24740 + Interview Questions in Mathematics Page 52 InterviewSolution

2551.	If a quadratic polynomial f(x) = ax^{2_{}} + bx + c is expressed as the product of two linear factors as (px + q) and (rx + s), where p, q, r & s are real numbers, then which of the following is one of the roots of f(x) = 0?
Answer» If a quadratic polynomial f(x) = ax^{2_{}} + bx + c is expressed as the product of two linear factors as (px + q) and (rx + s), where p, q, r & s are real numbers, then which of the following is one of the roots of f(x) = 0?

Discussion

2552.	If x=3−2√2 , then 1x= _____.
Answer» If $x = 3 - 2 \sqrt{2}$ , then $\frac{1}{x} =$ _____.

Discussion

2553.	Find the area in cm2 of the shaded region where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre. [2 MARKS]
Answer» Find the area in ${c m}^{2}$ of the shaded region where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre. [2 MARKS]

2553.

Find the area in cm2 of the shaded region where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre. [2 MARKS]

Answer»

Find the area in ${c m}^{2}$ of the shaded region where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre. [2 MARKS]

Discussion

2554.	if A= \{x: -1
Answer» if A= \{x: -1

Discussion

2555.	In the given figure area of Δ DAC is 60 cm2, then the area of of parallelogram ABCD is
Answer» In the given figure area of $Δ D A C$ is $60 c m^{2}$ , then the area of of parallelogram ABCD is

2555.

In the given figure area of Δ DAC is 60 cm2, then the area of of parallelogram ABCD is

Answer»

In the given figure area of $Δ D A C$ is $60 c m^{2}$ , then the area of of parallelogram ABCD is

Discussion

2556.	If (x−1)3 = 8, what is the value of (x+1)2
Answer» If $(x - 1)^{3}$ = 8, what is the value of $(x + 1)^{2}$

Discussion

2557.	Question 1Three angles of a quadrilateral are 75∘,90∘ and 75∘, then the fourth angle is(a) 90∘(b) 95∘(c) 105∘(d) 120∘
Answer» Question 1 Three angles of a quadrilateral are $75^{\circ}, 90^{\circ} a n d 75^{\circ}$ , then the fourth angle is (a) $90^{\circ}$ (b) $95^{\circ}$ (c) $105^{\circ}$ (d) $120^{\circ}$

Discussion

2558.	__________ is the equation of y-axis.
Answer» __________ is the equation of y-axis.

Discussion

2559.	factorisation of a2+1a2−27 is equal to .
Answer» factorisation of $a^{2} + \frac{1}{a^{2}} - 27$ is equal to .

Discussion

2560.	of the following rational numbers is a non-terminating and repeating decimal.
Answer» of the following rational numbers is a non-terminating and repeating decimal.

Discussion

2561.	7. Solve the following pair of linear equation using substitution method x+y=a-b ax-by=asq+bsq By getting the value of x from equation 1
Answer» 7. Solve the following pair of linear equation using substitution method x+y=a-b ax-by=asq+bsq By getting the value of x from equation 1

Discussion

2562.	Diagonals AC and BD of a trapezium ABCD with AB ∥ DC intersect each other at O. Prove that ar (△AOD) = ar (△BOC). [1 MARK]
Answer» Diagonals AC and BD of a trapezium ABCD with AB $∥$ DC intersect each other at O. Prove that ar ( $△$ AOD) = ar ( $△$ BOC). [1 MARK]

Discussion

2563.	Find an irrational number between 27 and 37.
Answer» Find an irrational number between $\frac{2}{7}$ and $\frac{3}{7}$ .

Discussion

2564.	Tap on the circle that has not been divided into halves.
Answer» Tap on the circle that has not been divided into halves.

Discussion

2565.	Which of the following tests cannot be undertaken for checking the construction of triangles?
Answer» Which of the following tests cannot be undertaken for checking the construction of triangles?

Discussion

2566.	Two identical prisms with base a right angled triangle are joined together to form a rectangular prism, as in the picture below: What is the surface area of this rectangular prism?
Answer» Two identical prisms with base a right angled triangle are joined together to form a rectangular prism, as in the picture below: What is the surface area of this rectangular prism?

2566.

Two identical prisms with base a right angled triangle are joined together to form a rectangular prism, as in the picture below: What is the surface area of this rectangular prism?

Answer»

Two identical prisms with base a right angled triangle are joined together to form a rectangular prism, as in the picture below:

What is the surface area of this rectangular prism?

Discussion

2567.	If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find the value of p. Also, find the length of AB.
Answer» If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find the value of p. Also, find the length of AB.

Discussion

2568.	Question 12 100 perons had food provision for 24 days. If 20 persons left the place, the provision will last for (a)30 days (b)965days (c)120 days (d)40 days
Answer» Question 12 100 perons had food provision for 24 days. If 20 persons left the place, the provision will last for (a)30 days $(b) \frac{96}{5} d a y s$ (c)120 days (d)40 days

2568.

Question 12 100 perons had food provision for 24 days. If 20 persons left the place, the provision will last for (a)30 days (b)965days (c)120 days (d)40 days

Answer»

Question 12

100 perons had food provision for 24 days. If 20 persons left the place, the provision will last for
(a)30 days
$(b) \frac{96}{5} d a y s$
(c)120 days
(d)40 days

Discussion

2569.	In a parallelogram ABCD, if ∠DAB = 75° and ∠DBC = 60°, then ∠BDC =(a) 75°(b) 60°(c) 45°(d) 55°
Answer» In a parallelogram ABCD, if ∠DAB = 75° and ∠DBC = 60°, then ∠BDC = (a) 75° (b) 60° (c) 45° (d) 55°

Discussion

2570.	Draw the graph of the equation-2x+y-7=0 check whether the point (-3, -2) is on the given line
Answer» Draw the graph of the equation-2x+y-7=0 check whether the point (-3, -2) is on the given line

Discussion

2571.	The sum of the digits of a two-digit number is 7. If the number formed by interchanging the digits is less than the original number by 27, then find the original number.
Answer» The sum of the digits of a two-digit number is 7. If the number formed by interchanging the digits is less than the original number by 27, then find the original number.

Discussion

2572.	A triangle ABC has ∠ B = ∠ C. Prove that : (i) The perpendiculars from the mid-point of BC to AB and AC are equal. (ii) The perpendiculars from B and C to the opposite sides are equal.
Answer» A triangle ABC has $∠$ B = $∠$ C. Prove that : (i) The perpendiculars from the mid-point of BC to AB and AC are equal. (ii) The perpendiculars from B and C to the opposite sides are equal.

2572.

A triangle ABC has ∠ B = ∠ C. Prove that : (i) The perpendiculars from the mid-point of BC to AB and AC are equal. (ii) The perpendiculars from B and C to the opposite sides are equal.

Answer»

A triangle ABC has $∠$ B = $∠$ C.
Prove that :

(i) The perpendiculars from the mid-point of BC to AB and AC are equal.

(ii) The perpendiculars from B and C to the opposite sides are equal.

Discussion

2573.	Question 10D and E are the mid-points of the sides AB and AC of ∆ABC and O is any point on Side BC. O is joined to A, if P and Q are the mid-points of OB and OC respectively, then DEQP is(A) a square(B) a rectangle(C) a rhombus(D) a parallelogram
Answer» Question 10 D and E are the mid-points of the sides AB and AC of ∆ABC and O is any point on Side BC. O is joined to A, if P and Q are the mid-points of OB and OC respectively, then DEQP is (A) a square (B) a rectangle (C) a rhombus (D) a parallelogram

Discussion

2574.	Find the values of cot θ and cosec θ in the figure given above.
Answer» Find the values of $c o t θ a n d c o s e c θ$ in the figure given above.

Discussion

2575.	Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.
Answer» Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.

Discussion

2576.	The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which asses through the points (–3, 1) and (2, –2) is(a) 5x2 + 3y2 = 32(b) 3x2 + 5y2 = 32(c) 5x2 – 3y2 = 32(d) 3x2 + 5y2 + 32 = 0
Answer» The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which asses through the points (–3, 1) and (2, –2) is (a) 5x² + 3y² = 32 (b) 3x² + 5y² = 32 (c) 5x² – 3y² = 32 (d) 3x² + 5y² + 32 = 0

Discussion

2577.	In triangle ABC, right angled at C, the number of values of x such that sin−1(x)=sin−1(axc)+sin−1(bxc), where a,b,c are the sides of triangle is
Answer» In triangle $A B C,$ right angled at $C,$ the number of values of $x$ such that ${sin}^{- 1} (x) = {sin}^{- 1} (\frac{a x}{c}) + {sin}^{- 1} (\frac{b x}{c})$ , where $a, b, c$ are the sides of triangle is

Discussion

2578.	Factorize: p3+27
Answer» Factorize: $p^{3} + 27$

2578.

Factorize: p3+27

Answer»

Factorize:

$p^{3} + 27$

Discussion

2579.	Question 8(i)Using (x+a)(x+b)=x2+(a+b)x+ab, find103×104
Answer» Question 8(i) Using $(x + a) (x + b) = x^{2} + (a + b) x + a b$ , find $103 \times 104$

Discussion

2580.	The consecutive class marks of a data having continuous class intervals having class width as 5, have a gap of ________ between them.
Answer» The consecutive class marks of a data having continuous class intervals having class width as 5, have a gap of ________ between them.

Discussion

2581.	The decimal expansion of pi is:
Answer» The decimal expansion of pi is:

Discussion

2582.	When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively. Find the polynomial.
Answer» When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively. Find the polynomial.

Discussion

2583.	PQR is a triangle in which \angle Q = 2\angle R. If a line PS is drawn from vertex P such that it bisects \angle QPR and cuts QR at S such that PQ = RS, then what is the value of \angle QPR + \angle QRP?
Answer» PQR is a triangle in which \angle Q = 2\angle R. If a line PS is drawn from vertex P such that it bisects \angle QPR and cuts QR at S such that PQ = RS, then what is the value of \angle QPR + \angle QRP?

Discussion

2584.	In Fig. 93, if AOC is a straight line, then x =(a) 42°(b) 52°(c) 142°(d) 38°
Answer» In Fig. 93, if AOC is a straight line, then x = (a) 42° (b) 52° (c) 142° (d) 38°

Discussion

2585.	Construct a △ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and ∠B=45∘.
Answer» Construct a $△$ ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and $∠ B = 45^{\circ}$ .

Discussion

2586.	The median of a triangle divides it into two
Answer» The median of a triangle divides it into two

Discussion

2587.	Question 1 (ii)In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that:AO bisects ∠ A
Answer» Question 1 (ii) In an isosceles triangle ABC, with AB = AC, the bisectors of $∠ B a n d ∠ C$ intersect each other at O. Join A to O. Show that: AO bisects $∠ A$

Discussion

2588.	ABCD is a rectangle with ∠ABD = 40°. Determine ∠DBC.
Answer» ABCD is a rectangle with ∠ABD = 40°. Determine ∠DBC.

Discussion

2589.	If A and B are square matrices of the same order and A is non-singular, then for a positive integer n,(A−1BA)n is always equal to
Answer» If $A$ and $B$ are square matrices of the same order and $A$ is non-singular, then for a positive integer $n, (A^{- 1} B A)^{n}$ is always equal to

Discussion

2590.	23.Find non zero values for p and q for which p and q are zeroes of x2+px+q
Answer» 23.Find non zero values for p and q for which p and q are zeroes of x2+px+q

Discussion

2591.	Construct a polynomial equation, of the least dgree with rational coefficient one of whose root is sin 10 degree
Answer» Construct a polynomial equation, of the least dgree with rational coefficient one of whose root is sin 10 degree

Discussion

2592.	Describe the sample space for the indicated experiment :A coin is tossed and then a die is rolled only in case a head is shown on the coin.
Answer» Describe the sample space for the indicated experiment : A coin is tossed and then a die is rolled only in case a head is shown on the coin.

Discussion

2593.	The amount of water required by a paddy sapling for growth is[(15÷5)3−(7+12)]×6 mL= mL
Answer» The amount of water required by a paddy sapling for growth is $[(15 \div 5)^{3} - (7 + 12)] \times 6$ mL = mL

Discussion

2594.	If 4x−5y3x+y=1,then 2x2+y22x2−y2=[1 Mark ]
Answer» $If \frac{4 x - 5 y}{3 x + y} = 1, then \frac{2 x^{2} + y^{2}}{2 x^{2} - y^{2}} =$ [1 Mark ]

Discussion

2595.	An element A crystallizes in fcc unit cell.Find the new packing fraction of the unit cell so obtained when a guest atom B having the largest possible size is present at the body centre in such a way that dimension of the unit cell doesn't change.Given :(√2−1)3≈0.07
Answer» An element A crystallizes in fcc unit cell. Find the new packing fraction of the unit cell so obtained when a guest atom B having the largest possible size is present at the body centre in such a way that dimension of the unit cell doesn't change. Given : $(\sqrt{2} - 1)^{3} \approx 0.07$

Discussion

2596.	In the given figure, if AB \|\| CD and CD \|\| EF, find ∠ACE.
Answer» In the given figure, if AB \|\| CD and CD \|\| EF, find ∠ACE.

Discussion

2597.	Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.
Answer» Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m³.

Discussion

2598.	A chord 8 cm long is 3 cm away from the centre of the circle. What is the length of a chord which is 4 cm away from the centre?
Answer» A chord 8 cm long is 3 cm away from the centre of the circle. What is the length of a chord which is 4 cm away from the centre?

Discussion

2599.	Why surface area and curved surface area is changed during the conversion of one shape to another and volume is not changed.
Answer» Why surface area and curved surface area is changed during the conversion of one shape to another and volume is not changed.

Discussion

2600.	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 length of BC, AB and AC respectively.
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 length of BC, AB and AC respectively.

Discussion

Explore topic-wise InterviewSolutions in .

If a quadratic polynomial f(x) = ax^{2_{}} + bx + c is expressed as the product of two linear factors as (px + q) and (rx + s), where p, q, r & s are real numbers, then which of the following is one of the roots of f(x) = 0?

If x=3−2√2 , then 1x= _____.

Find the area in cm2 of the shaded region where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre. [2 MARKS]

if A= \{x: -1

In the given figure area of Δ DAC is 60 cm2, then the area of of parallelogram ABCD is

If (x−1)3 = 8, what is the value of (x+1)2

Question 1Three angles of a quadrilateral are 75∘,90∘ and 75∘, then the fourth angle is(a) 90∘(b) 95∘(c) 105∘(d) 120∘

__________ is the equation of y-axis.

factorisation of a2+1a2−27 is equal to .

of the following rational numbers is a non-terminating and repeating decimal.

7. Solve the following pair of linear equation using substitution method x+y=a-b ax-by=asq+bsq By getting the value of x from equation 1

Diagonals AC and BD of a trapezium ABCD with AB ∥ DC intersect each other at O. Prove that ar (△AOD) = ar (△BOC). [1 MARK]

Find an irrational number between 27 and 37.

Tap on the circle that has not been divided into halves.

Which of the following tests cannot be undertaken for checking the construction of triangles?

Two identical prisms with base a right angled triangle are joined together to form a rectangular prism, as in the picture below: What is the surface area of this rectangular prism?

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find the value of p. Also, find the length of AB.

Question 12 100 perons had food provision for 24 days. If 20 persons left the place, the provision will last for (a)30 days (b)965days (c)120 days (d)40 days

In a parallelogram ABCD, if ∠DAB = 75° and ∠DBC = 60°, then ∠BDC =(a) 75°(b) 60°(c) 45°(d) 55°

Draw the graph of the equation-2x+y-7=0 check whether the point (-3, -2) is on the given line

The sum of the digits of a two-digit number is 7. If the number formed by interchanging the digits is less than the original number by 27, then find the original number.

A triangle ABC has ∠ B = ∠ C. Prove that : (i) The perpendiculars from the mid-point of BC to AB and AC are equal. (ii) The perpendiculars from B and C to the opposite sides are equal.

Question 10D and E are the mid-points of the sides AB and AC of ∆ABC and O is any point on Side BC. O is joined to A, if P and Q are the mid-points of OB and OC respectively, then DEQP is(A) a square(B) a rectangle(C) a rhombus(D) a parallelogram

Find the values of cot θ and cosec θ in the figure given above.

Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.

The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which asses through the points (–3, 1) and (2, –2) is(a) 5x2 + 3y2 = 32(b) 3x2 + 5y2 = 32(c) 5x2 – 3y2 = 32(d) 3x2 + 5y2 + 32 = 0

In triangle ABC, right angled at C, the number of values of x such that sin−1(x)=sin−1(axc)+sin−1(bxc), where a,b,c are the sides of triangle is

Factorize: p3+27

Question 8(i)Using (x+a)(x+b)=x2+(a+b)x+ab, find103×104

The consecutive class marks of a data having continuous class intervals having class width as 5, have a gap of ________ between them.

The decimal expansion of pi is:

When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively. Find the polynomial.

PQR is a triangle in which \angle Q = 2\angle R. If a line PS is drawn from vertex P such that it bisects \angle QPR and cuts QR at S such that PQ = RS, then what is the value of \angle QPR + \angle QRP?

In Fig. 93, if AOC is a straight line, then x =(a) 42°(b) 52°(c) 142°(d) 38°

Construct a △ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and ∠B=45∘.

The median of a triangle divides it into two

Question 1 (ii)In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that:AO bisects ∠ A

ABCD is a rectangle with ∠ABD = 40°. Determine ∠DBC.

If A and B are square matrices of the same order and A is non-singular, then for a positive integer n,(A−1BA)n is always equal to

23.Find non zero values for p and q for which p and q are zeroes of x2+px+q

Construct a polynomial equation, of the least dgree with rational coefficient one of whose root is sin 10 degree

Describe the sample space for the indicated experiment :A coin is tossed and then a die is rolled only in case a head is shown on the coin.

The amount of water required by a paddy sapling for growth is[(15÷5)3−(7+12)]×6 mL= mL

If 4x−5y3x+y=1,then 2x2+y22x2−y2=[1 Mark ]

An element A crystallizes in fcc unit cell.Find the new packing fraction of the unit cell so obtained when a guest atom B having the largest possible size is present at the body centre in such a way that dimension of the unit cell doesn't change.Given :(√2−1)3≈0.07

In the given figure, if AB || CD and CD || EF, find ∠ACE.

Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.

A chord 8 cm long is 3 cm away from the centre of the circle. What is the length of a chord which is 4 cm away from the centre?

Why surface area and curved surface area is changed during the conversion of one shape to another and volume is not changed.

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 length of BC, AB and AC respectively.