32581 + Interview Questions in Mathematics

1.	The technical phenomenon, embracing all the separate techniques, forms a whole.... It is useless to look for differentiations. They do exist, but only secondarily. The common features of the technical phenomenon are so sharply drawn that it is easy to discern that which is the technical phenomenon and that which is not. To analyze these common features is tricky, but it is simple to grasp them. Just as there are principles common to things as different as a wireless set and an internal combustion engine, so the organization of an office and the construction of an aircraft have certain identical features. This identity is the primary mark of that thoroughgoing unity which makes the technical phenomenon a single essence despite the extreme diversity of its appearances. As a corollary, it is impossible to analyze this or that element out of it—a truth which is today particularly misunderstood. The great tendency of all persons who study techniques is to make distinctions. They distinguish between the different elements of technique, maintaining some and discarding others. They distinguish between technique and the use to which it is put. These distinctions are completely invalid and show only that he who makes them has understood nothing of the technical phenomenon. Its parts are ontologically tied together; in it, use is inseparable from being. The ‘technical phenomenon” referred to in the opening line can best be defined as:
Answer» The technical phenomenon, embracing all the separate techniques, forms a whole.... It is useless to look for differentiations. They do exist, but only secondarily. The common features of the technical phenomenon are so sharply drawn that it is easy to discern that which is the technical phenomenon and that which is not. To analyze these common features is tricky, but it is simple to grasp them. Just as there are principles common to things as different as a wireless set and an internal combustion engine, so the organization of an office and the construction of an aircraft have certain identical features. This identity is the primary mark of that thoroughgoing unity which makes the technical phenomenon a single essence despite the extreme diversity of its appearances. As a corollary, it is impossible to analyze this or that element out of it—a truth which is today particularly misunderstood. The great tendency of all persons who study techniques is to make distinctions. They distinguish between the different elements of technique, maintaining some and discarding others. They distinguish between technique and the use to which it is put. These distinctions are completely invalid and show only that he who makes them has understood nothing of the technical phenomenon. Its parts are ontologically tied together; in it, use is inseparable from being. The ‘technical phenomenon” referred to in the opening line can best be defined as:

1.

The technical phenomenon, embracing all the separate techniques, forms a whole.... It is useless to look for differentiations. They do exist, but only secondarily. The common features of the technical phenomenon are so sharply drawn that it is easy to discern that which is the technical phenomenon and that which is not. To analyze these common features is tricky, but it is simple to grasp them. Just as there are principles common to things as different as a wireless set and an internal combustion engine, so the organization of an office and the construction of an aircraft have certain identical features. This identity is the primary mark of that thoroughgoing unity which makes the technical phenomenon a single essence despite the extreme diversity of its appearances. As a corollary, it is impossible to analyze this or that element out of it—a truth which is today particularly misunderstood. The great tendency of all persons who study techniques is to make distinctions. They distinguish between the different elements of technique, maintaining some and discarding others. They distinguish between technique and the use to which it is put. These distinctions are completely invalid and show only that he who makes them has understood nothing of the technical phenomenon. Its parts are ontologically tied together; in it, use is inseparable from being. The ‘technical phenomenon” referred to in the opening line can best be defined as:

Answer»

The technical phenomenon, embracing all the separate techniques, forms a whole.... It is useless to look for differentiations. They do exist, but only secondarily. The common features of the technical phenomenon are so sharply drawn that it is easy to discern that which is the technical phenomenon and that which is not.

To analyze these common features is tricky, but it is simple to grasp them. Just as there are principles common to things as different as a wireless set and an internal combustion engine, so the organization of an office and the construction of an aircraft have certain identical features. This identity is the primary mark of that thoroughgoing unity which makes the technical phenomenon a single essence despite the extreme diversity of its appearances.

As a corollary, it is impossible to analyze this or that element out of it—a truth which is today particularly misunderstood. The great tendency of all persons who study techniques is to make distinctions. They distinguish between the different elements of technique, maintaining some and discarding others. They distinguish between technique and the use to which it is put. These distinctions are completely invalid and show only that he who makes them has understood nothing of the technical phenomenon. Its parts are ontologically tied together; in it, use is inseparable from being.

The ‘technical phenomenon” referred to in the opening line can best be defined as:

2.	find the slope of line 3 x minus 4 Y = 1
Answer» find the slope of line 3 x minus 4 Y = 1

4.	If a card is drawn at random from the deck of 52 playing cards, then the probability of getting a red coloured face card is
Answer» If a card is drawn at random from the deck of 52 playing cards, then the probability of getting a red coloured face card is

5.	If the angle of elevation of a cloud from a point ‘h’ metres above a lake is θ1 and the angle of depression of its reflection in the lake is θ2. Find the height at which the cloud is located from the ground.
Answer» If the angle of elevation of a cloud from a point ‘h’ metres above a lake is $θ_{1}$ and the angle of depression of its reflection in the lake is $θ_{2}$ . Find the height at which the cloud is located from the ground.

6.	17. The integrating factor of differential equation dy/dx=(1+y)/x
Answer» 17. The integrating factor of differential equation dy/dx=(1+y)/x

7.	A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.
Answer» A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30^{\circ}$ with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.

8.	Raghu had to make a cylindrical aluminium tube. What is the area of the aluminium sheet he needs to make the tube if the tube has a length of 1m and base radius of 3.5cm? (π=227)
Answer» Raghu had to make a cylindrical aluminium tube. What is the area of the aluminium sheet he needs to make the tube if the tube has a length of 1m and base radius of 3.5cm? ( $π = \frac{22}{7}$ )

10.	If the mean of five observations x, x+2, x+4, x+6 and x+8 is 11, then the mean of first three observations is:
Answer» If the mean of five observations $x, x + 2, x + 4, x + 6 a n d x + 8$ is $11$ , then the mean of first three observations is:

11.	The system of pair of equations 4x−3y+12=0 and 2x+3y−15=0 has
Answer» The system of pair of equations $4 x - 3 y + 12 = 0$ and $2 x + 3 y - 15 = 0$ has

12.	Two integers are selected at random from integers 1 to 9. If the sum is even, then the probability that both the numbers are odd is
Answer» Two integers are selected at random from integers $1$ to $9$ . If the sum is even, then the probability that both the numbers are odd is

13.	The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.
Answer» The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.

14.	4x3+x2+5x+8 = (x+1) × .
Answer» $4 x^{3} + x^{2} + 5 x + 8$ = $(x + 1)$ $\times$ .

16.	In the given figure, LMN is the tangent to the circle with centre O. If ∠ PMN =60∘, find ∠MOP.
Answer» In the given figure, LMN is the tangent to the circle with centre O. If $∠$ PMN $= 60^{\circ}$ , find $∠$ MOP.

18.	If tanθ=512, find (1+cos θ)×(1−sinθ)(1+sinθ)×(1−cosθ).
Answer» If $t a n θ = \frac{5}{12}$ , find $\frac{(1 + c o s θ) \times (1 - s i n θ)}{(1 + s i n θ) \times (1 - c o s θ)}$ .

19.	If tan θ=ab, prove that a sin θ+b cos θa sin θ+b cos θ=a2-b2a2+b2.
Answer» If $\tan θ = \frac{a}{b}$ , prove that $\frac{a \sin θ + b \cos θ}{a \sin θ + b \cos θ} = \frac{a^{2} - b^{2}}{a^{2} + b^{2}}$ .

15.	Find the total surface area of the square pyramid with base edge of length 10 m and slant height of 12 m.
Answer» Find the total surface area of the square pyramid with base edge of length 10 m and slant height of 12 m.

17.	Tick the correct answer in the following: Area of a sector of angle p (in degrees) of a circle with radius R is
Answer» Tick the correct answer in the following: Area of a sector of angle p (in degrees) of a circle with radius R is

20.	A cubic vessel of height 1m full of water. The minimum workdone in taking water out from vessel will be
Answer» A cubic vessel of height 1m full of water. The minimum workdone in taking water out from vessel will be

21.	In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?
Answer» In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?

22.	Find the quadratic polynomial whose sum & product of the zeroes r 21/8 & 5/16 respectively.Thanks
Answer» Find the quadratic polynomial whose sum & product of the zeroes r 21/8 & 5/16 respectively.Thanks

23.	The first three terms of a proportion are 12, 21 and 8 respectively. Then 4th term is(a) 18(b) 16(c) 14(d) 20
Answer» The first three terms of a proportion are 12, 21 and 8 respectively. Then 4^th term is (a) 18 (b) 16 (c) 14 (d) 20

24.	If A and B are two matrices such that AB = B and BA = A, then
Answer» If A and B are two matrices such that AB = B and BA = A, then

26.	In a triangle ABC, P and Q are points on side AB and AC respectively,such that PQ is parallel to BC.If AP=2.4 cm, AQ=2cm, QC=3cm and BC=6cm, find AB and PQ.
Answer» In a triangle ABC, P and Q are points on side AB and AC respectively,such that PQ is parallel to BC.If AP=2.4 cm, AQ=2cm, QC=3cm and BC=6cm, find AB and PQ.

27.	Question 10 (ii)Show that a1,a2……,an,…… form an AP where an is defined as below.(ii) an=9−5nAlso find the sum of the first 15 terms in each case.
Answer» Question 10 (ii) Show that $a_{1}, a_{2} \dots \dots, a_{n}, \dots \dots$ form an AP where $a_{n}$ is defined as below. (ii) $a_{n} = 9 - 5 n$ Also find the sum of the first 15 terms in each case.

28.	Where does the point (6, 0) lie on the rectangular coordinate system?
Answer» Where does the point (6, 0) lie on the rectangular coordinate system?

Explore topic-wise InterviewSolutions in Current Affairs.

find the slope of line 3 x minus 4 Y = 1

The median is the

If a card is drawn at random from the deck of 52 playing cards, then the probability of getting a red coloured face card is

If the angle of elevation of a cloud from a point ‘h’ metres above a lake is θ1 and the angle of depression of its reflection in the lake is θ2. Find the height at which the cloud is located from the ground.

17. The integrating factor of differential equation dy/dx=(1+y)/x

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.

Raghu had to make a cylindrical aluminium tube. What is the area of the aluminium sheet he needs to make the tube if the tube has a length of 1m and base radius of 3.5cm? (π=227)

The frequency distribution table for the following will be Class Mark1525354555Frequency2165149

If the mean of five observations x, x+2, x+4, x+6 and x+8 is 11, then the mean of first three observations is:

The system of pair of equations 4x−3y+12=0 and 2x+3y−15=0 has

Two integers are selected at random from integers 1 to 9. If the sum is even, then the probability that both the numbers are odd is

The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.

4x3+x2+5x+8 = (x+1) × .

Find the total surface area of the square pyramid with base edge of length 10 m and slant height of 12 m.

In the given figure, LMN is the tangent to the circle with centre O. If ∠ PMN =60∘, find ∠MOP.

Tick the correct answer in the following: Area of a sector of angle p (in degrees) of a circle with radius R is

If tanθ=512, find (1+cos θ)×(1−sinθ)(1+sinθ)×(1−cosθ).

If tan θ=ab, prove that a sin θ+b cos θa sin θ+b cos θ=a2-b2a2+b2.

A cubic vessel of height 1m full of water. The minimum workdone in taking water out from vessel will be

In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?

Find the quadratic polynomial whose sum &amp; product of the zeroes r 21/8 &amp; 5/16 respectively.Thanks

The first three terms of a proportion are 12, 21 and 8 respectively. Then 4th term is(a) 18(b) 16(c) 14(d) 20

If A and B are two matrices such that AB = B and BA = A, then

Write the rationalizing factor (R.F) of the following surds(1) (2)(3) (4) (5)

In a triangle ABC, P and Q are points on side AB and AC respectively,such that PQ is parallel to BC.If AP=2.4 cm, AQ=2cm, QC=3cm and BC=6cm, find AB and PQ.

Question 10 (ii)Show that a1,a2……,an,…… form an AP where an is defined as below.(ii) an=9−5nAlso find the sum of the first 15 terms in each case.

Where does the point (6, 0) lie on the rectangular coordinate system?

Find the area of a square that can be inscribed in a circle of radius 8 cm.

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

A wall 24 m , 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm × 16 cm × 10 cm . If the mortar occupies 110th of the volume of the wall, then find the number of bricks used in constructing the wall.

A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc.

ABCD is a cyclic quadrilateral. If ∠BCD = 100∘ and ∠ ABD = 70∘. Find ∠ ADB.

In the given figure, A–D–C and B–E–C , DE∥AB. If AD=5, DC=3, BC=6.4 then Find BE.

determine the ratio in which the point P(m,6) divides the join of A(-4,3) and B(2,8).also, find the value of m.

A lawn is in the form of a rectangle whose sides are in the ratio 5:3.The area of the lawn is 3375 m2.Find the cost of fencing the lawn at Rs.65 per metre.

Find the mean and variance of first 10 multiples of 3.

If two opposite sides of a cyclic quadrilateral are equal,then the other two sides are parallel

Find coordinates of the points of trisection of the line segment joining points (4, -1) and (-2, -3).

Tangents are drawn to the circle x2 + y2 =16 at the points where it is met by the circle x2 + y2 -5x+3y-2=0, the point of intersection of these tangents is

20. Find the equation of circle touching y axis and passing through -2,1 and -4,3

If secθ=x, then write the value of tanθ.

If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then is common ratio is

In triangle ABC, DE || BC, AD=1.2 cm DB=3.6 cm, AE=1.6 cm. What must be the value of EC?

Find the values of x, which satisfy the inequation: −2≤ 12−2x3≤ 116 , x ϵ N.

Which term of the AP : 3, 8, 13, 18, . . . , is 78? ___

THE VALUE OF \sqrt{248+\sqrt{52+\sqrt{144 IS}

A helicopter takes off from a point 80 m away froman observer located on the ground, and risesvertically at 4 ms1. At what rate is elevation angleof the observer's line of sight to the helicopterchanging when the helicopter is 60 m above theground?2

Evaluate each of the following4cot2 30°+1sin2 60°-cos2 45°

Find the quadratic polynomial whose sum & product of the zeroes r 21/8 & 5/16 respectively.Thanks

29.	Find the area of a square that can be inscribed in a circle of radius 8 cm.
Answer» Find the area of a square that can be inscribed in a circle of radius $8 c m .$

30.	If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
Answer» If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

31.	A wall 24 m , 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm × 16 cm × 10 cm . If the mortar occupies 110th of the volume of the wall, then find the number of bricks used in constructing the wall.
Answer» A wall 24 m , 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm $\times$ 16 cm $\times$ 10 cm . If the mortar occupies $\frac{1}{10} t h$ of the volume of the wall, then find the number of bricks used in constructing the wall.

32.	A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc.
Answer» A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc.

33.	ABCD is a cyclic quadrilateral. If ∠BCD = 100∘ and ∠ ABD = 70∘. Find ∠ ADB.
Answer» ABCD is a cyclic quadrilateral. If $∠$ BCD = 100 $^{\circ}$ and $∠$ ABD = 70 $^{\circ}$ . Find $∠$ ADB.

35.	determine the ratio in which the point P(m,6) divides the join of A(-4,3) and B(2,8).also, find the value of m.
Answer» determine the ratio in which the point P(m,6) divides the join of A(-4,3) and B(2,8).also, find the value of m.

36.	A lawn is in the form of a rectangle whose sides are in the ratio 5:3.The area of the lawn is 3375 m2.Find the cost of fencing the lawn at Rs.65 per metre.
Answer» A lawn is in the form of a rectangle whose sides are in the ratio 5:3.The area of the lawn is 3375 $m^{2}$ .Find the cost of fencing the lawn at Rs.65 per metre.

37.	Find the mean and variance of first 10 multiples of 3.
Answer» Find the mean and variance of first 10 multiples of 3.

38.	If two opposite sides of a cyclic quadrilateral are equal,then the other two sides are parallel
Answer» If two opposite sides of a cyclic quadrilateral are equal,then the other two sides are parallel

39.	Find coordinates of the points of trisection of the line segment joining points (4, -1) and (-2, -3).
Answer» Find coordinates of the points of trisection of the line segment joining points (4, -1) and (-2, -3).