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351.

You are given two series in two rows. In the first row, a full series is given which follows a specific pattern. The second row has a series, similar to the first series but only first element of this series is produced followed by (A), (B), (C), (D) and (E) for the subsequent elements. You have to complete the series starting with a given number and answer the question that follows. {:("2","9","57","337","1681",),("3","A","B","C","D","E"):} What will come in place of E?

Answer»

673
3361
13441
17

Solution :The rule used is `xx8-7,xx7-6,xx6-5,xx5-4andxx4-3` using the same rule, starting from 3, the NEW SERIES is:
3, 17, 113, 673, 3361, 13441.
Discussion
352.

For what value of k will k + 9, 2k - 1, 2k + 7 be consecutive terms of a AP.

Answer»


Answer :`2K + 7 - (2k -1) = (2k -1)- (K+ 9)`
`6= k-8 rArr k = 14`.
Discussion
353.

Ratio of 3 angles of a traingle are 3:4:5. Find each angle.

Answer»


ANSWER :`45^@,60^@,75^@`
Discussion
354.

Choose from the four diagrams given below the one that illustrates the relationship among "Languages, French, German."

Answer»




SOLUTION :Both FRENCH and GERMAN are LANGUAGES,But both of them are DIFFERENT from each other.
Discussion
355.

Find the quadratic equation whose solution set is {-2, 3}.

Answer»


ANSWER :`X^(2)-x-6=0`; which is the REQUIRED quadreatic EQUATION.
Discussion
356.

ConstructtrianglePYQ such that, PY=6.3 cm,YQ=7.2 cm, PQ=5.8 cm. If (YZ)/(YQ)=(6)/(5), then construct triangle XYZ similar to triangle PYQ.

Answer»


Answer :If seg YQ is divided into 5 equal parts, then seg YZ will be 6 times each PART of seg YQ.
So, if we construct `triangle PYQ`, point Z will be on SIDE YQ, at a distance equal to 6 parts from Y.
Now, point X is the point of intersection of ray YP and a line through Z, PARALLEL to PQ.
`triangle XYZ` is the required triangle similar to `triangle PYQ`.
Discussion
357.

Length of a rectangular box is 20cm,width 5cm and height 10cm,find the length of its diagonal.

Answer»
Discussion
358.

Divide a line segment 6 cm long in the ratio 4 : 3. Given below are steps of construction. Which of the following steps is incorrect? Step 1 : Draw a line segment AB = 6 cm. Step 2 : Draw a ray AX making an acute angle BAX Step 3: Along AX mark 4 points A_1, A_2, A_3, and A_4 such that A A_1= A_1 A_2 = A_2A_3 = A_3 A_4. Step 4: Join A_4 B . Step 5: From A_3 drawn A_3 C || A_4 B meeting AB at C.

Answer»

STEP 3 only
Step 4 only
Step 3 and 4
Step 3, 4, and 5

Answer :D
Discussion
359.

A trader bought a number of articles for Rs900, five were damaged and he sold each of the rest at Rs2 more than what he paid for it. If on the whole he gains Rs80, find the number of articles bought.

Answer»


ANSWER :75
Discussion
360.

A man steadily goes 4 m due East and then 3 m due. North.(i) Find the distance from initial point to last point.(ii)whichmathematical concept is used in thisproblem ?(iii)What is its value ?

Answer»


Answer :(i)Hence, the man is at a distance of 5 m from the initialposition.
(II) Right-angled TRIANGLE,Pythagoras THEOREM.
(iii)Knowledge of direction and speed SAVES the TIME.
Discussion
361.

Point M(-3,7) and N(-1,6) divides segment AB into three equal parts. Find the coordinates of point A and Point B.

Answer»


ANSWER :`thereforeA(-5,8)`
`thereforeB(1,5)`
Discussion
362.

A cylindrical boiler, 2 m high, is 3.5 m in diameter. It has a hemispherical lid. Find the volume of its interior, including the part covered by the lid.

Answer»


ANSWER :`30.48 m ^(3)`
Discussion
363.

Check whether the following equations are consistent or inconsistent. Solve them graphically. (4)/(3)x+2y=8 , 2x+3y=12.

Answer»


ANSWER :They have INFINITELY MANY SOLUTIONS.
Discussion
364.

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day thatthe cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the number of articles produced and the cost of each article.

Answer»


Answer :NUMBER of ARTICLES = 6; COST of each ARTICLE = 15
Discussion
365.

Find two consecutive odd positive integers, sum of whose squares is 290.

Answer»


ANSWER :`11,13`
Discussion
366.

The numerical values and whole surface area of a solid hemisphere are equal. Find the length of radius of the hemisphere.

Answer»

Solution :Let the radius of the solid HEMISPHERE=r UNITS.
`therefore` the volume of the solid hemisphere `=(2)/(3)pir^(3)` cu. Units and its whole SURFACE area `=3pir^(2)` sq.units.
As PER question ,`(2)/(3)pir^(3)=3pir^(2) rArr r=(9)/(2)=4.5`
Hence the radius of the solid hemisphere =4.5 units.
Discussion
367.

Spherical marbles of diameter 1.4 cm. are dropped into a cylindrical beaker of diameter 7 cm., which contains some water. Find the number of marbles that should be dropped into the beaker, so that water level rises by 5.6 cm.

Answer»


ANSWER :150
Discussion
368.

Two customers A and B are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on: the same day?

Answer»


ANSWER :` (1)/(5)`
Discussion
369.

Two customers A and B are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on: consecutive days?

Answer»


ANSWER :` (8)/(25)`
Discussion
370.

Two customers A and B are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on: different days

Answer»


ANSWER :` (4)/(5)`
Discussion
371.

(a) Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents.(b)Construct a Delta PQR which the base PQ=4.5cm, R = 35^(@) and the median from R to RG is 6 cm.

Answer»


ANSWER :(a) `8.7 CM`
Discussion
372.

Find the mode of the given data8,5,4,6,7,4,4,3,5,4,5,4,4,4,3

Answer»
Discussion
373.

Fill in the blanks in the following , given that a is the first term, d the common difference and a_n the nth term of the A.P.

Answer»


ANSWER :a+(n-1)d
Discussion
374.

A cylinder of circumference 8 cm and length 21 cm rolls without sliding for 4 (1)/(2)seconds at the rate of 9 complete rounds per second. Find : the distance travelled by the cylinder in 4 (1)/(2)seconds ?

Answer»


ANSWER :`324 CM `
Discussion
375.

A cylinder of circumference 8 cm and length 21 cm rolls without sliding for 4 (1)/(2)seconds at the rate of 9 complete rounds per second. Find : the area covered by the cylinder in 4 (1)/(2)seconds.

Answer»


ANSWER :`6804 CM ^(2)`
Discussion
376.

Find the sum of first n odd natural numbers.

Answer»


ANSWER :`= (N)/(2) [ 2+ 2N-2] = (n)/(2) [ 2n] = n^(2)`.
Discussion
377.

If in a certain language REMOTE is coded as ROTEME, which word would be coded as PNIICC?

Answer»

NPIICC
PICCIN
PINCIC
PICNIC

Solution :The groups of second and THIRD LETTERS, fourth and fifth letters in the WORD interchange place in that code. Hence, the word PICNIC would be CODED as PNIICC
Discussion
378.

Now consider the numbers p, q, q + 2. What relation you get between these three numbers ?

Answer»


ANSWER :12, 35, 37 for a PYTHAGOREAN TRIPLET.
Discussion
379.

Solve the following equation:(1)/(x) - (1)/(x-2)3, x ne 0, 2

Answer»

Solution :`(1)/(X) =(1)/(x-2) = 3`
` (x-2-x)/(x(x-2))=(3)/(1)`
`3X^(2) - 6x = - 2`
` x= (6pmsqrt(12))/(6)`
`= (3pmsqrt(3))/(3), (3-sqrt(3))/(3)`
Discussion
380.

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Answer»


ANSWER :`214.5cm^(2)`.
Discussion
381.

The probabilty that a leap year selected at random has 53 Sundays, is:

Answer»

`1/7`
`2/7`
`3/7`
1

Answer :B
Discussion
382.

Find the values of the sqrt(23) by geometric method .

Answer»


ANSWER :4.8 APPROX
Discussion
383.

{:(x - y = - 1),(3x + 2y = 12):}

Answer»


ANSWER :x = 2, y = 3, (2, 3), (-1, 0), (4, 0) and AREA of `Delta = 7.5` square UNITS
Discussion
384.

A statue 1.6 m tall stands on the top of a pedestral . From a point on the ground, the angle of elevation of the top of the statue is 60^@ and from the same point the angle of elevation of the top of the pedestal is 45^@. Find the height of the pedestal.

Answer»


ANSWER :`4(3 + SQRT(3))m`
Discussion
385.

Draw a circle of radius 3.2 cm . Then construct a tangent to that circle on any point of that circle.

Answer»

Solution :Let r=3.2 cm and O is the centre of the circle. Let US DRAW a circle with centre at O and RADIUS =3.2 cm . Let P a POINT on the circle. We have to constructa tangent at the point P.
Discussion
386.

From the of a vertical building of 50sqrt3 mheight on a level ground the angle of depression of an object on the same ground is observed to be 60^@. Find the distance of the object from the foot of the building.

Answer»


ANSWER :50 m
Discussion
387.

If the angle of elevation of a cloud from a point h metres above a lake be alpha and the angle of depression of its reflection in the lake be beta, prove that the distance of the cloud from the point of observation is (2 h sec alpha)/(tan beta- tan alpha)

Answer»
Discussion
388.

Two dice are thrown together. What is probability of (a) having one number being twice the other. (b) having a product of 6 between the two numbers (c) having a sum of 9

Answer»


ANSWER :(a) `1/6`
(B) `1/9`
(C) `1/9`
Discussion
389.

Fear : Threat :: Anger : ?

Answer»

Compulsion
Pariec
Provocation
Force

SOLUTION : FIRST ARISES from the SECOND.
Discussion
390.

A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return down stream to the same spot. Find the speed of the stream.

Answer»


ANSWER :6 km/h.
Discussion
391.

Mrs. Gupta repays her total loan of 1,18,000 by paying instalments every month. If the instalment for the first month is 1.000 and it increases by 100 every month, what amount will she pay as the 30th instalment of loan ? What amount of loan she still has to pay after the 30th instalment ?

Answer»


ANSWER :3900 and 44500
Discussion
392.

Pointing out to a lady, Rajan said, "She is the daughter of the woman who is the mother of the husband of my mother.” Who is the lady to Rajan?

Answer»

DAUGHTER
Aunt
Sister
Grand daughter

SOLUTION :Mother.s husband mean FATHER, Father mother MEANS grand mother, grand mother.s daughter means father.s sister and so father. sister means Aunt. So the LADY is Rajan.s aunt.
Discussion
393.

"If " ax^2 - 4x + 3 = 1 "then" x = ...., a ne 0

Answer»

-1 or-2
2 or 7
`8 or 1/2`
`2 or -3`

Answer :A
Discussion
394.

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45^(@) to 60^(@) respectively. Find the height of the tower.

Answer»


ANSWER :14.6 m
Discussion
395.

Before three years, the age of a father was 5 times the age of his son. After 4 years, the age of father will be 7 times of his son's age 4 years ago. Find the present ages of both father and his son.

Answer»


ANSWER :38 YEARS, 10 years;
Discussion
396.

Formulate the following problems as a pair of equations and then find their solutions. ii. Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours if he tracels 120 km by train and rest by car. He takes 20 minutes more if he tracels 200km by train and rest by car. Find the speed of the train and the car.

Answer»


Answer :SPEED of TRAIN = 60 km/h; Speed of CAR = 80 km/h
Discussion
397.

Use ruler and compasses only for this question Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.

Answer»


ANSWER :3.6 CM
Discussion
398.

Construct a Delta PQR in which QR= 5 cm, P=40^(@) and the median PG from P to QR is 4.4 cm. Find the length of the altitude from P to QR.

Answer»


ANSWER :`PM = 2.1 CM`
Discussion
399.

A copper wire , 3 mm in diameter, is wound about a cylinde whose length is 12 cm, and diameter 10 cm. so as to cover the curved surface of the cylinder find the length and mass of the wire, assuming the density of copper to be 8.88g per cm^(3) (Use pi=3.14)

Answer»


ANSWER :788g (APPROX)
Discussion
400.

Find the value of x, given that: A^2=B,A=[{:(,2,12),(,0,1):}] and B=[{:(,4,x),(,0,1):}]

Answer»


ANSWER :`x=36 `
Discussion