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1cm3 of iron has approximately 8 g mass. (Use π=3.14)
Answer» A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that ${1 c m}^{3}$ of iron has approximately 8 g mass. (Use $π = 3.14$ )

Discussion

3560.	Question 4Classify the following numbers as rational or irrational with justification.(i)√196(ii)3√18(iii)√927(iv)√28343(v)−√0.4(vi)√12√75(vii) 0.5918(viii) (1+√5)−(4+√5) (ix) 10.124124 ....(x) 1.010010001....To classify, use the definition a rational number is in the form of pq, where p and q are integers and q≠0 and otherwise it is an irrational number.
Answer» Question 4 Classify the following numbers as rational or irrational with justification. $(i) \sqrt{196} (i i) 3 \sqrt{18} (i i i) \sqrt{\frac{9}{27}} (i v) \frac{\sqrt{28}}{343} (v) - \sqrt{0.4} (v i) \frac{\sqrt{12}}{\sqrt{75}}$ (vii) 0.5918 (viii) $(1 + \sqrt{5}) - (4 + \sqrt{5})$ (ix) 10.124124 .... (x) 1.010010001.... To classify, use the definition a rational number is in the form of $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ and otherwise it is an irrational number.

Discussion

3561.	If one angle of a triangle is equal to the sum of the other two angles which are equal, then the triangle is a/an _________ .
Answer» If one angle of a triangle is equal to the sum of the other two angles which are equal, then the triangle is a/an _________ .

Discussion

3562.	Match the following products with their respective correct values.
Answer» Match the following products with their respective correct values.

Discussion

3563.	log{logab a+1logb ab}=
Answer» $l o g {l o g_{a b} a + \frac{1}{l o g_{b} a b}} =$

Discussion

3564.	Question 62In the following question, state whether the statement is True (T) or False (F):The product of two negative terms is a negative term.
Answer» Question 62 In the following question, state whether the statement is True (T) or False (F): The product of two negative terms is a negative term.

3564.

Question 62In the following question, state whether the statement is True (T) or False (F):The product of two negative terms is a negative term.

Answer»

Question 62

In the following question, state whether the statement is True (T) or False (F):

The product of two negative terms is a negative term.

Discussion

3565.	\sqrt[3]2 × \sqrt[4]3
Answer» \sqrt[3]2 × \sqrt[4]3

Discussion

3566.	ntThree vectors a, b, c are such that a+b+c=0. If a=3,b=4,c=5, show that ab=bc=ca=-25n
Answer» ntThree vectors a, b, c are such that a+b+c=0. If a=3,b=4,c=5, show that ab=bc=ca=-25n

Discussion

3567.	A circular pond is 17.5 m is of diameter. It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of ₹25 per m2
Answer» A circular pond is 17.5 m is of diameter. It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of $₹ 25 p e r m^{2}$

Discussion

3568.	In the given figure, AD is a median of ABC and E is the mid-points of AD. Also, BE produced meets AC in F. Then AF =
Answer» In the given figure, AD is a median of ABC and E is the mid-points of AD. Also, BE produced meets AC in F. Then AF =

Discussion

3569.	A is greater than b by one third of a right angle. Find the values of a and b. When a and b forms a linear pair.
Answer» A is greater than b by one third of a right angle. Find the values of a and b. When a and b forms a linear pair.

Discussion

3570.	Match the following numbers on the left hand side with their correct pq form given on the right hand side.
Answer» Match the following numbers on the left hand side with their correct $\frac{p}{q}$ form given on the right hand side.

Discussion

3571.	Prime numbers with more than 1000 digits are called _______ primes
Answer» Prime numbers with more than 1000 digits are called _______ primes

Discussion

3572.	Factorise a3−0.064
Answer» Factorise $a^{3} - 0.064$

Discussion

3573.	Which of the following is an empty relation on AxB where A= {0, 2, 5}, B = {1, 4, 7}
Answer» Which of the following is an empty relation on AxB where A= {0, 2, 5}, B = {1, 4, 7}

Discussion

3574.	The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is(a) a rhombus of area 24 cm2(b) a rectangle of area 24 cm2(c) a square of area 26 cm2(d) a trapezium of area 14 cm2
Answer» The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is (a) a rhombus of area 24 cm² (b) a rectangle of area 24 cm² (c) a square of area 26 cm² (d) a trapezium of area 14 cm²

Discussion

3575.	find the coordinatesof the.point whose abscissa is 4 and ordinate is three fourth of abscissa.also find the quadrant in whisch the given point lie
Answer» find the coordinatesof the.point whose abscissa is 4 and ordinate is three fourth of abscissa.also find the quadrant in whisch the given point lie

Discussion

3576.	What is the degree of the polynomial P(x) = 11x6 + x5 + 3x4 + x3 + x2 + x +1, also find the maximum number of zeroes it can have
Answer» What is the degree of the polynomial P(x) = 11 $x^{6}$ + $x^{5}$ + 3 $x^{4}$ + $x^{3}$ + $x^{2}$ + x +1, also find the maximum number of zeroes it can have

Discussion

3577.	P(x)=ax2+bx+c P(0) =1, P(1)=11, P(-1)=3. What is the value of the expression ((a+b)2−(a−b)6−35c)2015 ?
Answer» $P (x) = a x^{2} + b x + c$ P(0) =1, P(1)=11, P(-1)=3. What is the value of the expression $((a + b)^{2} - (a - b)^{6} - 35 c)^{2015}$ ?

Discussion

3578.	We know =circumference of circle/diameter. Then why is called irrational number?
Answer» We know =circumference of circle/diameter. Then why is called irrational number?

Discussion

3579.	√8 × √50
Answer» √8 × √50

Discussion

3580.	How to construct number line.
Answer» How to construct number line.

Discussion

3581.	Slopes of lines which cuts off intercepts of equal lengths on the coordinate axis are(a) 0(b) ±13(c) ± 1(d) ±3
Answer» Slopes of lines which cuts off intercepts of equal lengths on the coordinate axis are (a) 0 (b) $\pm \frac{1}{\sqrt{3}}$ (c) ± 1 (d) $\pm \sqrt{3}$

Discussion

3582.	Equal chords AB and CD of a circle with centre O, cut at right angles at E. If M and N are the midpoints of AB and CD, respectively, then prove that OMEN is a square.
Answer» Equal chords AB and CD of a circle with centre O, cut at right angles at E. If M and N are the midpoints of AB and CD, respectively, then prove that OMEN is a square.

Discussion

3583.	An isosceles right triangle has an area equal to 8 sq.cm. Find the length of its hypotenuse.
Answer» An isosceles right triangle has an area equal to 8 sq.cm. Find the length of its hypotenuse.

Discussion

3584.	Equal chords AB and CD of a circle with centre O, cut at right angles at E. If M and N are the mid - points of AB and CD respectively, then OMEN is a __.
Answer» Equal chords AB and CD of a circle with centre O, cut at right angles at E. If M and N are the mid - points of AB and CD respectively, then OMEN is a __.

Discussion

3585.	For a polynomial p(x), p(-1) and p(2) are both equal to zero .So, we can conclude that,
Answer» For a polynomial p(x), p(-1) and p(2) are both equal to zero .So, we can conclude that,

Discussion

3586.

The number of students who have played various sports is shown in the table below.SportCricketTennisChessFootballNo. of Students 5 10 20 15Which of the following is the right bar graph to represent the data above?

Answer»

The number of students who have played various sports is shown in the table below.

Sport	Cricket	Tennis	Chess	Football
No. of Students	5	10	20	15

Which of the following is the right bar graph to represent the data above?

Discussion

3587.	Two kids, Goutham and Pavani are fighting for coins. Finally, Goutham won and stole a coin from Pavani's pocket which has four different coins (a 1 rupee coin, a 2 rupee coin, a 5 rupee coin, a 10 rupee coin), what is the probability that Goutham stole a 5 rupee coin?
Answer» Two kids, Goutham and Pavani are fighting for coins. Finally, Goutham won and stole a coin from Pavani's pocket which has four different coins (a 1 rupee coin, a 2 rupee coin, a 5 rupee coin, a 10 rupee coin), what is the probability that Goutham stole a 5 rupee coin?

Discussion

3588.	54. What is exactly anion and cation?
Answer» 54. What is exactly anion and cation?

Discussion

3589.	Question 3A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :(A) 12 cm(B) 13 cm(C) 8.5 cm(D) √119 cm
Answer» Question 3 A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is : (A) 12 cm (B) 13 cm (C) 8.5 cm (D) $\sqrt{119} c m$

Discussion

3590.	If x=1−√2 , find the value of (x−1x)3
Answer» If $x = 1 - \sqrt{2}$ , find the value of $(x - \frac{1}{x})^{3}$

Discussion

3591.	Find the total cost to paint external areas of all the 4 walls of a room with length, breadth and height as 10 cm, 20 cm and 5 cm respectively at the rate of ₹10 per sq. metre.
Answer» Find the total cost to paint external areas of all the 4 walls of a room with length, breadth and height as 10 cm, 20 cm and 5 cm respectively at the rate of ₹10 per sq. metre.

Discussion

3592.	The decimal expansion of 2 is _______ and _________.
Answer» The decimal expansion of $\sqrt{2}$ is _______ and _________.

Discussion

3593.	The range of the expression f(x)=3x2−12x+5 is
Answer» The range of the expression $f (x) = 3 x^{2} - 12 x + 5$ is

Discussion

3594.	Which of the following statements is not true about the figure given below?
Answer» Which of the following statements is not true about the figure given below?

3594.

Which of the following statements is not true about the figure given below?

Answer»

Which of the following statements is not true about the figure given below?

Discussion

3595.	In the given figure,ABCD is a trapezium such that AL⊥DC and BM⊥DC.If AB=7 cm,BC=AD=5 cm and AL=BM=4 cm then ar(trap.ABCD)=? (a) 24 cm2 (b) 40 cm2 (c) 55 cm2 (d) 27.5 cm2
Answer» In the given figure,ABCD is a trapezium such that $A L ⊥ D C$ and $B M ⊥ D C$ .If AB=7 cm,BC=AD=5 cm and AL=BM=4 cm then ar(trap.ABCD)=? (a) $24 c m^{2}$ (b) $40 c m^{2}$ (c) $55 c m^{2}$ (d) $27.5 c m^{2}$

3595.

In the given figure,ABCD is a trapezium such that AL⊥DC and BM⊥DC.If AB=7 cm,BC=AD=5 cm and AL=BM=4 cm then ar(trap.ABCD)=? (a) 24 cm2 (b) 40 cm2 (c) 55 cm2 (d) 27.5 cm2

Answer»

In the given figure,ABCD is a trapezium such that $A L ⊥ D C$ and $B M ⊥ D C$ .If AB=7 cm,BC=AD=5 cm and AL=BM=4 cm then ar(trap.ABCD)=?

(a) $24 c m^{2}$

(b) $40 c m^{2}$

(c) $55 c m^{2}$

(d) $27.5 c m^{2}$

Discussion

3596.	The maximum number of zeroes which a quadratic polynomial can have is _________.
Answer» The maximum number of zeroes which a quadratic polynomial can have is _________.

Discussion

3597.	The heights (in cm) of students of a class is tabulated below.HeightNumber of students150−1544155−1593160−1642165−1691170−1742175−1792180−1844185−1892Total20i) What type of frequency distribution is this?ii) Find the umber of students having height in the range of 160-174 cm.
Answer» The heights (in cm) of students of a class is tabulated below. $\begin{matrix} Height & Number of students 150 - 154 & 4 155 - 159 & 3 160 - 164 & 2 165 - 169 & 1 170 - 174 & 2 175 - 179 & 2 180 - 184 & 4 185 - 189 & 2 T o t a l & 20 \end{matrix}$ i) What type of frequency distribution is this? ii) Find the umber of students having height in the range of 160-174 cm.

Discussion

3598.	In a ΔABC, D, E, F are the mid-points of sides BC, CA and AB respectively. If ar (ΔABC) = 16cm2, then ar (trapezium FBCE) =(a) 4 cm2(b) 8 cm2(c) 12 cm2(d) 10 cm2
Answer» In a ΔABC, D, E, F are the mid-points of sides BC, CA and AB respectively. If ar (ΔABC) = 16cm², then ar (trapezium FBCE) = (a) 4 cm² (b) 8 cm² (c) 12 cm² (d) 10 cm²

Discussion

3599.	Measures of opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. Find the measure of its each angle.
Answer» Measures of opposite angles of a parallelogram are (3x − 2) $°$ and (50 − x) $°$ . Find the measure of its each angle.

Discussion

3600.	If ab= bc and a,b,c > 0 then show that, (i) (a + b + c) (b - c) = ab - c2 (ii) (a2 + b2) (b2 + c2 ) = (ab + bc)2 (iii) a2 + b2ab = a + c b
Answer» If $\frac{a}{b} = \frac{b}{c}$ and $a, b, c$ > 0 then show that, (i) (a + b + c) (b $-$ c) = ab $-$ c² (ii) (a²+ b²) (b²+ c²) = (ab + bc)² (iii) $\frac{a^{2} + b^{2}}{a b} = \frac{a + c}{b}$

Discussion

Explore topic-wise InterviewSolutions in .

In a parallelogram ABCD, if ∠D = 115°, then write the measure of ∠A.

In a Δ ABC, the internal bisectors of ∠B and ∠C meet at P and the external bisectors of ∠B and ∠C meet at Q, Prove that ∠BPC + ∠BQC = 180°.

Manu is 4 years younger than Mridula. 4 years back, Mridula’s age was one and a half times Manu’s age. What are their ages now?

Draw the graph of each of the following linear equations in two variables:(i) x + y = 4(ii) x − y = 0(iii) −x + y = 6(iv) y = 2x(v) 3x + 5y = 15(vi) x2-y3=2(vii) x-23= y-3(viii) 2y = −x + 1

What is the perpendicular distance of the point Q (5,7) from y-axis?

What does a geometry box consist of? What are the main instruments used for construction? [1 MARK]

What can you say about the sum of a rational number and an irrational number?

Question 3 (iv)Simplify:712.812

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1cm3 of iron has approximately 8 g mass. (Use π=3.14)

If one angle of a triangle is equal to the sum of the other two angles which are equal, then the triangle is a/an _________ .

Match the following products with their respective correct values.

log{logab a+1logb ab}=

Question 62In the following question, state whether the statement is True (T) or False (F):The product of two negative terms is a negative term.

\sqrt[3]2 × \sqrt[4]3

ntThree vectors a, b, c are such that a+b+c=0. If a=3,b=4,c=5, show that ab=bc=ca=-25n

A circular pond is 17.5 m is of diameter. It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of ₹25 per m2

In the given figure, AD is a median of ABC and E is the mid-points of AD. Also, BE produced meets AC in F. Then AF =

A is greater than b by one third of a right angle. Find the values of a and b. When a and b forms a linear pair.

Match the following numbers on the left hand side with their correct pq form given on the right hand side.

Prime numbers with more than 1000 digits are called _______ primes

Factorise a3−0.064

Which of the following is an empty relation on AxB where A= {0, 2, 5}, B = {1, 4, 7}

The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is(a) a rhombus of area 24 cm2(b) a rectangle of area 24 cm2(c) a square of area 26 cm2(d) a trapezium of area 14 cm2

find the coordinatesof the.point whose abscissa is 4 and ordinate is three fourth of abscissa.also find the quadrant in whisch the given point lie

What is the degree of the polynomial P(x) = 11x6 + x5 + 3x4 + x3 + x2 + x +1, also find the maximum number of zeroes it can have

P(x)=ax2+bx+c P(0) =1, P(1)=11, P(-1)=3. What is the value of the expression ((a+b)2−(a−b)6−35c)2015 ?

We know =circumference of circle/diameter. Then why is called irrational number?

√8 × √50

How to construct number line.

Slopes of lines which cuts off intercepts of equal lengths on the coordinate axis are(a) 0(b) ±13(c) ± 1(d) ±3

Equal chords AB and CD of a circle with centre O, cut at right angles at E. If M and N are the midpoints of AB and CD, respectively, then prove that OMEN is a square.

An isosceles right triangle has an area equal to 8 sq.cm. Find the length of its hypotenuse.

Equal chords AB and CD of a circle with centre O, cut at right angles at E. If M and N are the mid - points of AB and CD respectively, then OMEN is a __.

For a polynomial p(x), p(-1) and p(2) are both equal to zero .So, we can conclude that,

The number of students who have played various sports is shown in the table below.SportCricketTennisChessFootballNo. of Students 5 10 20 15Which of the following is the right bar graph to represent the data above?

Two kids, Goutham and Pavani are fighting for coins. Finally, Goutham won and stole a coin from Pavani's pocket which has four different coins (a 1 rupee coin, a 2 rupee coin, a 5 rupee coin, a 10 rupee coin), what is the probability that Goutham stole a 5 rupee coin?

54. What is exactly anion and cation?

Question 3A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :(A) 12 cm(B) 13 cm(C) 8.5 cm(D) √119 cm

If x=1−√2 , find the value of (x−1x)3

Find the total cost to paint external areas of all the 4 walls of a room with length, breadth and height as 10 cm, 20 cm and 5 cm respectively at the rate of ₹10 per sq. metre.

The decimal expansion of 2 is _______ and _________.

The range of the expression f(x)=3x2−12x+5 is

Which of the following statements is not true about the figure given below?

In the given figure,ABCD is a trapezium such that AL⊥DC and BM⊥DC.If AB=7 cm,BC=AD=5 cm and AL=BM=4 cm then ar(trap.ABCD)=? (a) 24 cm2 (b) 40 cm2 (c) 55 cm2 (d) 27.5 cm2

The maximum number of zeroes which a quadratic polynomial can have is _________.

The heights (in cm) of students of a class is tabulated below.HeightNumber of students150−1544155−1593160−1642165−1691170−1742175−1792180−1844185−1892Total20i) What type of frequency distribution is this?ii) Find the umber of students having height in the range of 160-174 cm.

In a ΔABC, D, E, F are the mid-points of sides BC, CA and AB respectively. If ar (ΔABC) = 16cm2, then ar (trapezium FBCE) =(a) 4 cm2(b) 8 cm2(c) 12 cm2(d) 10 cm2

Measures of opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. Find the measure of its each angle.

If ab= bc and a,b,c &gt; 0 then show that, (i) (a + b + c) (b - c) = ab - c2 (ii) (a2 + b2) (b2 + c2 ) = (ab + bc)2 (iii) a2 + b2ab = a + c b

The decimal expansion of 2 is _ and ___.

If ab= bc and a,b,c > 0 then show that, (i) (a + b + c) (b - c) = ab - c2 (ii) (a2 + b2) (b2 + c2 ) = (ab + bc)2 (iii) a2 + b2ab = a + c b