24740 + Interview Questions in Mathematics Page 157 InterviewSolution

7801.	If A3=O, then I+A+A2 equals to
Answer» If $A^{3} = O$ , then $I + A + A^{2}$ equals to

Discussion

7802.	A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.
Answer» A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

Discussion

7803.	If g{f(x)}=\|sin x\| and f{g(x)}=(sin√x)2, then
Answer» If $g {f (x)} = \| s i n x \|$ and $f {g (x)} = (s i n \sqrt{x})^{2}$ , then

Discussion

7804.	If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 +c2.
Answer» If a + b + c = 9 and ab + bc + ca = 40, find a² + b² +c².

Discussion

7805.	A circle of radius 7.5 is inscribed in a square, then the area of shaded region is (π=3.14)
Answer» A circle of radius 7.5 is inscribed in a square, then the area of shaded region is ( $π = 3.14$ )

Discussion

7806.	Question 2Diagonals of a trapezium ABCD with AB \|\| DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD.
Answer» Question 2 Diagonals of a trapezium ABCD with AB \|\| DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD.

Discussion

7807.	The set {78,89,910,1011,1112} expressed in set-builder form is ____. (Here, N represents the set of natural numbers.)
Answer» The set ${\frac{7}{8}, \frac{8}{9}, \frac{9}{10}, \frac{10}{11}, \frac{11}{12}}$ expressed in set-builder form is ____. (Here, N represents the set of natural numbers.)

Discussion

7808.	Find a quadratic equation whose sum of zeros is 3 and product of zeros is 2
Answer» Find a quadratic equation whose sum of zeros is 3 and product of zeros is 2

Discussion

7809.	P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
Answer» P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.

Discussion

7810.	The number 665625 will terminate after how many decimal places?
Answer» The number $\frac{665}{625}$ will terminate after how many decimal places?

Discussion

7811.	Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm,supposing the material of which it is made weighs 10 grams per cubic cm.
Answer» Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm,supposing the material of which it is made weighs 10 grams per cubic cm.

Discussion

7812.	In the adjoining figure. line p ∥ line q. line l ∥ line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.
Answer» In the adjoining figure. line p ∥ line q. line l ∥ line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.

Discussion

7813.	Find two irrational number between 0.5 and 0.55
Answer» Find two irrational number between 0.5 and 0.55

Discussion

7814.	In figure AB = CB and O is the centre of the circle. Prove that BO bisects ∠ABC.
Answer» In figure AB = CB and O is the centre of the circle. Prove that BO bisects $∠$ ABC.

Discussion

7815.	Question 64 Fill in the blanks to make the statements true. The measure of each angle of a regular pentagon is .
Answer» Question 64 Fill in the blanks to make the statements true. The measure of each angle of a regular pentagon is .

Discussion

7816.	Which of the following is a false statement? (a) If the diagonals of a rhombus are 18 cm and 14 cm then its area is 126 cm2 (b) Area of a \|\|gm=12×base×corresponding height. (c) A parallelogram and a rectangle on the same base and between the same parallels are equal in area. (d) If the area of a \|\|gm with one side 24 cm and corresponding height h cm is 192 cm2 then h=8 cm.
Answer» Which of the following is a false statement? (a) If the diagonals of a rhombus are 18 cm and 14 cm then its area is $126 c m^{2}$ (b) Area of a \|\|gm= $\frac{1}{2} \times b a s e \times c o r r e s p o n d i n g h e i g h t$ . (c) A parallelogram and a rectangle on the same base and between the same parallels are equal in area. (d) If the area of a \|\|gm with one side 24 cm and corresponding height h cm is $192 c m^{2}$ then h=8 cm.

7816.

Which of the following is a false statement? (a) If the diagonals of a rhombus are 18 cm and 14 cm then its area is 126 cm2 (b) Area of a ||gm=12×base×corresponding height. (c) A parallelogram and a rectangle on the same base and between the same parallels are equal in area. (d) If the area of a ||gm with one side 24 cm and corresponding height h cm is 192 cm2 then h=8 cm.

Answer»

Which of the following is a false statement?

(a) If the diagonals of a rhombus are 18 cm and 14 cm then its area is $126 c m^{2}$

(b) Area of a ||gm= $\frac{1}{2} \times b a s e \times c o r r e s p o n d i n g h e i g h t$ .

(c) A parallelogram and a rectangle on the same base and between the same parallels are equal in area.

(d) If the area of a ||gm with one side 24 cm and corresponding height h cm is $192 c m^{2}$ then h=8 cm.

Discussion

7817.	If abc = 1, show that 11+a+b-1+11+b+c-1+11+c+a-1=1.
Answer» If abc = 1, show that $\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}} = 1$ .

Discussion

7818.	Simplify : 4−2+4−1+40+42
Answer» Simplify : $4^{- 2} + 4^{- 1} + 4^{0} + 4^{2}$

Discussion

7819.	3. The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go40 km upstream and 55 km downstream. Determine the speed of stream and that of theboat in still water.
Answer» 3. The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go40 km upstream and 55 km downstream. Determine the speed of stream and that of theboat in still water.

Discussion

7820.	U={x:x is a natural number & x≤10}A={a:a is an even number & a≤10}B={b:b is a prime number & b≤9}Then, Ac∩Bc is
Answer» $U = {x : x is a natural number & x \leq 10}$ $A = {a : a is an even number & a \leq 10}$ $B = {b : b is a prime number & b \leq 9}$ Then, $A^{c} \cap B^{c}$ is

7820.

U={x:x is a natural number & x≤10}A={a:a is an even number & a≤10}B={b:b is a prime number & b≤9}Then, Ac∩Bc is

Answer»

$U = {x : x is a natural number & x \leq 10}$

$A = {a : a is an even number & a \leq 10}$

$B = {b : b is a prime number & b \leq 9}$

Then, $A^{c} \cap B^{c}$ is

Discussion

7821.	If every side of a triangle is doubled, then increase in the area of the triangle is(a) 1002%(b) 200%(c) 300%(d) 400%
Answer» If every side of a triangle is doubled, then increase in the area of the triangle is (a) $100 \sqrt{2} %$ (b) 200% (c) 300% (d) 400%

Discussion

7822.	Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (A) 10 cm(B) 15 cm(C) 21 cm
Answer» Find the angle in radian through which a pendulum swings if its length is $75$ cm and the tip describes an arc of length $(A) 10$ cm $(B) 15$ cm $(C) 21$ cm

Discussion

7823.

An organisation selected 2400 families at random and surveyed them to determine a relationship between the income level and the number of vehicles in a family. The information gathered is listed in the table below: Monthly income (in ₹) Number of vehicles per family 0 1 2 3 or more Less than ₹ 25000 10 160 25 0 ₹ 25000 – ₹ 30000 0 305 27 2 ₹ 30000 – ₹ 35000 1 535 29 1 ₹ 35000 – ₹ 40000 2 469 59 25 ₹ 40000 or more 1 579 82 88 Suppose a family is chosen at random. Find the probability that the family chosen is(i) earning ₹ 25000 – ₹ 30000 per month and owning exactly 2 vehicles.(ii) earning ₹ 40000 or more per month and owning exactly 1 vehicle.(iii) earning less than ₹ 25000 per month and not owning any vehicle.(iv) earning ₹ 35000 – ₹ 40000 per month and owning 2 or more vehicles.(v) owning not more than 1 vehicle.

Answer» An organisation selected 2400 families at random and surveyed them to determine a relationship between the income level and the number of vehicles in a family. The information gathered is listed in the table below:

Monthly income (in ₹)	Number of vehicles per family
Monthly income (in ₹)	0	1	2	3 or more
Less than ₹ 25000	10	160	25	0
₹ 25000 – ₹ 30000	0	305	27	2
₹ 30000 – ₹ 35000	1	535	29	1
₹ 35000 – ₹ 40000	2	469	59	25
₹ 40000 or more	1	579	82	88

Suppose a family is chosen at random. Find the probability that the family chosen is

(i) earning ₹ 25000 – ₹ 30000 per month and owning exactly 2 vehicles.

(ii) earning ₹ 40000 or more per month and owning exactly 1 vehicle.

(iii) earning less than ₹ 25000 per month and not owning any vehicle.

(iv) earning ₹ 35000 – ₹ 40000 per month and owning 2 or more vehicles.

(v) owning not more than 1 vehicle.

Discussion

7824.	Divide the given polynomial by the given monomial(p3q6−p6q3)÷p3q3
Answer» Divide the given polynomial by the given monomial $(p^{3} q^{6} - p^{6} q^{3}) \div p^{3} q^{3}$

Discussion

7825.	The difference between simple interest and compound interest on Rs 1200 for one year at 10 per annum reckoned half-yearly is __________ ___
Answer» The difference between simple interest and compound interest on Rs $1200$ for one year at $10$ per annum reckoned half-yearly is __________ ___

Discussion

7826.	Factorise:6x2 + 17x + 12
Answer» Factorise: 6x²+ 17x + 12

Discussion

7827.	Question 20Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than 23 of a right angle.
Answer» Question 20 Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than $\frac{2}{3}$ of a right angle.

Discussion

7828.	P(x)= (5x^2-7x+1) then find the value of alpha and beta.
Answer» P(x)= (5x^2-7x+1) then find the value of alpha and beta.

Discussion

7829.	If the diagonals of a Quadrilateral do not lie in the interior of the Quadrilateral, then what kind of Quadrilateral is it?
Answer» If the diagonals of a Quadrilateral do not lie in the interior of the Quadrilateral, then what kind of Quadrilateral is it?

Discussion

7830.	Factorise the given polynomial x5y5+x3y3+x2y2
Answer» Factorise the given polynomial $x^{5} y^{5} + x^{3} y^{3} + x^{2} y^{2}$

Discussion

7831.	4^(x-√((x^2)-5)) -12×2^(x-1-√((x^2)-5)) +8=0
Answer» 4^(x-√((x^2)-5)) -12×2^(x-1-√((x^2)-5)) +8=0

Discussion

7832.	Q1. Find the value of (x-a)3+(x-b)3+(x-c)3-3(x-a)(x-b)(x-c), if a+b+c=3x.
Answer» Q1. Find the value of (x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c), if a+b+c=3x.

Discussion

7833.	If the flow rate of water from a pipe is 2m3/s, then how much time it will take to fill a bucket of volume 1200m3?
Answer» If the flow rate of water from a pipe is $2 m^{3} / s$ , then how much time it will take to fill a bucket of volume $1200 m^{3}$ ?

Discussion

7834.	If AD is median of ΔABC and P is a point on AC such thatar (ΔADP) : ar (ΔABD) = 2 : 3, then ar (Δ PDC) : ar (Δ ABC)(a) 1 : 5(b) 1 : 5(c) 1 : 6(d) 3 : 5
Answer» If AD is median of ΔABC and P is a point on AC such that ar (ΔADP) : ar (ΔABD) = 2 : 3, then ar (Δ PDC) : ar (Δ ABC) (a) 1 : 5 (b) 1 : 5 (c) 1 : 6 (d) 3 : 5

Discussion

7835.	Find the value of a, if 10a = (11 x 11) - (9 x 9).
Answer» Find the value of a, if 10a = (11 x 11) - (9 x 9).

Discussion

7836.	log10(x+1)+log10(x−1)=log1011+2log103Calculate the value of x.
Answer» ${log}_{10} (x + 1) + l o g_{10} (x - 1) = l o g_{10} 11 + 2 l o g_{10} 3$ Calculate the value of x.

Discussion

7837.	A cylindrical tube, open at both ends, is made of metal. The internal diameter of tube, is 10 cm. and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.
Answer» A cylindrical tube, open at both ends, is made of metal. The internal diameter of tube, is 10 cm. and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.

Discussion

7838.	What is the expansion of NSSO?
Answer» What is the expansion of NSSO?

Discussion

7839.	Solve using appropriate proper properties. 25×−37−114−37×35
Answer» Solve using appropriate proper properties. $\frac{2}{5} \times \frac{- 3}{7} - \frac{1}{14} - \frac{3}{7} \times \frac{3}{5}$

7839.

Solve using appropriate proper properties. 25×−37−114−37×35

Answer»

Solve using appropriate proper properties.

$\frac{2}{5} \times \frac{- 3}{7} - \frac{1}{14} - \frac{3}{7} \times \frac{3}{5}$

Discussion

7840.	Find unit and dimensions of a, b, and c.K.E= ax - bx^2 + cx^3
Answer» Find unit and dimensions of a, b, and c. K.E= ax - bx^2 + cx^3

Discussion

7841.	A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m2, what will be the cost of painting all these cones? (Use π = 3.14 and take= 1.02).
Answer» A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m², what will be the cost of painting all these cones? (Use π = 3.14 and take= 1.02).

Discussion

7842.	Name the type of quadrilateral formed, if any by the given points.(-3,5),(3,1),(0,3),(-1,-4).
Answer» Name the type of quadrilateral formed, if any by the given points. (-3,5),(3,1),(0,3),(-1,-4).

Discussion

7843.	Consider the sequence of numbers 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, .. Identify 5th,8th & 12th term in the above sequence.
Answer» Consider the sequence of numbers 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, .. Identify $5^{t h}$ , $8^{t h}$ & $12^{t h}$ term in the above sequence.

7843.

Consider the sequence of numbers 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, .. Identify 5th,8th & 12th term in the above sequence.

Answer»

Consider the sequence of numbers

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, ..

Identify $5^{t h}$ , $8^{t h}$ & $12^{t h}$ term in the above sequence.

Discussion

7844.	The following is the data of wages per day : 5, 4, 7, 5, 8, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8The mode of the data is(a) 7(b) 5(c) 8(d) 10
Answer» The following is the data of wages per day : 5, 4, 7, 5, 8, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8 The mode of the data is (a) 7 (b) 5 (c) 8 (d) 10

Discussion

7845.	Let f(x) and g(x) be two continuous functions and h(x)=limn→∞x2n⋅f(x)+x2m⋅g(x)(x2n+1),m∈R. If limx→1h(x) exists, then one root of f(x)−g(x)=0 is
Answer» Let $f (x)$ and $g (x)$ be two continuous functions and $h (x) = lim n \to \infty \frac{x^{2 n} \cdot f (x) + x^{2 m} \cdot g (x)}{(x^{2 n} + 1)}, m \in R$ . If $lim x \to 1 h (x)$ exists, then one root of $f (x) - g (x) = 0$ is

Discussion

7846.	If x = 2 and y = 4, then xyx-y+yxy-x =(a) 4(b) 8(c) 12(d) 2
Answer» If x = 2 and y = 4, then ${(\frac{x}{y})}^{x - y} + {(\frac{y}{x})}^{y - x} =$ (a) 4 (b) 8 (c) 12 (d) 2

Discussion

7847.	The perimeter of the given triangle is 12 cm. Find the measure of the side AB.4
Answer» The perimeter of the given triangle is 12 cm. Find the measure of the side AB. 4

Discussion

7848.	16. If a point T is 6 units from the centre of a circle of radius 10 units, then the total number of different chords of the circle passing through T and have integral length is (A) 8 (B) 4 (C) 5 (D) 10
Answer» 16. If a point T is 6 units from the centre of a circle of radius 10 units, then the total number of different chords of the circle passing through T and have integral length is (A) 8 (B) 4 (C) 5 (D) 10

Discussion

7849.	If a transversal intersects two parallel lines, then, which of the following statements holds true?
Answer» If a transversal intersects two parallel lines, then, which of the following statements holds true?

Discussion

7850.

A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively.If quadrilateral ABCD is a rectangle, what can be said about quadrilateral PQRS?

Answer»

A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively.

If quadrilateral ABCD is a rectangle, what can be said about quadrilateral PQRS?

Discussion

Explore topic-wise InterviewSolutions in .

If A3=O, then I+A+A2 equals to

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

If g{f(x)}=|sin x| and f{g(x)}=(sin√x)2, then

If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 +c2.

A circle of radius 7.5 is inscribed in a square, then the area of shaded region is (π=3.14)

Question 2Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD.

The set {78,89,910,1011,1112} expressed in set-builder form is ____. (Here, N represents the set of natural numbers.)

Find a quadratic equation whose sum of zeros is 3 and product of zeros is 2

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

The number 665625 will terminate after how many decimal places?

Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm,supposing the material of which it is made weighs 10 grams per cubic cm.

In the adjoining figure. line p ∥ line q. line l ∥ line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.

Find two irrational number between 0.5 and 0.55

In figure AB = CB and O is the centre of the circle. Prove that BO bisects ∠ABC.

Question 64 Fill in the blanks to make the statements true. The measure of each angle of a regular pentagon is .

If abc = 1, show that 11+a+b-1+11+b+c-1+11+c+a-1=1.

Simplify : 4−2+4−1+40+42

3. The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go40 km upstream and 55 km downstream. Determine the speed of stream and that of theboat in still water.

U={x:x is a natural number &amp; x≤10}A={a:a is an even number &amp; a≤10}B={b:b is a prime number &amp; b≤9}Then, Ac∩Bc is

If every side of a triangle is doubled, then increase in the area of the triangle is(a) 1002%(b) 200%(c) 300%(d) 400%

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (A) 10 cm(B) 15 cm(C) 21 cm

Divide the given polynomial by the given monomial(p3q6−p6q3)÷p3q3

The difference between simple interest and compound interest on Rs 1200 for one year at 10 per annum reckoned half-yearly is __________ ___

Factorise:6x2 + 17x + 12

Question 20Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than 23 of a right angle.

P(x)= (5x^2-7x+1) then find the value of alpha and beta.

If the diagonals of a Quadrilateral do not lie in the interior of the Quadrilateral, then what kind of Quadrilateral is it?

Factorise the given polynomial x5y5+x3y3+x2y2

4^(x-√((x^2)-5)) -12×2^(x-1-√((x^2)-5)) +8=0

Q1. Find the value of (x-a)3+(x-b)3+(x-c)3-3(x-a)(x-b)(x-c), if a+b+c=3x.

If the flow rate of water from a pipe is 2m3/s, then how much time it will take to fill a bucket of volume 1200m3?

If AD is median of ΔABC and P is a point on AC such thatar (ΔADP) : ar (ΔABD) = 2 : 3, then ar (Δ PDC) : ar (Δ ABC)(a) 1 : 5(b) 1 : 5(c) 1 : 6(d) 3 : 5

Find the value of a, if 10a = (11 x 11) - (9 x 9).

log10(x+1)+log10(x−1)=log1011+2log103Calculate the value of x.

A cylindrical tube, open at both ends, is made of metal. The internal diameter of tube, is 10 cm. and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.

What is the expansion of NSSO?

Solve using appropriate proper properties. 25×−37−114−37×35

Find unit and dimensions of a, b, and c.K.E= ax - bx^2 + cx^3

Name the type of quadrilateral formed, if any by the given points.(-3,5),(3,1),(0,3),(-1,-4).

Consider the sequence of numbers 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, .. Identify 5th,8th &amp; 12th term in the above sequence.

The following is the data of wages per day : 5, 4, 7, 5, 8, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8The mode of the data is(a) 7(b) 5(c) 8(d) 10

Let f(x) and g(x) be two continuous functions and h(x)=limn→∞x2n⋅f(x)+x2m⋅g(x)(x2n+1),m∈R. If limx→1h(x) exists, then one root of f(x)−g(x)=0 is

If x = 2 and y = 4, then xyx-y+yxy-x =(a) 4(b) 8(c) 12(d) 2

The perimeter of the given triangle is 12 cm. Find the measure of the side AB.4

16. If a point T is 6 units from the centre of a circle of radius 10 units, then the total number of different chords of the circle passing through T and have integral length is (A) 8 (B) 4 (C) 5 (D) 10

If a transversal intersects two parallel lines, then, which of the following statements holds true?

A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively.If quadrilateral ABCD is a rectangle, what can be said about quadrilateral PQRS?

U={x:x is a natural number & x≤10}A={a:a is an even number & a≤10}B={b:b is a prime number & b≤9}Then, Ac∩Bc is

The difference between simple interest and compound interest on Rs 1200 for one year at 10 per annum reckoned half-yearly is ________ _

Consider the sequence of numbers 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, .. Identify 5th,8th & 12th term in the above sequence.