32581 + Interview Questions in Mathematics Page 83 InterviewSolution

4101.	Carry out the following subtarctions involving rational numbers.(i) 711-37(ii) 1336-240(iii) 123-356(iv) 412-313
Answer» Carry out the following subtarctions involving rational numbers. (i) $\frac{7}{11} - \frac{3}{7}$ (ii) $\frac{13}{36} - \frac{2}{40}$ (iii) $1 \frac{2}{3} - 3 \frac{5}{6}$ (iv) $4 \frac{1}{2} - 3 \frac{1}{3}$

Discussion

4102.	locus of the middle points of chords of the circle x^2+y^2=16 which subtend a right angle at the centre is
Answer» locus of the middle points of chords of the circle x^2+y^2=16 which subtend a right angle at the centre is

Discussion

4103.	Find the points which divide the line segment joining A(-4, 0) and B(0, 6) into four equal parts.
Answer» Find the points which divide the line segment joining A(-4, 0) and B(0, 6) into four equal parts.

Discussion

4104.	The area of a rhombus is 2016cm2 . If it's one side is 65 cm then find it's diagonal.
Answer» The area of a rhombus is 2016cm2 . If it's one side is 65 cm then find it's diagonal.

Discussion

4105.	The three vertices of a parallelogram ABCD takenin order are A(4, 3), B(-1, 2) and C(-2, -3). Find the coordinates of the fourth vertex.
Answer» The three vertices of a parallelogram ABCD takenin order are A(4, 3), B(-1, 2) and C(-2, -3). Find the coordinates of the fourth vertex.

Discussion

4106.	Question 3 (i)In the given figure, ABD is a triangle right angled at A and AC⊥BD. Show that(i)AB2=BC×BD
Answer» Question 3 (i) In the given figure, ABD is a triangle right angled at A and $A C ⊥ B D$ . Show that $(i) A B^{2} = B C \times B D$

Discussion

4107.	Prove that 2-\surd3 is an irrationa
Answer» Prove that 2-\surd3 is an irrationa

Discussion

4108.	(√3-1)/(√3+1)=a+b√(3 ). Find a, b
Answer» (√3-1)/(√3+1)=a+b√(3 ). Find a, b

Discussion

4109.	149. If f(x)=ax+b/cx+d, then (fof)(x)=x,prove that d+a=0
Answer» 149. If f(x)=ax+b/cx+d, then (fof)(x)=x,prove that d+a=0

Discussion

4110.	If - 1,3 are zeros of the polynomial p(x) =2x3-9x2+4x+15, then third zero of p(x) is
Answer» If - 1,3 are zeros of the polynomial p(x) =2x3-9x2+4x+15, then third zero of p(x) is

Discussion

4111.	Match the following to their roots.
Answer» Match the following to their roots.

Discussion

4112.	Distance between two points P and Q is 100 km. At the same time a bus is moving from point P and another bus is moving from point Q.When they are moving in same direction they meet after 5 hours and when they move in opposite direction then they meet after 1 hours .Find the velocity of two buses.
Answer» Distance between two points P and Q is 100 km. At the same time a bus is moving from point P and another bus is moving from point Q.When they are moving in same direction they meet after 5 hours and when they move in opposite direction then they meet after 1 hours .Find the velocity of two buses.

Discussion

4113.	The side of a rhombus is 18 cm and one of its diagonals is 11 cm. The area of the rhombus is
Answer» The side of a rhombus is 18 cm and one of its diagonals is 11 cm. The area of the rhombus is

Discussion

4114.	An integer is chosen at random between 1and 100. Find probability of Multiple of 8 Not multiple of 8
Answer» An integer is chosen at random between 1and 100. Find probability of Multiple of 8 Not multiple of 8

4114.

An integer is chosen at random between 1and 100. Find probability of Multiple of 8 Not multiple of 8

Answer»

An integer is chosen at random between 1and 100. Find probability of

Multiple of 8

Not multiple of 8

Discussion

4115.	A triangle ABC is drawn to circumscribe a circle such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 20 cm respectively. If the area of the triangle is 120 cm2, what is the value of AB + AC?
Answer» A triangle ABC is drawn to circumscribe a circle such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 20 cm respectively. If the area of the triangle is 120 ${c m}^{2}$ , what is the value of AB + AC?

4115.

A triangle ABC is drawn to circumscribe a circle such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 20 cm respectively. If the area of the triangle is 120 cm2, what is the value of AB + AC?

Answer»

A triangle ABC is drawn to circumscribe a circle such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 20 cm respectively. If the area of the triangle is 120 ${c m}^{2}$ , what is the value of AB + AC?

Discussion

4116.	The least value of &quotP" for which the two curves arg(z)=/6 and \|z-23i\|=P intersect each other
Answer» The least value of "P" for which the two curves arg(z)=/6 and \|z-23i\|=P intersect each other

Discussion

4117.	In the given figure, H and I are the points on side GJ of aΔFGJ, such that BD = CE and FH = FI. Show that ΔFGH ≅ ΔFJI.
Answer» In the given figure, H and I are the points on side GJ of a ΔFGJ, such that BD = CE and FH = FI. Show that ΔFGH ≅ ΔFJI.

Discussion

4118.	Find the roots of the quadratic equation √2x2+7x+5√2 = 0 using factorization method.
Answer» Find the roots of the quadratic equation $\sqrt{2} x^{2} + 7 x + 5 \sqrt{2}$ = 0 using factorization method.

Discussion

4119.	What is the distance between two parallel tangents of a circle of the radius 4 cm?
Answer» What is the distance between two parallel tangents of a circle of the radius 4 cm?

Discussion

4120.	In the figure below, two tangents are drawn from a point P to a circle meeting it at points A and C.If ∠AOC=120∘, what is the value of ∠APC?
Answer» In the figure below, two tangents are drawn from a point P to a circle meeting it at points A and C. If $∠ A O C = 120^{\circ}$ , what is the value of $∠ A P C$ ?

Discussion

4121.	37. In an A.P.,if the pth term is 1/q and the qth term is 1/p(p is not equal to q), prove that the sum of first pq term must be 1/2(pq+1)
Answer» 37. In an A.P.,if the pth term is 1/q and the qth term is 1/p(p is not equal to q), prove that the sum of first pq term must be 1/2(pq+1)

Discussion

4122.	The printed price of a computer is Rs.24,000. The seller allows a discount of 8% on the printed price. He gives a further off season discount of 5% on the balance. But sales tax at 10% is charged on the remaining amount. Find (i) the sales tax amounts a customer has to pay (ii) the final price he has to pay for computer.
Answer» The printed price of a computer is Rs.24,000. The seller allows a discount of $8 %$ on the printed price. He gives a further off season discount of 5% on the balance. But sales tax at $10 %$ is charged on the remaining amount. Find (i) the sales tax amounts a customer has to pay (ii) the final price he has to pay for computer.

Discussion

4123.	AB is a line segment and M is its mid-point. Semi-circles are drawn with AM, MB and AB as diameters on the same side of AB. A circle is drawn to touch all the three semi-circles. Its radius is:
Answer» AB is a line segment and M is its mid-point. Semi-circles are drawn with AM, MB and AB as diameters on the same side of AB. A circle is drawn to touch all the three semi-circles. Its radius is:

Discussion

4124.	On selling a chair of Rs. 736, a shopkeeper suffers a loss of 8%. At what price should he sell it, so as to gain 8%?
Answer» On selling a chair of $R s . 736$ , a shopkeeper suffers a loss of $8 %$ . At what price should he sell it, so as to gain $8 %$ ?

Discussion

4125.	Rs 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs 12 less. Find 'x'. [4 MARKS]
Answer» Rs 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs 12 less. Find 'x'. [4 MARKS]

Discussion

4126.	Some students planned a picnic. The total budget for hiring a bus was Rs.1440. Later on, eight of these refused to go and instead paid their total share of money towards the fee of one economically weak student, and thus the cost of each member, who went for picnic increased by Rs. 30 How many students attended the picnic and how much money was paid towards the fees?
Answer» Some students planned a picnic. The total budget for hiring a bus was Rs.1440. Later on, eight of these refused to go and instead paid their total share of money towards the fee of one economically weak student, and thus the cost of each member, who went for picnic increased by $R s . 30$ How many students attended the picnic and how much money was paid towards the fees?

Discussion

4127.	Sum of three consecutive terms in an AP is 15 and their product is 0. The sequence is?
Answer» Sum of three consecutive terms in an AP is 15 and their product is 0. The sequence is?

Discussion

4128.	Find the roots of the following quadratic equations by the factorisation method.2x2+53x−2=0
Answer» Find the roots of the following quadratic equations by the factorisation method. $2 x^{2} + \frac{5}{3} x - 2 = 0$

Discussion

4129.	Cosec theta+cot theta/ cosec theta - cot theta = 81/49. Find cosec theta + sin theta / sin theta - cosec theta
Answer» Cosec theta+cot theta/ cosec theta - cot theta = 81/49. Find cosec theta + sin theta / sin theta - cosec theta

Discussion

4130.	The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:Length(in mm)Number of leaves118−1263127−1355136−1449145−15312154−1625163−1714172−1802 Convert given table into a continuous group frequency distribution.
Answer» The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table: $\begin{matrix} Length(in mm) & Number of leaves 118 - 126 & 3 127 - 135 & 5 136 - 144 & 9 145 - 153 & 12 154 - 162 & 5 163 - 171 & 4 172 - 180 & 2 \end{matrix}$ Convert given table into a continuous group frequency distribution.

Discussion

4131.	Prove that the tangent at any point of a circle is perpendicular to the radius through the points of contact.
Answer» Prove that the tangent at any point of a circle is perpendicular to the radius through the points of contact.

Discussion

4132.	Question 4Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Answer» Question 4 Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Discussion

4133.	if the coordinates of two vertices of an equilateral triangle is (C,a) and (2C,-a), then find the coordinates of third vertex of equilateral triangle?
Answer» if the coordinates of two vertices of an equilateral triangle is (C,a) and (2C,-a), then find the coordinates of third vertex of equilateral triangle?

Discussion

4134.	Can the line segment be divided by using a single ray constructed at an obtuse angle to any one side? If not, Why?
Answer» Can the line segment be divided by using a single ray constructed at an obtuse angle to any one side? If not, Why?

Discussion

4135.	If point P(1,0) on the curve y2+xy+2x−2=0 is at the shortest distance from y=mx+c. Then the value of m is
Answer» If point $P (1, 0)$ on the curve $y^{2} + x y + 2 x - 2 = 0$ is at the shortest distance from $y = m x + c .$ Then the value of $m$ is

Discussion

4136.	9. If sin theta + cos theta =root 2 sin theta, then show that sin theta-cos theta = root 2 sin theta.
Answer» 9. If sin theta + cos theta =root 2 sin theta, then show that sin theta-cos theta = root 2 sin theta.

Discussion

4137.	A circular cylinder shaped container having diameter 24 cm and height 10 cm is full of ice-cream. The ice-cream is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. The number of such cones which can be filled with ice-cream is
Answer» A circular cylinder shaped container having diameter 24 cm and height 10 cm is full of ice-cream. The ice-cream is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. The number of such cones which can be filled with ice-cream is

Discussion

4138.	Find the value of cos 36^°
Answer» Find the value of cos 36^°

Discussion

4139.	13. Point p lies on the line y=x and point q lies on the line y=2x, then the equation of locus of the mid point of pq, if \|pq\|=4.
Answer» 13. Point p lies on the line y=x and point q lies on the line y=2x, then the equation of locus of the mid point of pq, if \|pq\|=4.

Discussion

4140.	2. The area of the region bounded by the curves y=\|x-1\| and y=3-\|x\| is:- (1)2 (2)3 (3)4 (4)1
Answer» 2. The area of the region bounded by the curves y=\|x-1\| and y=3-\|x\| is:- (1)2 (2)3 (3)4 (4)1

Discussion

4141.	What is the formula for the n th term of an A.P.?
Answer» What is the formula for the n th term of an A.P.?

Discussion

4142.	Express as rupees using decimals: 7 paise
Answer» Express as rupees using decimals: $7$ paise

Discussion

4143.	A point B on the level ground is x m away from the foot of a h meter tall tower. If the angle of elevation of the top of the tower from the point B is B°, then the height of the tower is ______ m.
Answer» A point B on the level ground is x m away from the foot of a h meter tall tower. If the angle of elevation of the top of the tower from the point B is B°, then the height of the tower is ______ m.

Discussion

4144.	Question 2 For which of the following, diagonals bisect each other? a) Square b) Kite c) Trapezium d) Quadrilateral
Answer» Question 2 For which of the following, diagonals bisect each other? a) Square b) Kite c) Trapezium d) Quadrilateral

Discussion

4145.	For what value of p the following set of equations will have no solutions?2x+3y=53x+py=10 4.5
Answer» For what value of p the following set of equations will have no solutions? 2x+3y=5 3x+py=10 4.5

Discussion

4146.	The graph of y = p(x) is given. How many zeroes can exist?
Answer» The graph of y = p(x) is given. How many zeroes can exist?

4146.

The graph of y = p(x) is given. How many zeroes can exist?

Answer»

The graph of y = p(x) is given. How many zeroes can exist?

Discussion

4147.	In the figure below XYQZ is a quadrilateral with its vertices on a circle and XYZ is an equilateral triangle. Find the value of ∠ YQZ.
Answer» In the figure below XYQZ is a quadrilateral with its vertices on a circle and XYZ is an equilateral triangle. Find the value of $∠$ YQZ.

4147.

In the figure below XYQZ is a quadrilateral with its vertices on a circle and XYZ is an equilateral triangle. Find the value of ∠ YQZ.

Answer»

In the figure below XYQZ is a quadrilateral with its vertices on a circle and XYZ is an equilateral triangle. Find the value of $∠$ YQZ.

Discussion

4148.	Prove that sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A
Answer» Prove that sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A

Discussion

4149.	Prove that sin θ−2 sin3 θ2 cos3 θ−cos θ=tan θ [4 MARKS]
Answer» Prove that $\frac{s i n θ - 2 s i n^{3} θ}{2 c o s^{3} θ - c o s θ} = t a n θ$ [4 MARKS]

Discussion

4150.	The diameter of a football is 24 cm. What is the volume of air inside 50 such footballs?
Answer» The diameter of a football is 24 cm. What is the volume of air inside 50 such footballs?

Discussion

Explore topic-wise InterviewSolutions in .

Carry out the following subtarctions involving rational numbers.(i) 711-37(ii) 1336-240(iii) 123-356(iv) 412-313

locus of the middle points of chords of the circle x^2+y^2=16 which subtend a right angle at the centre is

Find the points which divide the line segment joining A(-4, 0) and B(0, 6) into four equal parts.

The area of a rhombus is 2016cm2 . If it's one side is 65 cm then find it's diagonal.

The three vertices of a parallelogram ABCD takenin order are A(4, 3), B(-1, 2) and C(-2, -3). Find the coordinates of the fourth vertex.

Question 3 (i)In the given figure, ABD is a triangle right angled at A and AC⊥BD. Show that(i)AB2=BC×BD

Prove that 2-\surd3 is an irrationa

(√3-1)/(√3+1)=a+b√(3 ). Find a, b

149. If f(x)=ax+b/cx+d, then (fof)(x)=x,prove that d+a=0

If - 1,3 are zeros of the polynomial p(x) =2x3-9x2+4x+15, then third zero of p(x) is

Match the following to their roots.

Distance between two points P and Q is 100 km. At the same time a bus is moving from point P and another bus is moving from point Q.When they are moving in same direction they meet after 5 hours and when they move in opposite direction then they meet after 1 hours .Find the velocity of two buses.

The side of a rhombus is 18 cm and one of its diagonals is 11 cm. The area of the rhombus is

An integer is chosen at random between 1and 100. Find probability of Multiple of 8 Not multiple of 8

A triangle ABC is drawn to circumscribe a circle such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 20 cm respectively. If the area of the triangle is 120 cm2, what is the value of AB + AC?

The least value of &quotP" for which the two curves arg(z)=/6 and |z-23i|=P intersect each other

In the given figure, H and I are the points on side GJ of aΔFGJ, such that BD = CE and FH = FI. Show that ΔFGH ≅ ΔFJI.

Find the roots of the quadratic equation √2x2+7x+5√2 = 0 using factorization method.

What is the distance between two parallel tangents of a circle of the radius 4 cm?

In the figure below, two tangents are drawn from a point P to a circle meeting it at points A and C.If ∠AOC=120∘, what is the value of ∠APC?

37. In an A.P.,if the pth term is 1/q and the qth term is 1/p(p is not equal to q), prove that the sum of first pq term must be 1/2(pq+1)

AB is a line segment and M is its mid-point. Semi-circles are drawn with AM, MB and AB as diameters on the same side of AB. A circle is drawn to touch all the three semi-circles. Its radius is:

On selling a chair of Rs. 736, a shopkeeper suffers a loss of 8%. At what price should he sell it, so as to gain 8%?

Rs 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs 12 less. Find 'x'. [4 MARKS]

Sum of three consecutive terms in an AP is 15 and their product is 0. The sequence is?

Find the roots of the following quadratic equations by the factorisation method.2x2+53x−2=0

Cosec theta+cot theta/ cosec theta - cot theta = 81/49. Find cosec theta + sin theta / sin theta - cosec theta

Prove that the tangent at any point of a circle is perpendicular to the radius through the points of contact.

Question 4Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

if the coordinates of two vertices of an equilateral triangle is (C,a) and (2C,-a), then find the coordinates of third vertex of equilateral triangle?

Can the line segment be divided by using a single ray constructed at an obtuse angle to any one side? If not, Why?

If point P(1,0) on the curve y2+xy+2x−2=0 is at the shortest distance from y=mx+c. Then the value of m is

9. If sin theta + cos theta =root 2 sin theta, then show that sin theta-cos theta = root 2 sin theta.

A circular cylinder shaped container having diameter 24 cm and height 10 cm is full of ice-cream. The ice-cream is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. The number of such cones which can be filled with ice-cream is

Find the value of cos 36^°

13. Point p lies on the line y=x and point q lies on the line y=2x, then the equation of locus of the mid point of pq, if |pq|=4.

2. The area of the region bounded by the curves y=|x-1| and y=3-|x| is:- (1)2 (2)3 (3)4 (4)1

What is the formula for the n th term of an A.P.?

Express as rupees using decimals: 7 paise

A point B on the level ground is x m away from the foot of a h meter tall tower. If the angle of elevation of the top of the tower from the point B is B°, then the height of the tower is ______ m.

Question 2 For which of the following, diagonals bisect each other? a) Square b) Kite c) Trapezium d) Quadrilateral

For what value of p the following set of equations will have no solutions?2x+3y=53x+py=10 4.5

The graph of y = p(x) is given. How many zeroes can exist?

In the figure below XYQZ is a quadrilateral with its vertices on a circle and XYZ is an equilateral triangle. Find the value of ∠ YQZ.

Prove that sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A

Prove that sin θ−2 sin3 θ2 cos3 θ−cos θ=tan θ [4 MARKS]

The diameter of a football is 24 cm. What is the volume of air inside 50 such footballs?