32581 + Interview Questions in Mathematics Page 197 InterviewSolution

9801.	A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the minor segments (given, π = 3.14) is (a) 32.5cm2 (b) 34.5cm2 (c) 28.5cm2 (d) 30.5cm2
Answer» A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the minor segments (given, $π$ = 3.14) is (a) $32.5 c m^{2}$ (b) $34.5 c m^{2}$ (c) $28.5 c m^{2}$ (d) $30.5 c m^{2}$

9801.

A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the minor segments (given, π = 3.14) is (a) 32.5cm2 (b) 34.5cm2 (c) 28.5cm2 (d) 30.5cm2

Answer»

A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the minor segments (given, $π$ = 3.14) is

(a) $32.5 c m^{2}$ (b) $34.5 c m^{2}$ (c) $28.5 c m^{2}$ (d) $30.5 c m^{2}$

Discussion

9802.	Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :x − 2y = 63x − 6y = 0
Answer» Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) : x − 2y = 6 3x − 6y = 0

Discussion

9803.	Question 1 (ii)Evaluate the following:(ii) 2tan245∘+cos230∘−sin260∘
Answer» Question 1 (ii) Evaluate the following: (ii) $2 t a n^{2} 45^{\circ} + c o s^{2} 30^{\circ} - s i n^{2} 60^{\circ}$

Discussion

9804.	Areas of some circles are given below find their diameters.(1) 176 sq cm(2) 394.24 sq cm(3) 12474 sq cm
Answer» Areas of some circles are given below find their diameters. (1) 176 sq cm (2) 394.24 sq cm (3) 12474 sq cm

Discussion

9805.	The equation of the straight line which bisects the intercepts between the axes of the lines x+y=2 and 2x+3y=6 is
Answer» The equation of the straight line which bisects the intercepts between the axes of the lines $x + y = 2$ and $2 x + 3 y = 6$ is

Discussion

9806.	If A=diag(2,−5,9),B=diag(1,1,−4), then A−2B is:
Answer» If $A = diag (2, - 5, 9), B = diag (1, 1, - 4)$ , then $A - 2 B$ is:

Discussion

9807.	The base of a conical tent is of area 616 sq. cm. A 48 cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?
Answer» The base of a conical tent is of area $616$ sq. cm. A $48$ cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?

9807.

The base of a conical tent is of area 616 sq. cm. A 48 cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?

Answer»

The base of a conical tent is of area $616$ sq. cm. A $48$ cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?

Discussion

9808.	In a competitive examination, one mark is awarded for each correct answer while 12 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?
Answer» In a competitive examination, one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

Discussion

9809.	Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Answer» Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.

Discussion

9810.	Write the standard form of a linear polynomial with real coefficients.
Answer» Write the standard form of a linear polynomial with real coefficients.

Discussion

9811.	sec^2A + tan^2A = 2, 0
Answer» sec^2A + tan^2A = 2, 0

Discussion

9812.	Equation of trajectory
Answer» Equation of trajectory

Discussion

9813.	If a = 3[arc sin(6/11)] and b = 3[arc cos(4/9)] , where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are) A) cosb > 0B) sinb < 0C) cos(a+b) > 0D) cosa < 0
Answer» If a = 3[arc sin(6/11)] and b = 3[arc cos(4/9)] , where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are) A) cosb > 0 B) sinb < 0 C) cos(a+b) > 0 D) cosa < 0

Discussion

9814.	Find the coordinates of centroid of the triangles if points D(–7, 6), E(8, 5) and F(2, –2) are the mid points of the sides of that triangle.
Answer» Find the coordinates of centroid of the triangles if points D(–7, 6), E(8, 5) and F(2, –2) are the mid points of the sides of that triangle.

Discussion

9815.	Find the arithmetic mean of the following frequency distribution using step-deviation method: Age(in years)18−2424−3030−3636−4242−4848−54Number of workers6812842
Answer» Find the arithmetic mean of the following frequency distribution using step-deviation method: $\begin{matrix} Age(in years) & 18 - 24 & 24 - 30 & 30 - 36 & 36 - 42 & 42 - 48 & 48 - 54 Number of workers & 6 & 8 & 12 & 8 & 4 & 2 \end{matrix}$

Discussion

9816.	Modern Marbles Ltd. was registered with an authorised capital of ₹10,00,000 divided into 7,500 Equity Shares of ₹ 100 each and, 2,500 Preference Shares of ₹100 each. 1,000 Equity Shares and 500; 9% Preference Shares were offered to public on the following terms – Equity Shares payable ₹10 on application, ₹40 on allotment and the balance in two calls of ₹ 25 each. Preference Shares are payable ₹ 25 on application, ₹ 25 on allotment and ₹50 on first and final call. All the shares were applied for and allotted . Amount due was duly received. Prepare Cash Book and pass necessary Journal entries to record the above issue of shares and show how the Share Capital will appear in the Balance Sheet.
Answer» Modern Marbles Ltd. was registered with an authorised capital of ₹10,00,000 divided into 7,500 Equity Shares of ₹ 100 each and, 2,500 Preference Shares of ₹100 each. 1,000 Equity Shares and 500; 9% Preference Shares were offered to public on the following terms – Equity Shares payable ₹10 on application, ₹40 on allotment and the balance in two calls of ₹ 25 each. Preference Shares are payable ₹ 25 on application, ₹ 25 on allotment and ₹50 on first and final call. All the shares were applied for and allotted . Amount due was duly received. Prepare Cash Book and pass necessary Journal entries to record the above issue of shares and show how the Share Capital will appear in the Balance Sheet.

Discussion

9817.	A 15 m long ladder is placed against a wall in such away that the foot of the ladder is 9 m away from the wall. Up to what height does the ladder reach the wall?(a) 13 m(b) 10 m(c) 8 m(d) 12 m
Answer» A 15 m long ladder is placed against a wall in such away that the foot of the ladder is 9 m away from the wall. Up to what height does the ladder reach the wall? (a) 13 m (b) 10 m (c) 8 m (d) 12 m

Discussion

9818.	Find the zeros of the polynomial x2+x−p(p+1).
Answer» Find the zeros of the polynomial $x^{2} + x - p (p + 1)$ .

Discussion

9819.	If √3 tan 2θ - 3 = 0 then θ = ? (a) 15o (b) 30o (c) 45o (d) 60o
Answer» If $\sqrt{3}$ tan $2 θ$ - 3 = 0 then $θ$ = ? (a) $15^{o}$ (b) $30^{o}$ (c) $45^{o}$ (d) $60^{o}$

9819.

If √3 tan 2θ - 3 = 0 then θ = ? (a) 15o (b) 30o (c) 45o (d) 60o

Answer»

If $\sqrt{3}$ tan $2 θ$ - 3 = 0 then $θ$ = ?

(a) $15^{o}$ (b) $30^{o}$ (c) $45^{o}$ (d) $60^{o}$

Discussion

9820.	Akhila went to a fair in her village. She wanted to enjoy rides in the Giant Wheel and play Hoopla (a game in which you throw a rig on the items kept in the stall, and if the ring covers any object completely you get it.) The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs Rs 3, and a game of Hoopla costs Rs 4. If she spent Rs 20 in the fair, represent this situation algebraically and graphically.
Answer» Akhila went to a fair in her village. She wanted to enjoy rides in the Giant Wheel and play Hoopla (a game in which you throw a rig on the items kept in the stall, and if the ring covers any object completely you get it.) The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs Rs 3, and a game of Hoopla costs Rs 4. If she spent Rs 20 in the fair, represent this situation algebraically and graphically.

Discussion

9821.	The mean and median of the numbers 1, 2, 3,4, y, 8, 9, 10, 12 and x written in increasing order are both 10, then the values of x and y are _____.
Answer» The mean and median of the numbers 1, 2, 3,4, $y$ , 8, 9, 10, 12 and $x$ written in increasing order are both 10, then the values of $x$ and $y$ are _____.

Discussion

9822.	Prove the following trignometric identities: tan θ+1tan θ=sec θ cosec θ
Answer» Prove the following trignometric identities: $t a n θ + \frac{1}{t a n θ} = s e c θ c o s e c θ$

9822.

Prove the following trignometric identities: tan θ+1tan θ=sec θ cosec θ

Answer»

Prove the following trignometric identities:

$t a n θ + \frac{1}{t a n θ} = s e c θ c o s e c θ$

Discussion

9823.	In triangle abc,AB=AC, BD perpendicular to AC. Show that db square minus cd square is 2× cd × ad
Answer» In triangle abc,AB=AC, BD perpendicular to AC. Show that db square minus cd square is 2× cd × ad

Discussion

9824.	Find the value of k for which each of the following system of equations have infinitely many solutions :4x+5y=3kx+15y=9
Answer» Find the value of k for which each of the following system of equations have infinitely many solutions : $4 x + 5 y = 3 k x + 15 y = 9$

Discussion

9825.	The length of the hypotenuse in the figure is:
Answer» The length of the hypotenuse in the figure is:

9825.

The length of the hypotenuse in the figure is:

Answer»

The length of the hypotenuse in the figure is:

Discussion

9826.	If in ∆ABC and ∆DEF, ABDE=BCFD, then ∆ABC ∼ ∆DEF when(a) ∠A = ∠F(b) ∠A = ∠D(c) ∠B = ∠D(d) ∠B = ∠E
Answer» If in ∆ABC and ∆DEF, $\frac{AB}{DE} = \frac{BC}{FD}$ , then ∆ABC ∼ ∆DEF when (a) ∠A = ∠F (b) ∠A = ∠D (c) ∠B = ∠D (d) ∠B = ∠E

Discussion

9827.	A line is parallel to x-axis if all the points on the line have equal______________________.
Answer» A line is parallel to x-axis if all the points on the line have equal______________________.

Discussion

9828.	If 3+√52√5+3=a+b√5, then the values of irrational numbers a and b are
Answer» If $\frac{3 + \sqrt{5}}{2 \sqrt{5} + 3} = a + b \sqrt{5}$ , then the values of irrational numbers $a$ and $b$ are

Discussion

9829.	In the given figure, a circle touches the side BC of ΔABC at P. AR and AQ are two tangents drawn from a point A outside the circle. If AQ = 15 cm, find the perimeter of ΔABC (in cm). 30
Answer» $In the given figure, a circle touches the side BC of Δ A B C at P. AR and AQ are two tangents drawn from a point A outside the circle. If AQ = 15 cm, find the perimeter of Δ A B C (in cm) .$ 30

Discussion

9830.	The angle of elevation of the top of a tower at a point on the ground 50 m away from the foot of the tower is 45º. Then the height of the tower (in metres) is(a) 503 (b) 50 (c) 502 (d) 503 [CBSE 2014]
Answer» The angle of elevation of the top of a tower at a point on the ground 50 m away from the foot of the tower is 45º. Then the height of the tower (in metres) is (a) $50 \sqrt{3}$ (b) 50 (c) $\frac{50}{\sqrt{2}}$ (d) $\frac{50}{\sqrt{3}}$ [CBSE 2014]

Discussion

9831.	Salman invests a sum of money in Rs 50 shares, paying 15% dividend quoted at 20% permium. If his annual dividend is Rs 600, calculate : (i) the number of shares he bought. (ii) his total investment (iii) the rate of return on his investment.
Answer» Salman invests a sum of money in Rs 50 shares, paying 15% dividend quoted at 20% permium. If his annual dividend is Rs 600, calculate : (i) the number of shares he bought. (ii) his total investment (iii) the rate of return on his investment.

9831.

Salman invests a sum of money in Rs 50 shares, paying 15% dividend quoted at 20% permium. If his annual dividend is Rs 600, calculate : (i) the number of shares he bought. (ii) his total investment (iii) the rate of return on his investment.

Answer»

Salman invests a sum of money in Rs 50 shares, paying 15% dividend quoted at 20% permium. If his annual dividend is Rs 600, calculate :

(i) the number of shares he bought.

(ii) his total investment

(iii) the rate of return on his investment.

Discussion

9832.	If cosecθ=2x and cotθ=2x, then find the value of 2x2-1x2. CBSE 2010
Answer» $If cosec θ = 2 x and \cot θ = \frac{2}{x}, then find the value of 2 (x^{2} - \frac{1}{x^{2}}) . [CBSE 2010]$

Discussion

9833.	77. Find the relation between x and y such that the points (x, y) is equidistant from the points (7,1) and (3,5)
Answer» 77. Find the relation between x and y such that the points (x, y) is equidistant from the points (7,1) and (3,5)

Discussion

9834.	29. ab-b+1=0 and bc-c+1=0 find the value of (a-ac)
Answer» 29. ab-b+1=0 and bc-c+1=0 find the value of (a-ac)

Discussion

9835.	Which of the following represents a pair of dependent equations?
Answer» Which of the following represents a pair of dependent equations?

Discussion

9836.	Question 3 (iv)Are the following pair of linear equations consistent? Justify your answerx + 3y = 11 and 2(2x + 6y) = 22
Answer» Question 3 (iv) Are the following pair of linear equations consistent? Justify your answer x + 3y = 11 and 2(2x + 6y) = 22

Discussion

9837.	Question 7P and Q are the mid – points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram.
Answer» Question 7 P and Q are the mid – points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram.

Discussion

9838.	Question 4 A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts
Answer» Question 4 A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts

Discussion

9839.	Solve:- 7x2=8–26x
Answer» Solve:- $7 x^{2} = 8 - 26 x$

Discussion

9840.	Find the the roots of −3x2+5x+12=0 by using the quadratic formula.
Answer» Find the the roots of $- 3 x^{2} + 5 x + 12 = 0$ by using the quadratic formula.

Discussion

9841.	If ∆ABC ∼ ∆DEF such that AB = 5 cm, area (∆ABC) = 20 cm2 and area (∆DEF) = 45 cm2, determine DE.
Answer» If ∆ABC ∼ ∆DEF such that AB = 5 cm, area (∆ABC) = 20 cm² and area (∆DEF) = 45 cm², determine DE.

Discussion

9842.	The 16th term of an AP is 5 times its 3rd term. If its 10th term is 41, find the sum of its first 15 terms. [CBSE 2015]
Answer» The 16th term of an AP is 5 times its 3rd term. If its 10th term is 41, find the sum of its first 15 terms. [CBSE 2015]

Discussion

9843.	Question 4 (iv)State whether the following are true or false. Justify your answer.(iv) sinθ=cosθ for all values of θ.
Answer» Question 4 (iv) State whether the following are true or false. Justify your answer. (iv) $s i n θ = c o s θ$ for all values of $θ$ .

Discussion

9844.	In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.
Answer» In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.

Discussion

9845.	If tanθ=43, what is the value of cosθ?0.6
Answer» If $tan θ = \frac{4}{3}$ , what is the value of $cos θ$ ? 0.6

Discussion

9846.	Construct two chords of length 5.6 cm. each on either side of the centre, of a circle of radius 3.5 cm. Measure the distance between the centre and the chords.
Answer» Construct two chords of length 5.6 cm. each on either side of the centre, of a circle of radius 3.5 cm. Measure the distance between the centre and the chords.

Discussion

9847.	Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere (see Fig). The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take π=227) [4 MARKS]
Answer» Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere (see Fig). The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take $π = \frac{22}{7}$ ) [4 MARKS]

9847.

Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere (see Fig). The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take π=227) [4 MARKS]

Answer»

Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere (see Fig). The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take $π = \frac{22}{7}$ ) [4 MARKS]

Discussion

9848.	Find the zeros of each of the following quadratic polynomial.1.p(x)=x^2+2√2x+6
Answer» Find the zeros of each of the following quadratic polynomial. 1.p(x)=x^2+2√2x+6

Discussion

9849.	If a cone is cut into two parts by a horizontal plane passing through the mid-points of its axis, the ratio of the volumes of the upper part and the cone is
Answer» If a cone is cut into two parts by a horizontal plane passing through the mid-points of its axis, the ratio of the volumes of the upper part and the cone is

Discussion

9850.	The number of solutions for the equation x2−k=0 is/are ____
Answer» The number of solutions for the equation $x^{2} - k = 0$ is/are ____

Discussion

Explore topic-wise InterviewSolutions in .

A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the minor segments (given, π = 3.14) is (a) 32.5cm2 (b) 34.5cm2 (c) 28.5cm2 (d) 30.5cm2

Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :x − 2y = 63x − 6y = 0

Question 1 (ii)Evaluate the following:(ii) 2tan245∘+cos230∘−sin260∘

Areas of some circles are given below find their diameters.(1) 176 sq cm(2) 394.24 sq cm(3) 12474 sq cm

The equation of the straight line which bisects the intercepts between the axes of the lines x+y=2 and 2x+3y=6 is

If A=diag(2,−5,9),B=diag(1,1,−4), then A−2B is:

The base of a conical tent is of area 616 sq. cm. A 48 cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?

In a competitive examination, one mark is awarded for each correct answer while 12 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.

Write the standard form of a linear polynomial with real coefficients.

sec^2A + tan^2A = 2, 0

Equation of trajectory

If a = 3[arc sin(6/11)] and b = 3[arc cos(4/9)] , where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are) A) cosb > 0B) sinb < 0C) cos(a+b) > 0D) cosa < 0

Find the coordinates of centroid of the triangles if points D(–7, 6), E(8, 5) and F(2, –2) are the mid points of the sides of that triangle.

Find the arithmetic mean of the following frequency distribution using step-deviation method: Age(in years)18−2424−3030−3636−4242−4848−54Number of workers6812842

A 15 m long ladder is placed against a wall in such away that the foot of the ladder is 9 m away from the wall. Up to what height does the ladder reach the wall?(a) 13 m(b) 10 m(c) 8 m(d) 12 m

Find the zeros of the polynomial x2+x−p(p+1).

If √3 tan 2θ - 3 = 0 then θ = ? (a) 15o (b) 30o (c) 45o (d) 60o

The mean and median of the numbers 1, 2, 3,4, y, 8, 9, 10, 12 and x written in increasing order are both 10, then the values of x and y are _____.

Prove the following trignometric identities: tan θ+1tan θ=sec θ cosec θ

In triangle abc,AB=AC, BD perpendicular to AC. Show that db square minus cd square is 2× cd × ad

Find the value of k for which each of the following system of equations have infinitely many solutions :4x+5y=3kx+15y=9

The length of the hypotenuse in the figure is:

If in ∆ABC and ∆DEF, ABDE=BCFD, then ∆ABC ∼ ∆DEF when(a) ∠A = ∠F(b) ∠A = ∠D(c) ∠B = ∠D(d) ∠B = ∠E

A line is parallel to x-axis if all the points on the line have equal______________________.

If 3+√52√5+3=a+b√5, then the values of irrational numbers a and b are

In the given figure, a circle touches the side BC of ΔABC at P. AR and AQ are two tangents drawn from a point A outside the circle. If AQ = 15 cm, find the perimeter of ΔABC (in cm). 30

The angle of elevation of the top of a tower at a point on the ground 50 m away from the foot of the tower is 45º. Then the height of the tower (in metres) is(a) 503 (b) 50 (c) 502 (d) 503 [CBSE 2014]

Salman invests a sum of money in Rs 50 shares, paying 15% dividend quoted at 20% permium. If his annual dividend is Rs 600, calculate : (i) the number of shares he bought. (ii) his total investment (iii) the rate of return on his investment.

If cosecθ=2x and cotθ=2x, then find the value of 2x2-1x2. CBSE 2010

77. Find the relation between x and y such that the points (x, y) is equidistant from the points (7,1) and (3,5)

29. ab-b+1=0 and bc-c+1=0 find the value of (a-ac)

Which of the following represents a pair of dependent equations?

Question 3 (iv)Are the following pair of linear equations consistent? Justify your answerx + 3y = 11 and 2(2x + 6y) = 22

Question 7P and Q are the mid – points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram.

Question 4 A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts

Solve:- 7x2=8–26x

Find the the roots of −3x2+5x+12=0 by using the quadratic formula.

If ∆ABC ∼ ∆DEF such that AB = 5 cm, area (∆ABC) = 20 cm2 and area (∆DEF) = 45 cm2, determine DE.

The 16th term of an AP is 5 times its 3rd term. If its 10th term is 41, find the sum of its first 15 terms. [CBSE 2015]

Question 4 (iv)State whether the following are true or false. Justify your answer.(iv) sinθ=cosθ for all values of θ.

In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.

If tanθ=43, what is the value of cosθ?0.6

Construct two chords of length 5.6 cm. each on either side of the centre, of a circle of radius 3.5 cm. Measure the distance between the centre and the chords.

Find the zeros of each of the following quadratic polynomial.1.p(x)=x^2+2√2x+6

If a cone is cut into two parts by a horizontal plane passing through the mid-points of its axis, the ratio of the volumes of the upper part and the cone is

The number of solutions for the equation x2−k=0 is/are ____