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| 651. |
In the given figure seg PS is the median of ∆PQR and PT ⊥ QR. Prove that,(1) PR2=PS2+QR×ST+QR22(2) PQ2=PS2-QR×ST+QR22 |
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Answer» In the given figure seg PS is the median of ∆PQR and PT ⊥ QR. Prove that, (1) (2)
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| 652. |
Consider a plane inclined at an angle 45∘ with the horizontal has two slits S1andS2 separated by a distance d=√2 mm. The screen is placed at a distance of D=10 m from the midpoint of the slits, as shown in the figure. A parallel monochromatic light beam of wavelength 5000 ˙A is incident on the slits as shown. If the fringe width of interference pattern on the screen is k×10−3 m, then the value of k is . |
Answer» Consider a plane inclined at an angle 45∘ with the horizontal has two slits S1andS2 separated by a distance d=√2 mm. The screen is placed at a distance of D=10 m from the midpoint of the slits, as shown in the figure. A parallel monochromatic light beam of wavelength 5000 ˙A is incident on the slits as shown. If the fringe width of interference pattern on the screen is k×10−3 m, then the value of k is |
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| 653. |
Question 52When the number of observations is large, the observations are usually organised in groups of equal width called ___, |
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Answer» Question 52 When the number of observations is large, the observations are usually organised in groups of equal width called |
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| 654. |
Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes : OutcomeNo headOne headTwo headsThree headsFrequency14383612 If the three coins are simultaneously tossed again, compute the compute the probability of : (i) 2 heads coming up. (ii)3 heads coming up. (iii) at least one head coming up. (iv) getting more heads than tails. (v) getting more tails heads. |
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Answer» Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes : OutcomeNo headOne headTwo headsThree headsFrequency14383612 If the three coins are simultaneously tossed again, compute the compute the probability of : (i) 2 heads coming up. (ii)3 heads coming up. (iii) at least one head coming up. (iv) getting more heads than tails. (v) getting more tails heads. |
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| 655. |
The diagonals AC and BD of a cyclic quadrilateral ABCD intersect at P.Let O be the circumcentre of triangle APB and H the orthocentre of triangle CPD.Show that H,P,O are colinear. |
| Answer» The diagonals AC and BD of a cyclic quadrilateral ABCD intersect at P.Let O be the circumcentre of triangle APB and H the orthocentre of triangle CPD.Show that H,P,O are colinear. | |
| 656. |
In fig. ∠ABP=∠ACQ, ∠BAC=68∘. Measure of ∠ABC is: |
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Answer» In fig. ∠ABP=∠ACQ, ∠BAC=68∘. Measure of ∠ABC is: |
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| 657. |
Q55. Consider the following figures: What is the missing number? निम्नलिखित आकृति पर विचार कीजिएः लुप्त संख्या क्या है? |
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Answer» Q55. Consider the following figures:
What is the missing number?
निम्नलिखित आकृति पर विचार कीजिएः
लुप्त संख्या क्या है? |
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| 658. |
46. The zeroes of the polynomial f(x)=2x-9x+x+12 are |
| Answer» 46. The zeroes of the polynomial f(x)=2x-9x+x+12 are | |
| 659. |
If AB=CD and ∠AOB=50∘, then ∠ODC = _____ . |
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Answer» If AB=CD and ∠AOB=50∘, then ∠ODC = _____ . |
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| 660. |
The condition that the point (x , y) lies on the line joining (3 , 4) and (-5 , -6) is (1) 5x - 4y + 2 = 0 (2) 4x - 5y + 1 = 0(3) 4x - 5y + 2 = 0 (4) 5x - 4y + 1 = 0 |
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Answer» The condition that the point (x , y) lies on the line joining (3 , 4) and (-5 , -6) is (1) 5x - 4y + 2 = 0 (2) 4x - 5y + 1 = 0 (3) 4x - 5y + 2 = 0 (4) 5x - 4y + 1 = 0 |
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| 661. |
On 31st March, 2019, Cash Book of a merchant showed bank overdraft of ₹ 1,72,985. On comparing the Cash Book with Bank Statement, following discrepancies were noted:(i) Cheques issued for ₹ 60,000 were not presented in the bank till 7th April, 2019.(ii) Cheques amounting to ₹ 75,000 were deposited in the bank but were not collected.(iii) A Cheque of ₹ 15,000 received from Mahesh Chand and deposited in the bank was dishonoured but the non-payment advice was not received from the bank till 1st April, 2019.(iv) ₹ 1,50,000 being the proceeds of a bill receivable collected appeared in the Pass Book but not in the Cash Book.(v) Bank charges ₹ 1,500 and interest on overdraft ₹ 8,500 appeared in the Pass Book but not in the Cash Book.(vi) Overdraft balance as per Cash Book of ₹ 500 on 28th February, 2019 was wrongly carried forward as debit balance. The error was noted at the time of preparing the Bank Reconciliation Statement as on 31st March, 2019.Prepare Bank Reconciliation Statement. |
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Answer» On 31st March, 2019, Cash Book of a merchant showed bank overdraft of ₹ 1,72,985. On comparing the Cash Book with Bank Statement, following discrepancies were noted: (i) Cheques issued for ₹ 60,000 were not presented in the bank till 7th April, 2019. (ii) Cheques amounting to ₹ 75,000 were deposited in the bank but were not collected. (iii) A Cheque of ₹ 15,000 received from Mahesh Chand and deposited in the bank was dishonoured but the non-payment advice was not received from the bank till 1st April, 2019. (iv) ₹ 1,50,000 being the proceeds of a bill receivable collected appeared in the Pass Book but not in the Cash Book. (v) Bank charges ₹ 1,500 and interest on overdraft ₹ 8,500 appeared in the Pass Book but not in the Cash Book. (vi) Overdraft balance as per Cash Book of ₹ 500 on 28th February, 2019 was wrongly carried forward as debit balance. The error was noted at the time of preparing the Bank Reconciliation Statement as on 31st March, 2019. Prepare Bank Reconciliation Statement. |
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| 662. |
Express 0.237 bar on 237 in p/q form |
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Answer» Express 0.237 bar on 237 in p/q form |
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| 663. |
A theatre, in the shape of a quadrilateral ABCD, has ∠ C=90∘, AB=9 m,BC=12 m,CD=5 m and AD=8 m. If the total area of theatre is 90 m2, then what will be the area of △BAD ? |
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Answer» A theatre, in the shape of a quadrilateral ABCD, has ∠ C=90∘, AB=9 m,BC=12 m,CD=5 m and AD=8 m. If the total area of theatre is 90 m2, then what will be the area of △BAD ? |
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| 664. |
Consider the following distribution of the number of mangoes being packed in cardboard boxes where these boxes contain varying number of mangoes. Find the mean number of mangoes kept in a packing box using assumed mean method?Number of mangoes50−5253−5556−5859−6162−64Number of boxes1511013511525 |
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Answer» Consider the following distribution of the number of mangoes being packed in cardboard boxes where these boxes contain varying number of mangoes. Find the mean number of mangoes kept in a packing box using assumed mean method? Number of mangoes50−5253−5556−5859−6162−64Number of boxes1511013511525 |
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| 665. |
Fill in the blanks so as to make the following statements true:(i) Two distinct points in a plane determine a ........line.(ii) Two distinct ........... in a plane cannot have more than one point in common.(iii) Given a line and a point, not on the line, there is one and only ......... line which passes through the given point and is ......... to the given line.(iv) A line separates a plane into ......... parts namely the ...........and the ........... itself. |
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Answer» Fill in the blanks so as to make the following statements true: (i) Two distinct points in a plane determine a ........line. (ii) Two distinct ........... in a plane cannot have more than one point in common. (iii) Given a line and a point, not on the line, there is one and only ......... line which passes through the given point and is ......... to the given line. (iv) A line separates a plane into ......... parts namely the ...........and the ........... itself. |
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| 666. |
Represent √2 & √3 on the number line |
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Answer» Represent √2 & √3 on the number line |
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| 667. |
In the given figure, D is the mid-point of AB and PC=12AP=3 cm. If AD=DB=4 cm and DE||BP , then AE is |
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Answer» In the given figure, D is the mid-point of AB and PC=12AP=3 cm. If AD=DB=4 cm and DE||BP , then AE is |
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| 668. |
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=70∘,∠BAC=30∘ and AB=BC, then find ∠ECD. |
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Answer» ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=70∘,∠BAC=30∘ and AB=BC, then find ∠ECD. |
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| 669. |
If the length of a median of an equilateral triangle is x cm, then its area is |
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Answer» If the length of a median of an equilateral triangle is x cm, then its area is |
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| 670. |
Question 18 The coefficient of x in the expansion of (x+3)3 is A) 1 B) 9 C) 18 D) 27 |
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Answer» Question 18 The coefficient of x in the expansion of (x+3)3 is A) 1 B) 9 C) 18 D) 27 |
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| 671. |
Question 1 (vii)Without actually performing the long division, state whether 12922×57×75 will have a terminating decimal expansion or a non-terminating repeating decimal expansion. |
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Answer» Question 1 (vii) |
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| 672. |
Virat Kohli's scores in 8 innings are given as : 46 , 120 , 144 , 82 , 15 , 76 , 54 and 31. What is his average? |
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Answer» Virat Kohli's scores in 8 innings are given as : 46 , 120 , 144 , 82 , 15 , 76 , 54 and 31. What is his average? |
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| 673. |
15, 6, 16, 8, 22, 21, 9, 18, 25 |
| Answer» 15, 6, 16, 8, 22, 21, 9, 18, 25 | |
| 674. |
All the angles of a quadrilateral can be obtuse. Is this statement true? Give reasons for your answer. |
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Answer» All the angles of a quadrilateral can be obtuse. Is this statement true? Give reasons for your answer. |
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| 675. |
The factors of x3 −x2y − xy2 + y3 are(a)(x + y) (x2 − xy + y2)(b) (x + y) (x2 + xy + y2)(c) (x + y)2 (x − y)(d) (x − y)2 (x + y) |
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Answer» The factors of x3 −x2y − xy2 + y3 are (a)(x + y) (x2 − xy + y2) (b) (x + y) (x2 + xy + y2) (c) (x + y)2 (x − y) (d) (x − y)2 (x + y) |
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| 676. |
In an isosceles triangle ABC, AB = AC and BA is produced to D, such that AB = AD. What is the value of ∠BCD? |
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Answer» In an isosceles triangle ABC, AB = AC and BA is produced to D, such that AB = AD. What is the value of ∠BCD? |
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| 677. |
The diameter of a coin is 1 cm (in the following figure). If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take π = 3.1416). |
Answer» The diameter of a coin is 1 cm (in the following figure). If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take π = 3.1416).
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| 678. |
Mary bought a video game as birthday gift to Sam. Sam likes stamp collection and hence Mary wants to cover the video game gift box with square shaped stamps, each of side 2 cm . If the gift box has length, breadth and height as 8 cm, 6 cm and 2 cm respectively, then how many stamps she has to collect so as to cover the entire gift box? |
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Answer» Mary bought a video game as birthday gift to Sam. Sam likes stamp collection and hence Mary wants to cover the video game gift box with square shaped stamps, each of side 2 cm . If the gift box has length, breadth and height as 8 cm, 6 cm and 2 cm respectively, then how many stamps she has to collect so as to cover the entire gift box? |
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| 679. |
Which of the following is irrational number? |
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Answer» Which of the following is irrational number? |
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| 680. |
value of (3/2+iroot3/2)^30 equals |
| Answer» value of (3/2+iroot3/2)^30 equals | |
| 681. |
The length of hypotenuse of a right angled triangle is 15. Find the length of median of its hypotenuse. |
| Answer» The length of hypotenuse of a right angled triangle is 15. Find the length of median of its hypotenuse. | |
| 682. |
Find the number of coins, each of which are 1.5 cm in diameter and 0.2 cm thick, required to form a right circular cylinder of height 10 cm and diameter 4.5 cm |
| Answer» Find the number of coins, each of which are 1.5 cm in diameter and 0.2 cm thick, required to form a right circular cylinder of height 10 cm and diameter 4.5 cm | |
| 683. |
1. Represent 10.5 and 7.5 on the number line step by step |
| Answer» 1. Represent 10.5 and 7.5 on the number line step by step | |
| 684. |
9. Find the number of degrees subtended at the centre of a circle by an Arc whose length is 0.357 times the radius |
| Answer» 9. Find the number of degrees subtended at the centre of a circle by an Arc whose length is 0.357 times the radius | |
| 685. |
22. WHICH ON AMONG SIN 1 AND SIN 2 IS SMALLER? |
| Answer» 22. WHICH ON AMONG SIN 1 AND SIN 2 IS SMALLER? | |
| 686. |
The volume of the rectangular block is (x)(x2)(3x3) cubic centimetres. It can be simplified as. |
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Answer» The volume of the rectangular block is (x)(x2)(3x3) cubic centimetres. |
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| 687. |
In a survey of 364 children aged 2-4 years, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is: |
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Answer» In a survey of 364 children aged 2-4 years, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is: |
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| 688. |
let f(theta)= sin theta+2sin2theta-sin3theta-3 then in theta belongs to (0, 180 degree) no of solutions of f(theta)=0 is |
| Answer» let f(theta)= sin theta+2sin2theta-sin3theta-3 then in theta belongs to (0, 180 degree) no of solutions of f(theta)=0 is | |
| 689. |
In a parallelogram ABCD, the line drawn through a point P on AB; parallel to BC, meets AC at Q. The line through Q, parallel to AB meets AD at R. Then, APPB= |
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Answer» In a parallelogram ABCD, the line drawn through a point P on AB; parallel to BC, meets AC at Q. The line through Q, parallel to AB meets AD at R. Then, APPB= |
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| 690. |
If the linear density of a rod of length 3m is proportional to X where X is the distance from one end of the rod the distance of the centre of gravity of the rod from this end is1)2.5m2)1m3)1.5m4)2m |
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Answer» If the linear density of a rod of length 3m is proportional to X where X is the distance from one end of the rod the distance of the centre of gravity of the rod from this end is 1)2.5m 2)1m 3)1.5m 4)2m |
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| 691. |
Question 123 |
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Answer» Question 123
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| 692. |
log 100000 = ____ . ___ |
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Answer» log 100000 = ____ . |
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| 693. |
Find the value of 8sin 2x cos 4x sin 6x, when x = 15∘ |
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Answer» Find the value of 8sin 2x cos 4x sin 6x, when x = 15∘ |
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| 694. |
Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. Its area is ___. |
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Answer» Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. Its area is |
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| 695. |
If A+B+C=45 ° , then the value of ∑(†an A+†an A†an B) is |
| Answer» If A+B+C=45 ° , then the value of ∑(†an A+†an A†an B) is | |
| 696. |
Which among the following is a cubic polynomial? |
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Answer» Which among the following is a cubic polynomial? |
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| 697. |
1,2,3,4,5......The above set of numbers are known as _______. |
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Answer» 1,2,3,4,5...... |
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| 698. |
A rectangle is 5 cm wide and 20 cm long. The ratio of its width to its length is |
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Answer» A rectangle is 5 cm wide and 20 cm long. The ratio of its width to its length is |
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| 699. |
If x=0.¯18, which of the following statements are true?(i) 100x=18.¯18 (ii) 100x−x=17.¯18 (iii) 99x=18 |
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Answer» If x=0.¯18, which of the following statements are true? (i) 100x=18.¯18 |
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| 700. |
If x+1x=2, find the value of x64+1x64 |
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Answer» If x+1x=2, find the value of x64+1x64 |
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