24740 + Interview Questions in Mathematics Page 129 InterviewSolution

6401.	Question 177(vi)Find x.5x+5x−1=750
Answer» Question 177(vi) Find x. $5^{x} + 5^{x - 1} = 750$

6401.

Question 177(vi)Find x.5x+5x−1=750

Answer»

Question 177(vi)

Find x.

$5^{x} + 5^{x - 1} = 750$

6402.	If \|x\|<1then ddx(1−2x+3x2−........)=
Answer» $I f \| x \| < 1 t h e n \frac{d}{d x} (1 - 2 x + 3 x^{2} - . . . . . . . .) =$

Discussion

6403.	Which of the following statements is true?(a) Product of two irrational numbers is always irrational(b) Product of a rational and an irrational number is always irrational(c) Sum of two irrational numbers can never be irrational(d) Sum of an integer and a rational number can never be an integer
Answer» Which of the following statements is true? (a) Product of two irrational numbers is always irrational (b) Product of a rational and an irrational number is always irrational (c) Sum of two irrational numbers can never be irrational (d) Sum of an integer and a rational number can never be an integer

Discussion

6404.	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

6405.	A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown figure. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each types of paper needed to make the hand fan.
Answer» A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown figure. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each types of paper needed to make the hand fan.

Discussion

6406.	ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
Answer» ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.

6406.

ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.

Answer»

ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.

Discussion

6407.	Let a, b, c be the sides of a triangle. The least value of expressionE=ab+c−a+bc+a−b+ca+b−c is ___
Answer» Let a, b, c be the sides of a triangle. The least value of expression $E = \frac{a}{b + c - a} + \frac{b}{c + a - b} + \frac{c}{a + b - c}$ is ___

Discussion

6408.	Question 6 Which of the following is irrational? Thinking process An irrational number cannot be expressed as a fraction. It cannot be represented as a terminating or repeating decimal. A) √49 B) √123 C) √7 D) √81
Answer» Question 6 Which of the following is irrational? Thinking process An irrational number cannot be expressed as a fraction. It cannot be represented as a terminating or repeating decimal. A) $\sqrt{\frac{4}{9}}$ B) $\sqrt{\frac{12}{3}}$ C) $\sqrt{7}$ D) $\sqrt{81}$

Discussion

6409.	What is cartesian product?
Answer» What is cartesian product?

Discussion

6410.	For what value of k, the system of equations x + 2y = 5, 3x + ky + 15 = 0 has no solution? __
Answer» For what value of k, the system of equations x + 2y = 5, 3x + ky + 15 = 0 has no solution? __

Discussion

6411.	The construction of ΔABC, given that BC=3 cm, is possible when the difference of the sides AB and AC is equal to
Answer» The construction of $Δ A B C,$ given that $B C = 3 c m$ , is possible when the difference of the sides $A B$ and $A C$ is equal to

Discussion

6412.	Which of the following numbers mean the same as whole numbers?
Answer» Which of the following numbers mean the same as whole numbers?

Discussion

6413.	What is the maximum number of zeroes in cubic polynomial?
Answer» What is the maximum number of zeroes in cubic polynomial?

Discussion

6414.	From the options given below, choose the option which has all the measurements you will require to construct a quadrilateral ABCD.
Answer» From the options given below, choose the option which has all the measurements you will require to construct a quadrilateral ABCD.

Discussion

6415.	From the following particulars of a trader, prepare a Bank Reconcilation Statement as on 31st March, 2019.(i) Bank overdraft as per Cash Book ₹ 52,100.(ii) During the month, the total amount of cheques for ₹ 94,400 were deposited into the bank but of these, one cheque for ₹ 11,160 has been entered into the Pass Book on 5th April.(iii) During the month, cheques for ₹ 89,580 were drawn in favour of creditors. Of them, one creditor for ₹ 38,580 encashed his cheque on 7th April whereas another for ₹ 4,320 have not yet been encashed.(iv) As per instructions the bank on 28th March paid out ₹ 10,500 to a creditor but by mistake, the same has not been entered in the Cash Book.(v) According to agreement, on 25th March, a debtor deposited directly into the bank ₹ 9,000 but the same has not been recorded in the Cash Book.(vi) In the month of March, the bank without any intimation, debited his account for ₹ 120 as bank charges and credited the same for ₹ 180 as interest.(vii) Cash deposit of ₹ 5,780 in bank was recorded as ₹ 7,580. The error was rectified by the Bank before 31st March, 2019.
Answer» From the following particulars of a trader, prepare a Bank Reconcilation Statement as on 31st March, 2019. (i) Bank overdraft as per Cash Book ₹ 52,100. (ii) During the month, the total amount of cheques for ₹ 94,400 were deposited into the bank but of these, one cheque for ₹ 11,160 has been entered into the Pass Book on 5th April. (iii) During the month, cheques for ₹ 89,580 were drawn in favour of creditors. Of them, one creditor for ₹ 38,580 encashed his cheque on 7th April whereas another for ₹ 4,320 have not yet been encashed. (iv) As per instructions the bank on 28th March paid out ₹ 10,500 to a creditor but by mistake, the same has not been entered in the Cash Book. (v) According to agreement, on 25th March, a debtor deposited directly into the bank ₹ 9,000 but the same has not been recorded in the Cash Book. (vi) In the month of March, the bank without any intimation, debited his account for ₹ 120 as bank charges and credited the same for ₹ 180 as interest. (vii) Cash deposit of ₹ 5,780 in bank was recorded as ₹ 7,580. The error was rectified by the Bank before 31st March, 2019.

Discussion

6416.	How is 'a' raise to zero equal to one
Answer» How is 'a' raise to zero equal to one

Discussion

6417.	13. Let P(3 2 6) be a point in space and Q be a point on the line r(vector)=(i-j+2k)+(3i+j+5k) then the value of for which the vector PQ is parallel to the plane x+4y+3z=1 is a)1/4. b)-1/4. c)1/8. d)-1/8
Answer» 13. Let P(3 2 6) be a point in space and Q be a point on the line r(vector)=(i-j+2k)+(3i+j+5k) then the value of for which the vector PQ is parallel to the plane x+4y+3z=1 is a)1/4. b)-1/4. c)1/8. d)-1/8

Discussion

6418.	Question 1Write True or False and justify your answer :ABCD is a parallelogram and X is the mid - point of AB. If ar (AXCD) = 24 cm2, then ar (ABC) = 24 cm2
Answer» Question 1 Write True or False and justify your answer : ABCD is a parallelogram and X is the mid - point of AB. If ar (AXCD) = $24 c m^{2}$ , then ar (ABC) = $24 c m^{2}$

Discussion

6419.	The 4 term of a H.P is 35 and 8th term is 13, then its 6th term is
Answer» The 4 term of a H.P is $\frac{3}{5}$ and 8th term is $\frac{1}{3}$ , then its 6th term is

Discussion

6420.	The tent for an exhibition is as shown below, with a half-cylinder on top of a rectangular prism. What is the cost of making it, at the rate of 2000 rupees per square metre.
Answer» The tent for an exhibition is as shown below, with a half-cylinder on top of a rectangular prism. What is the cost of making it, at the rate of 2000 rupees per square metre.

6420.

The tent for an exhibition is as shown below, with a half-cylinder on top of a rectangular prism. What is the cost of making it, at the rate of 2000 rupees per square metre.

Answer»

The tent for an exhibition is as shown below, with a half-cylinder on top of a rectangular prism.

What is the cost of making it, at the rate of 2000 rupees per square metre.

Discussion

6421.	A well with 10 m inside diameter is dug 14m Deep Earth taken out of it is spread all around to a width of 5m to form an embankment
Answer» A well with 10 m inside diameter is dug 14m Deep Earth taken out of it is spread all around to a width of 5m to form an embankment

Discussion

6422.	Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. Find the measure of each angle of the parallelogram.
Answer» Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. Find the measure of each angle of the parallelogram.

Discussion

6423.	The volume of metallic cylinderical pipe is 784cm cu. Unit . It's length is 14cm and it's external radius is 9cm. Find its thickness.
Answer» The volume of metallic cylinderical pipe is 784cm cu. Unit . It's length is 14cm and it's external radius is 9cm. Find its thickness.

Discussion

6424.	The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm, what is the measure of shorter side?
Answer» The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm, what is the measure of shorter side?

Discussion

6425.	The equation y = a represents a straight line parallel to __
Answer» The equation y = a represents a straight line parallel to __

Discussion

6426.	The lengths of the sides of Δ ABC are consecutive integers. It Δ ABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?(a) 4(b) 6(c) 8(d) 10
Answer» The lengths of the sides of Δ ABC are consecutive integers. It Δ ABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC? (a) 4 (b) 6 (c) 8 (d) 10

Discussion

6427.	The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Show that the quadrilateral is a trapezium.
Answer» The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Show that the quadrilateral is a trapezium.

Discussion

6428.	If axn is a zero degree polynomial in x, what can be said about a and n?
Answer» If $a x^{n}$ is a zero degree polynomial in $x$ , what can be said about $a$ and $n$ ?

Discussion

6429.	In the given figure, M, N, and P are the mid-points of AB, AC, and BC, respectively. If MN = 3 cm, NP = 3.5 cm, and MP = 2.5 cm, find the perimeter of the triangle ABC (in cm).
Answer» In the given figure, M, N, and P are the mid-points of AB, AC, and BC, respectively. If MN = 3 cm, NP = 3.5 cm, and MP = 2.5 cm, find the perimeter of the triangle ABC (in cm).

Discussion

6430.	Factorise: x2+3√3x+6
Answer» Factorise: $x^{2} + 3 \sqrt{3} x + 6$

Discussion

6431.	If 4sin2Θ−1=0 and angle Θ is less than 90°, find the value of cos2+tan2Θ ?
Answer» If $4 s i n^{2} Θ - 1 = 0$ and angle $Θ$ is less than 90°, find the value of $c o s^{2} + t a n^{2} Θ$ ?

Discussion

6432.	Question 13 Write the denominator of rational number 2575000 in the form 2m×5n, where m, n are non - negative integers. Hence, write its decimal expansion, without actual division.
Answer» Question 13 Write the denominator of rational number $\frac{257}{5000}$ in the form $2^{m} \times 5^{n}$ , where m, n are non - negative integers. Hence, write its decimal expansion, without actual division.

Discussion

6433.	Read the following bar graph and answer the following questions: (i) What information is given by the bar graph? (ii) Which state is the largest producer of rice? (iii) Which state is the largest producer of wheat? (iv) Which state has total production of rice and wheat as its maximum? (v) Which state has the total production of wheat and rice minimum?
Answer» Read the following bar graph and answer the following questions: (i) What information is given by the bar graph? (ii) Which state is the largest producer of rice? (iii) Which state is the largest producer of wheat? (iv) Which state has total production of rice and wheat as its maximum? (v) Which state has the total production of wheat and rice minimum?

6433.

Read the following bar graph and answer the following questions: (i) What information is given by the bar graph? (ii) Which state is the largest producer of rice? (iii) Which state is the largest producer of wheat? (iv) Which state has total production of rice and wheat as its maximum? (v) Which state has the total production of wheat and rice minimum?

Answer»

Read the following bar graph and answer the following questions:

(i) What information is given by the bar graph?
(ii) Which state is the largest producer of rice?
(iii) Which state is the largest producer of wheat?
(iv) Which state has total production of rice and wheat as its maximum?
(v) Which state has the total production of wheat and rice minimum?

Discussion

6434.	A parallelogram having base 10 cm and height 8 cm is cut along its diagonal into two portions. What is the area of each portion?
Answer» A parallelogram having base 10 cm and height 8 cm is cut along its diagonal into two portions. What is the area of each portion?

Discussion

6435.	A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Answer» A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Discussion

6436.	Express each of the following decimals in the form pq : (i) 0.39 (ii) 0.750(iii) 2.15
Answer» Express each of the following decimals in the form $\frac{p}{q}$ : (i) 0.39 (ii) 0.750 (iii) 2.15

6436.

Express each of the following decimals in the form pq : (i) 0.39 (ii) 0.750(iii) 2.15

Answer»

Express each of the following decimals in the form $\frac{p}{q}$ :

(i) 0.39

(ii) 0.750

(iii) 2.15

Discussion

6437.	Calculate the measure of ∠AOC.
Answer» Calculate the measure of $∠ A O C .$

6437.

Calculate the measure of ∠AOC.

Answer»

Calculate the measure of $∠ A O C .$

Discussion

6438.	Find the values of a and b if 7+√57−√5−7−√57+√5=a+711√5b
Answer» Find the values of a and b if $\frac{7 + \sqrt{5}}{7 - \sqrt{5}} - \frac{7 - \sqrt{5}}{7 + \sqrt{5}} = a + \frac{7}{11} \sqrt{5} b$

Discussion

6439.	Define Irrational numbers.
Answer» Define Irrational numbers.

Discussion

6440.	Question 7 (i)P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that:(i)ar(PRQ)=12ar(ARC)
Answer» Question 7 (i) P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that: $(i) a r (P R Q) = \frac{1}{2} a r (A R C)$

Discussion

6441.	Have you seen long highway roads that never meet and are the same distance apart everywhere? What would such roads be called, in mathematical terms?
Answer» Have you seen long highway roads that never meet and are the same distance apart everywhere? What would such roads be called, in mathematical terms?

Discussion

6442.	The mirror image of point P(2, 3) taken about the origin is point P'. Find the coordinates of P'.
Answer» The mirror image of point P(2, 3) taken about the origin is point P'. Find the coordinates of P'.

Discussion

6443.	When (m/x) is plotted against 1/p for x/m=ap/1+bp , we get a straight line with slope and intercept are -
Answer» When (m/x) is plotted against 1/p for x/m=ap/1+bp , we get a straight line with slope and intercept are -

Discussion

6444.	O is the centre of the given circle, AB and CD are chords such that ON < OM. Which of the following is not correct?
Answer» O is the centre of the given circle, AB and CD are chords such that ON < OM. Which of the following is not correct?

Discussion

6445.	Meena and Anand each lent the same sum of money for 2 years at 5% simple interest rate and at 5% compound interest rate respectively. Anand received ₹15 more than Meena. Find the amount of money lent by them?
Answer» Meena and Anand each lent the same sum of money for 2 years at 5% simple interest rate and at 5% compound interest rate respectively. Anand received ₹15 more than Meena. Find the amount of money lent by them?

Discussion

6446.	If u:v = 2:3, find the ratio 15u + 12v : 20u + 16v
Answer» If u:v = 2:3, find the ratio 15u + 12v : 20u + 16v

Discussion

6447.	A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.
Answer» A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

Discussion

6448.	In the following figure, AD and EF are medians. What’s the length of FC?
Answer» In the following figure, AD and EF are medians. What’s the length of FC?

6448.

In the following figure, AD and EF are medians. What’s the length of FC?

Answer»

In the following figure, AD and EF are medians. What’s the length of FC?

Discussion

6449.	If ABCD is a rectangle, E and F are the mid-points of BC and AD respectively and G is any point on EF. Then ar(ΔGAB) : ar (rectangle ABCD) = _________.
Answer» If ABCD is a rectangle, E and F are the mid-points of BC and AD respectively and G is any point on EF. Then ar(ΔGAB) : ar (rectangle ABCD) = _________.

Discussion

6450.	33. In triangle ABC tan1/2(A+B).cot1/2(A-B) is equal to
Answer» 33. In triangle ABC tan1/2(A+B).cot1/2(A-B) is equal to

Discussion

Explore topic-wise InterviewSolutions in .

Question 177(vi)Find x.5x+5x−1=750

If |x|&lt;1then ddx(1−2x+3x2−........)=

Which of the following statements is true?(a) Product of two irrational numbers is always irrational(b) Product of a rational and an irrational number is always irrational(c) Sum of two irrational numbers can never be irrational(d) Sum of an integer and a rational number can never be an integer

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

A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown figure. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each types of paper needed to make the hand fan.

ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.

Let a, b, c be the sides of a triangle. The least value of expressionE=ab+c−a+bc+a−b+ca+b−c is ___

Question 6 Which of the following is irrational? Thinking process An irrational number cannot be expressed as a fraction. It cannot be represented as a terminating or repeating decimal. A) √49 B) √123 C) √7 D) √81

What is cartesian product?

For what value of k, the system of equations x + 2y = 5, 3x + ky + 15 = 0 has no solution? __

The construction of ΔABC, given that BC=3 cm, is possible when the difference of the sides AB and AC is equal to

Which of the following numbers mean the same as whole numbers?

What is the maximum number of zeroes in cubic polynomial?

From the options given below, choose the option which has all the measurements you will require to construct a quadrilateral ABCD.

How is 'a' raise to zero equal to one

13. Let P(3 2 6) be a point in space and Q be a point on the line r(vector)=(i-j+2k)+(3i+j+5k) then the value of for which the vector PQ is parallel to the plane x+4y+3z=1 is a)1/4. b)-1/4. c)1/8. d)-1/8

Question 1Write True or False and justify your answer :ABCD is a parallelogram and X is the mid - point of AB. If ar (AXCD) = 24 cm2, then ar (ABC) = 24 cm2

The 4 term of a H.P is 35 and 8th term is 13, then its 6th term is

The tent for an exhibition is as shown below, with a half-cylinder on top of a rectangular prism. What is the cost of making it, at the rate of 2000 rupees per square metre.

A well with 10 m inside diameter is dug 14m Deep Earth taken out of it is spread all around to a width of 5m to form an embankment

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

The volume of metallic cylinderical pipe is 784cm cu. Unit . It's length is 14cm and it's external radius is 9cm. Find its thickness.

The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm, what is the measure of shorter side?

The equation y = a represents a straight line parallel to __

The lengths of the sides of Δ ABC are consecutive integers. It Δ ABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?(a) 4(b) 6(c) 8(d) 10

The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Show that the quadrilateral is a trapezium.

If axn is a zero degree polynomial in x, what can be said about a and n?

In the given figure, M, N, and P are the mid-points of AB, AC, and BC, respectively. If MN = 3 cm, NP = 3.5 cm, and MP = 2.5 cm, find the perimeter of the triangle ABC (in cm).

Factorise: x2+3√3x+6

If 4sin2Θ−1=0 and angle Θ is less than 90°, find the value of cos2+tan2Θ ?

Question 13 Write the denominator of rational number 2575000 in the form 2m×5n, where m, n are non - negative integers. Hence, write its decimal expansion, without actual division.

A parallelogram having base 10 cm and height 8 cm is cut along its diagonal into two portions. What is the area of each portion?

Express each of the following decimals in the form pq : (i) 0.39 (ii) 0.750(iii) 2.15

Calculate the measure of ∠AOC.

Find the values of a and b if 7+√57−√5−7−√57+√5=a+711√5b

Define Irrational numbers.

Question 7 (i)P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that:(i)ar(PRQ)=12ar(ARC)

Have you seen long highway roads that never meet and are the same distance apart everywhere? What would such roads be called, in mathematical terms?

The mirror image of point P(2, 3) taken about the origin is point P'. Find the coordinates of P'.

When (m/x) is plotted against 1/p for x/m=ap/1+bp , we get a straight line with slope and intercept are -

O is the centre of the given circle, AB and CD are chords such that ON &lt; OM. Which of the following is not correct?

Meena and Anand each lent the same sum of money for 2 years at 5% simple interest rate and at 5% compound interest rate respectively. Anand received ₹15 more than Meena. Find the amount of money lent by them?

If u:v = 2:3, find the ratio 15u + 12v : 20u + 16v

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

In the following figure, AD and EF are medians. What’s the length of FC?

If ABCD is a rectangle, E and F are the mid-points of BC and AD respectively and G is any point on EF. Then ar(ΔGAB) : ar (rectangle ABCD) = _________.

33. In triangle ABC tan1/2(A+B).cot1/2(A-B) is equal to

If |x|<1then ddx(1−2x+3x2−........)=

O is the centre of the given circle, AB and CD are chords such that ON < OM. Which of the following is not correct?