32581 + Interview Questions in Mathematics Page 72 InterviewSolution

3551.	An arc of length 15 cm subtends an angle of 45° at the centre of a circle. Find in terms of π, the radius of the circle.
Answer» An arc of length 15 cm subtends an angle of 45° at the centre of a circle. Find in terms of π, the radius of the circle.

Discussion

3552.

The mean of the following distribution is 50. x 10 30 50 70 90 f 17 5a + 3 32 7a – 11 19 Find the value of a and hence the frequencies of 30 and 70.

Answer» The mean of the following distribution is 50.

x	10	30	50	70	90
f	17	5a + 3	32	7a – 11	19

Find the value of a and hence the frequencies of 30 and 70.

Discussion

3553.	Find the sum of first n terms of an AP whose nth term is (5 − 6n). Hence, find the sum of its first 20 terms.
Answer» Find the sum of first n terms of an AP whose nth term is (5 − 6n). Hence, find the sum of its first 20 terms.

Discussion

3554.	In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, ∠B = 90o and DS = 5 cm, then the radius of the circle (in cm) is:
Answer» In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, ∠B = 90^o and DS = 5 cm, then the radius of the circle (in cm) is:

3554.

In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, ∠B = 90o and DS = 5 cm, then the radius of the circle (in cm) is:

Answer»

In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, ∠B = 90^o and DS = 5 cm, then the radius of the circle (in cm) is:

Discussion

3555.	Two numbers are in the ratio 17:13.If their HCF is 15, find the numbers.
Answer» Two numbers are in the ratio $17 : 13$ .If their HCF is $15$ , find the numbers.

Discussion

3556.	Question 84 Devangi's phone subscription charges for the period 17 - 02 - 09 to 16 - 03 - 09 were as follows PeriodAmount(in Rs)Service tax%17−02−09to23−02−09199.7512%24−02−09to16−03−09599.2510% Find the final bill amount,if 3 %education cess was also charged on service tax.
Answer» Question 84 Devangi's phone subscription charges for the period 17 - 02 - 09 to 16 - 03 - 09 were as follows $\begin{matrix} Period & Amount(in Rs) & Service tax % 17 - 02 - 09 t o 23 - 02 - 09 & 199.75 & 12 % 24 - 02 - 09 t o 16 - 03 - 09 & 599.25 & 10 % \end{matrix}$ Find the final bill amount,if 3 $%$ education cess was also charged on service tax.

3556.

Question 84 Devangi's phone subscription charges for the period 17 - 02 - 09 to 16 - 03 - 09 were as follows PeriodAmount(in Rs)Service tax%17−02−09to23−02−09199.7512%24−02−09to16−03−09599.2510% Find the final bill amount,if 3 %education cess was also charged on service tax.

Answer»

Question 84

Devangi's phone subscription charges for the period 17 - 02 - 09 to 16 - 03 - 09 were as follows
$\begin{matrix} Period & Amount(in Rs) & Service tax % 17 - 02 - 09 t o 23 - 02 - 09 & 199.75 & 12 % 24 - 02 - 09 t o 16 - 03 - 09 & 599.25 & 10 % \end{matrix}$
Find the final bill amount,if 3 $%$ education cess was also charged on service tax.

Discussion

3557.	Mr. Chacko of the Padyatra Party wanted to go from Delhi to Dehradun. The party travelled 150 km straight and then took a 45∘ turn towards Varanasi and walked straight for another 120 km. Approximately how far was the party from the starting point?
Answer» Mr. Chacko of the Padyatra Party wanted to go from Delhi to Dehradun. The party travelled 150 km straight and then took a $45^{\circ}$ turn towards Varanasi and walked straight for another 120 km. Approximately how far was the party from the starting point?

Discussion

3558.	Let P and Q be the point of trisection of the line segment joining the points A(2,-2) and B(-7,4) such that P is nearer to A. What is the coordinates of P and Q ?
Answer» Let P and Q be the point of trisection of the line segment joining the points A(2,-2) and B(-7,4) such that P is nearer to A. What is the coordinates of P and Q ?

Discussion

3559.	Prove that the tangents at the extremities of any chord make equal angles with the chord.
Answer» Prove that the tangents at the extremities of any chord make equal angles with the chord.

3559.

Prove that the tangents at the extremities of any chord make equal angles with the chord.

Answer»

Prove that the tangents at the extremities of any chord make equal angles with the chord.

Discussion

3560.	The students of Byjus were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Byjus was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?
Answer» The students of Byjus were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Byjus was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

Discussion

3561.	In Fig. 7, AB ⊥ BC, FG ⊥ BC and DE ⊥ AC. Prove that Δ ADE ~ ΔGCF
Answer» In Fig. 7, AB $⊥$ BC, FG $⊥$ BC and DE $⊥$ AC. Prove that Δ ADE $~$ ΔGCF

Discussion

3562.	An observer, 1.5 m tall, is 28.5 m away from a a tower 30 m high. Determine the angle elevation of the top of the tower from his eye.
Answer» An observer, 1.5 m tall, is 28.5 m away from a a tower 30 m high. Determine the angle elevation of the top of the tower from his eye.

Discussion

3563.	The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.
Answer» The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

Discussion

3564.	Solve the following quadratic equations by factorization:43x2+5x-23=0
Answer» Solve the following quadratic equations by factorization: $4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 0$

Discussion

3565.	Choose the correct answer of the following question:The radii of the circular ends of a bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the bucket is(a) 41 (b) 43 (c) 49 (d) 51 [CBSE 2012]
Answer» Choose the correct answer of the following question: The radii of the circular ends of a bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the bucket is (a) 41 (b) 43 (c) 49 (d) 51 [CBSE 2012]

Discussion

3566.	Batsman A gets an average of 64 runs per innings with standard deviation of 18 runs. While batsman B gets an average score of 43 runs with standard deviation of 9 runs in an equal number of innings. Discuss the efficiency and consistency of both the batsmen.
Answer» Batsman A gets an average of 64 runs per innings with standard deviation of 18 runs. While batsman B gets an average score of 43 runs with standard deviation of 9 runs in an equal number of innings. Discuss the efficiency and consistency of both the batsmen.

Discussion

3567.	Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers.
Answer» Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers.

Discussion

3568.	A box contains 90 discs which are numbered from 1 to 90 . If one discs is drawn at random from the box , find the probability that it bears (i) a two digit number(ii) a perfect square number(iii) a number divisible by 5.
Answer» A box contains 90 discs which are numbered from 1 to 90 . If one discs is drawn at random from the box , find the probability that it bears (i) a two digit number (ii) a perfect square number (iii) a number divisible by 5.

Discussion

3569.	Saraswati Ltd. purchased a machinery costing Rs 10,00,000 on January 01, 2011. A new machinery was purchased on 01 May, 2012 for Rs 15,00,000 and another on July 01, 2014 for Rs 12,00,000. A part of the machinery which originally cost Rs 2,00,000 in 2011 was sold for Rs 75,000 on April 30, 2014. Show the machinery account, provision for depreciation account and machinery disposal account from 2011 to 2015 if depreciation is provided at 10% p.a. on original cost and account are closed on December 31, every year.
Answer» Saraswati Ltd. purchased a machinery costing Rs 10,00,000 on January 01, 2011. A new machinery was purchased on 01 May, 2012 for Rs 15,00,000 and another on July 01, 2014 for Rs 12,00,000. A part of the machinery which originally cost Rs 2,00,000 in 2011 was sold for Rs 75,000 on April 30, 2014. Show the machinery account, provision for depreciation account and machinery disposal account from 2011 to 2015 if depreciation is provided at 10% p.a. on original cost and account are closed on December 31, every year.

Discussion

3570.	What is the coefficient of x5 in the polynomial p(x)=x5+3x4+2x2+1 ?
Answer» What is the coefficient of $x^{5}$ in the polynomial p(x)= $x^{5} + 3 x^{4} + 2 x^{2} + 1$ ?

Discussion

3571.	The sum of the numerator and denominator of a fraction is 12. If the denominator is incresed by 3, the fraction becomes 1/2. Find the fraction.
Answer» The sum of the numerator and denominator of a fraction is 12. If the denominator is incresed by 3, the fraction becomes 1/2. Find the fraction.

Discussion

3572.	In Figure 4, a circle is inscribed in a triangle PQR with PQ = 10 cm, QR = 8 cm and PR = 12 cm. Find the lengths QM, RN and PL.
Answer» In Figure 4, a circle is inscribed in a triangle PQR with PQ = 10 cm, QR = 8 cm and PR = 12 cm. Find the lengths QM, RN and PL.

Discussion

3573.	The H.C.F. and L.C.M of two expression are (a − 7) and (a3 − 10a2 + 11a + 70) respectively. If one of the expressions is (a2 − 12a + 35) find the other.
Answer» The H.C.F. and L.C.M of two expression are (a − 7) and (a³ − 10a² + 11a + 70) respectively. If one of the expressions is (a² − 12a + 35) find the other.

Discussion

3574.	Find the solution of the given system of equation. x+y−82 = x+2y−148 = 3x+y−1211
Answer» Find the solution of the given system of equation. $\frac{x + y - 8}{2}$ = $\frac{x + 2 y - 14}{8}$ = $\frac{3 x + y - 12}{11}$

3574.

Find the solution of the given system of equation. x+y−82 = x+2y−148 = 3x+y−1211

Answer»

Find the solution of the given system of equation.

$\frac{x + y - 8}{2}$ = $\frac{x + 2 y - 14}{8}$ = $\frac{3 x + y - 12}{11}$

Discussion

3575.	If AB=CD and ∠AOB=50∘, then ∠ODC = _____ .
Answer» If $A B = C D$ and $∠ A O B = 50^{\circ}$ , then $∠ O D C$ = _____ .

Discussion

3576.	If a2+b2=1 then find the value of 1+b+ia/1+b-ia
Answer» If a2+b2=1 then find the value of 1+b+ia/1+b-ia

Discussion

3577.	Without using a set square or protractor, construct a rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Find the point R on AD such that RB = RC. What is the length of AR?
Answer» Without using a set square or protractor, construct a rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Find the point R on AD such that RB = RC. What is the length of AR?

Discussion

3578.	Prove that the sum of the first five terms of any arithmetic sequence is five times the middle number. What about the sum of the first seven terms? Can you formulate a general principle from these examples?
Answer» Prove that the sum of the first five terms of any arithmetic sequence is five times the middle number. What about the sum of the first seven terms? Can you formulate a general principle from these examples?

Discussion

3579.	Show that if A⊂B, then C−B⊂C−A.
Answer» Show that if $A \subset B,$ then $C - B \subset C - A$ .

Discussion

3580.	Point A = (3,5) , P = (1,3), and Q = (2,5).If line AB is parallel to line PQ, find the equation of line AB.
Answer» Point A = (3,5) , P = (1,3), and Q = (2,5). If line AB is parallel to line PQ, find the equation of line AB.

Discussion

3581.	Which term of the A.P 9, 12, 15, 18, .... is 39 more than its 36th term?
Answer» Which term of the A.P 9, 12, 15, 18, .... is 39 more than its 36^th term?

Discussion

3582.	Question 2 Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: (i)2x+3y=9.35 (ii)x−y5−10=0 (iii)−2x+3y=6 (iv)x=3y (v)2x=−5y (vi)3x+2=0 (vii)y−2=0 (viii)5=2x
Answer» Question 2 Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: $(i) 2 x + 3 y = 9.35 (i i) x - \frac{y}{5} - 10 = 0 (i i i) - 2 x + 3 y = 6 (i v) x = 3 y$ $(v) 2 x = - 5 y (v i) 3 x + 2 = 0 (v i i) y - 2 = 0 (v i i i) 5 = 2 x$

Discussion

3583.	If A + B = 90° and tan A=34, what is cot B?
Answer» If A + B = 90° and $\tan A = \frac{3}{4}$ , what is cot B?

Discussion

3584.	ABCD is a rhombus such that ∠ACB = 50°. Then, ∠ADB = ?(a) 40°(b) 25°(c) 65°(d) 130°
Answer» ABCD is a rhombus such that ∠ACB = 50°. Then, ∠ADB = ? (a) 40° (b) 25° (c) 65° (d) 130°

Discussion

3585.	The sides of a quadrilateral are all positive integers and three of them are 5,10 ,20. How many possible values are there fir the fourth side
Answer» The sides of a quadrilateral are all positive integers and three of them are 5,10 ,20. How many possible values are there fir the fourth side

Discussion

3586.	A signal x(t)=e−tu(t) is passed through an ideal low pass filter with cut-off frequency ofωcrad/sec, then the value of ωc for the output energy of low pass filter is 90% of theinput energy will be ________rad/sec6.314
Answer» $A signal x (t) = e^{- t} u (t) is passed through an ideal low pass filter with cut-off frequency of ω_{c} rad/sec, then the value of ω_{c} for the output energy of low pass filter is 90% of the input energy will be ________rad/sec$ 6.314

Discussion

3587.	The sides of a triangle are 3 cm, 4 cm, and 5 cm in length. The greatest angle of this triangle is .
Answer» The sides of a triangle are 3 cm, 4 cm, and 5 cm in length. The greatest angle of this triangle is .

Discussion

3588.	In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?
Answer» In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

3588.

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

Answer»

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

Discussion

3589.	Obtain all other zeroes of 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.
Answer» Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ , if two of its zeroes are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ .

Discussion

3590.	If f(x)=\begin{vmatrix}x-2&(x-1)^2&x^3 x-1&x^2&(x+1)^3 x&(x+1)^2&(x+2)^3\end{vmatrix} , then coefficient of x in f(x) is
Answer» If f(x)=\begin{vmatrix}x-2&(x-1)^2&x^3 x-1&x^2&(x+1)^3 x&(x+1)^2&(x+2)^3\end{vmatrix} , then coefficient of x in f(x) is

Discussion

3591.

The length of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table: Length (in mm): 118−126 127−135 136−144 145−153 154−162 163−171 172−180 No. of leaves 3 5 9 12 5 4 2 Find the mean length of leaf.

Answer» The length of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

Length (in mm):	118−126	127−135	136−144	145−153	154−162	163−171	172−180
No. of leaves	3	5	9	12	5	4	2

Find the mean length of leaf.

Discussion

3592.	If p, q are real and p≠q, then show that the roots of the equation (p−q)x2+5(p+q)x−2(p−q)=0 are real and unequal.
Answer» If p, q are real and $p \neq q,$ then show that the roots of the equation $(p - q) x^{2} + 5 (p + q) x - 2 (p - q) = 0$ are real and unequal.

Discussion

3593.	Q. In which of the following choices the mirror image of the word “TRIANGLE” will be formed below the x-axis?
Answer» Q. In which of the following choices the mirror image of the word “TRIANGLE” will be formed below the x-axis?

Discussion

3594.	Solve for x and y:10x+y+2x-y=415x+y-9x-y=-2
Answer» Solve for x and y: $\frac{10}{x + y} + \frac{2}{x - y} = 4 \frac{15}{x + y} - \frac{9}{x - y} = - 2$

Discussion

3595.	A cone of height 36 cm and base radius 9 cm is reshaped into a sphere. Find the radius of the sphere formed.
Answer» A cone of height 36 cm and base radius 9 cm is reshaped into a sphere. Find the radius of the sphere formed.

Discussion

3596.	On January 1, 2011, Rao sold goods Rs. 10,000 to Reddy. Half of the payment was made immediately and for the remaining half, Rao drew a bill of exchange upon Reddy payable after 30 days. Reddy accepted the bill and returned it to Rao. On the due date, Rao presented the bill to Reddy and received the payment. Journalise the above transactions in the books of Rao and prepare Rao's account in the books of Reddy.
Answer» On January 1, 2011, Rao sold goods Rs. 10,000 to Reddy. Half of the payment was made immediately and for the remaining half, Rao drew a bill of exchange upon Reddy payable after 30 days. Reddy accepted the bill and returned it to Rao. On the due date, Rao presented the bill to Reddy and received the payment. Journalise the above transactions in the books of Rao and prepare Rao's account in the books of Reddy.

Discussion

3597.	If f(x)=x−1x+1, then find f(f(x)).
Answer» $If f (x) = \frac{x - 1}{x + 1}, then find f(f(x)).$

Discussion

3598.

Find the mean, median and mode of the following data: Classes: 0−50 50−100 100−150 150−200 200−250 250−300 300−350 Frequency: 2 3 5 6 5 3 1

Answer» Find the mean, median and mode of the following data:

Classes:	0−50	50−100	100−150	150−200	200−250	250−300	300−350
Frequency:	2	3	5	6	5	3	1

Discussion

3599.	Check wether given equation is a quadratic equation or not : x+51 = 2x+10x−6
Answer» Check wether given equation is a quadratic equation or not : $\frac{x + 5}{1}$ = $\frac{2 x + 10}{x - 6}$

Discussion

3600.	The sum of the first ___ natural numbers is 210.
Answer» The sum of the first ___ natural numbers is 210.

Discussion

Explore topic-wise InterviewSolutions in .

An arc of length 15 cm subtends an angle of 45° at the centre of a circle. Find in terms of π, the radius of the circle.

The mean of the following distribution is 50. x 10 30 50 70 90 f 17 5a + 3 32 7a – 11 19 Find the value of a and hence the frequencies of 30 and 70.

Find the sum of first n terms of an AP whose nth term is (5 − 6n). Hence, find the sum of its first 20 terms.

In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, ∠B = 90o and DS = 5 cm, then the radius of the circle (in cm) is:

Two numbers are in the ratio 17:13.If their HCF is 15, find the numbers.

Question 84 Devangi's phone subscription charges for the period 17 - 02 - 09 to 16 - 03 - 09 were as follows PeriodAmount(in Rs)Service tax%17−02−09to23−02−09199.7512%24−02−09to16−03−09599.2510% Find the final bill amount,if 3 %education cess was also charged on service tax.

Mr. Chacko of the Padyatra Party wanted to go from Delhi to Dehradun. The party travelled 150 km straight and then took a 45∘ turn towards Varanasi and walked straight for another 120 km. Approximately how far was the party from the starting point?

Let P and Q be the point of trisection of the line segment joining the points A(2,-2) and B(-7,4) such that P is nearer to A. What is the coordinates of P and Q ?

Prove that the tangents at the extremities of any chord make equal angles with the chord.

In Fig. 7, AB ⊥ BC, FG ⊥ BC and DE ⊥ AC. Prove that Δ ADE ~ ΔGCF

An observer, 1.5 m tall, is 28.5 m away from a a tower 30 m high. Determine the angle elevation of the top of the tower from his eye.

The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

Solve the following quadratic equations by factorization:43x2+5x-23=0

Choose the correct answer of the following question:The radii of the circular ends of a bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the bucket is(a) 41 (b) 43 (c) 49 (d) 51 [CBSE 2012]

Batsman A gets an average of 64 runs per innings with standard deviation of 18 runs. While batsman B gets an average score of 43 runs with standard deviation of 9 runs in an equal number of innings. Discuss the efficiency and consistency of both the batsmen.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers.

A box contains 90 discs which are numbered from 1 to 90 . If one discs is drawn at random from the box , find the probability that it bears (i) a two digit number(ii) a perfect square number(iii) a number divisible by 5.

What is the coefficient of x5 in the polynomial p(x)=x5+3x4+2x2+1 ?

The sum of the numerator and denominator of a fraction is 12. If the denominator is incresed by 3, the fraction becomes 1/2. Find the fraction.

In Figure 4, a circle is inscribed in a triangle PQR with PQ = 10 cm, QR = 8 cm and PR = 12 cm. Find the lengths QM, RN and PL.

The H.C.F. and L.C.M of two expression are (a − 7) and (a3 − 10a2 + 11a + 70) respectively. If one of the expressions is (a2 − 12a + 35) find the other.

Find the solution of the given system of equation. x+y−82 = x+2y−148 = 3x+y−1211

If AB=CD and ∠AOB=50∘, then ∠ODC = _____ .

If a2+b2=1 then find the value of 1+b+ia/1+b-ia

Without using a set square or protractor, construct a rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Find the point R on AD such that RB = RC. What is the length of AR?

Prove that the sum of the first five terms of any arithmetic sequence is five times the middle number. What about the sum of the first seven terms? Can you formulate a general principle from these examples?

Show that if A⊂B, then C−B⊂C−A.

Point A = (3,5) , P = (1,3), and Q = (2,5).If line AB is parallel to line PQ, find the equation of line AB.

Which term of the A.P 9, 12, 15, 18, .... is 39 more than its 36th term?

Question 2 Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: (i)2x+3y=9.35 (ii)x−y5−10=0 (iii)−2x+3y=6 (iv)x=3y (v)2x=−5y (vi)3x+2=0 (vii)y−2=0 (viii)5=2x

If A + B = 90° and tan A=34, what is cot B?

ABCD is a rhombus such that ∠ACB = 50°. Then, ∠ADB = ?(a) 40°(b) 25°(c) 65°(d) 130°

The sides of a quadrilateral are all positive integers and three of them are 5,10 ,20. How many possible values are there fir the fourth side

A signal x(t)=e−tu(t) is passed through an ideal low pass filter with cut-off frequency ofωcrad/sec, then the value of ωc for the output energy of low pass filter is 90% of theinput energy will be ________rad/sec6.314

The sides of a triangle are 3 cm, 4 cm, and 5 cm in length. The greatest angle of this triangle is .

In the figure; P and Q are the points of intersection of two circles with centres O &amp; O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

Obtain all other zeroes of 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.

If f(x)=\begin{vmatrix}x-2&(x-1)^2&x^3 x-1&x^2&(x+1)^3 x&(x+1)^2&(x+2)^3\end{vmatrix} , then coefficient of x in f(x) is

The length of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table: Length (in mm): 118−126 127−135 136−144 145−153 154−162 163−171 172−180 No. of leaves 3 5 9 12 5 4 2 Find the mean length of leaf.

If p, q are real and p≠q, then show that the roots of the equation (p−q)x2+5(p+q)x−2(p−q)=0 are real and unequal.

Q. In which of the following choices the mirror image of the word “TRIANGLE” will be formed below the x-axis?

Solve for x and y:10x+y+2x-y=415x+y-9x-y=-2

A cone of height 36 cm and base radius 9 cm is reshaped into a sphere. Find the radius of the sphere formed.

If f(x)=x−1x+1, then find f(f(x)).

Find the mean, median and mode of the following data: Classes: 0−50 50−100 100−150 150−200 200−250 250−300 300−350 Frequency: 2 3 5 6 5 3 1

Check wether given equation is a quadratic equation or not : x+51 = 2x+10x−6

The sum of the first ___ natural numbers is 210.

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?