Question 1 :
Two line segments AB and AC include an angle of 60$^{\circ}$ where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = $\frac{3}{4}$ AB and AQ = $\frac{1}{4}$ AC. Join P and Q and measure the length PQ.
Question 2 :
Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60$^{\circ}$, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD' C' similar to ∆BDC with scale factor $\frac{4}{3}$ . Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram?
Question 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b55273b23058497997e.PNG' />
In the above figure, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, what is the length of AB?
Question 4 :
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60$^{\circ}$, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be?(in degrees)
Question 5 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b36273b230584979955.jpg' />
In the above figure, dimensions are given. Find the area of the flower bed (with semi-circular ends).
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bad273b2305849799f2.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the red scoring region.
Question 7 :
State True or False: Area of segment of a circle = area of the corresponding sector - area of the corresponding triangle.
Question 8 :
If the circumference of a circle and perimeter of a square are equal, then
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc1273b230584979a0c.png' />
In the above figure , ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter . Find the area of the shaded region.
Question 10 :
Is it TRUE or FALSE, that If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ?
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcb273b230584979a19.PNG' />
In the above case, PQ is called a non-intersecting line with respect to the circle . TRUE OR FALSE ?
Question 13 :
A tangent to a circle intersects it in _____ point (s)
Question 14 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?
Question 15 :
If A $\left(–5, 7\right)$, B $\left(– 4, –5\right)$, C $\left(–1, –6\right)$ and D $\left(4, 5\right)$ are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.
Question 16 :
Find the coordinates of the point R on the line segment joining the points P (–1, 3) and Q (2, 5) such that PR = $\frac {3}{5}$PQ.
Question 17 :
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b57273b230584979982.PNG' />
In the above figure, students of a school standing in rows and columns in their playground for a drill practice are shown. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
Question 19 :
Find the area of the triangle ABC with A (1, –4) and the mid-points of sides through A being (2, – 1) and (0, – 1).
Question 20 :
Is $(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2 A + cot^2 A$?
Question 23 :
(1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ____
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdb273b230584979a2e.png' />
In the above fig, the lines represents ____________ lines.
Question 26 :
Solve the following pair of equations by substitution method: $s-7t+42=0 ; s-3t=6$
Question 27 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdc273b230584979a30.png' />
In the above fig, the lines represents ____________ lines.
Question 28 :
Is x = 1, y = 1 a solution of $2x + 3y = 5$?
Question 29 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4} ; \frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = \frac{-1}{8}$.
Question 30 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $-\frac{8}{3}$, $\frac{4}{3}$
Question 31 :
State true or false: If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
Question 32 :
Divide $3x^2 – x^3 – 3x + 5$ by $x – 1 – x^2$ and find the remainder. Is the remainder independent of $x$ ?
Question 33 :
If on division of a non-zero polynomial $p\left(x\right)$ by a $g\left(x\right)$, the remainder is zero, what is the relation between the degrees of $p\left(x\right)$ and $g\left(x\right)$ ?
Question 34 :
For which values of a and b, are the zeroes of $q\left(x\right)=x^3+2x^2+a$ also the zeroes of the polynomial $p\left(x\right)=x^5-x^4-4x^3+3x^2+3x+b$?
Question 35 :
If P(E) = 0.05, what is the probability of ‘not E’?
Question 36 :
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.
Question 37 :
Harpreet tosses two different coins simultaneously (say, one is of Rs.1 and other of Rs.2). What is the probability that she gets at least one head?
Question 38 :
A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red?
Question 39 :
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting the jack of hearts.
Question 40 :
State True or False whether the following quadratic equation has two distinct real roots: $2x^2+x-1=0$
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b60273b23058497998d.png' />
In the centre of a rectangular lawn of dimensions $50m×40m$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 $m^2$ in the above figure. Find the length of the pond.
Question 42 :
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Question 44 :
The product of Sunita’s age (in years) two years ago and her age four years from now is one more than twice her present age. What is her present age?
Question 45 :
State whether the square of any positive integer can be of the form 3m + 2, where m is a natural number.
Question 46 :
A/An __________ is a series of well defined steps which gives a procedure for solving a type of problem.
Question 47 :
Without actually performing the long division, state whether $\frac{6}{15}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 48 :
The cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m. Is it true?
Question 49 :
Choose the correct answer from the given four options in the question: If two positive integers a and b are written as $a = x^3y^2$ and $b = xy^3$; x, y are prime numbers, then HCF (a, b) is ________.
Question 50 :
State true or false: The square of an odd positive integer is of the form 8m + 1, for some whole number m.
Question 51 :
Choose the correct answer from the given four options in the question: If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ________ .
Question 52 :
The rational number $\frac{257}{5000}$ in the form $2^m × 5^n$ , where m, n are non-negative integers. Find the value of n.
Question 53 :
The cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r. Is it True or False?
Question 55 : <img style='object-fit:contain' src='61b19a96273b23058497993a' />
To find out the concentration of $SO_2$ in the air (in parts per million, i.e. ppm), the data was collected for 30 localities in a certain city and is presented above. Find the mean concentration of $SO_2$ in the air.
Question 56 : <img style='object-fit:contain' src='61b19a6b273b230584979935' />
Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as above. Find the mean heart beats per minute for these women, choosing a suitable method.
Question 57 :
For finding the median of ungrouped data, we first arrange the data values of the observations in ascending order. TRUE OR FALSE?
Question 58 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c1a273b230584979a77.PNG' />
A life insurance agent found the above data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.
Question 59 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0a273b230584979a64.PNG' />
Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as given above. Find the mean heartbeats per minute for these women, choosing a suitable method.
Question 61 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfb273b230584979a53.PNG' />
Find the mean of the above given data.
Question 62 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c1b273b230584979a78.PNG' />
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the above table. Find the median length of the leaves
Question 63 : <img style='object-fit:contain' src='61b19a9e273b23058497993b' />
The above table shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency.
Question 64 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfe273b230584979a56.PNG' />
The marks distribution of 30 students in a mathematics examination are given above. Find the mode of this data.
Question 65 :
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foof of the tower, is 30°. Find the height of the tower.
Question 66 :
Two poless of equal heights are standing opposite to each ofher on either side of the road, which is 80 m wide. From a point between them on the road, the Angles of elevation of the top of the poless are 60° and 30°, respectively. Find the height of the poless.
Question 67 :
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 $45^\circ and 60^\circ$, respectively. Find the height of the tower.
Question 68 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a60273b230584979931.jpeg' />
In the above image, a circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with ground level is 30°.
Question 69 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a62273b230584979933.jpeg' />
In the above image, a 1.2 m tall girl spofs a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
Question 70 :
A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?
Question 71 :
A wall 24 m long, 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 $\frac{1}{10}$th of the volume of the wall, then find the number of bricks used in constructing the wall.
Question 72 :
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Question 73 :
If two solid hemispheres of same radius r are joined together along their bases, then curved surface area of this new solid is
Question 74 :
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open is 5 cm. It is filled with water upto brim. When lead shots each in the shape of a sphere with radius 0.5 cm are dropped into the vessel, the one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Question 75 :
What is the formulae for volume of a spherical shell?(where $r_1$ and $r_2$ are respectively its external and internal radii)
Question 76 :
Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
Question 77 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b99273b2305849799d7.png' />
In the given figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, $\angle$ APB = 50° and $\angle$ CDP = 30°. Then, $\angle$ PBA is equal to
Question 78 :
It is given that $\Delta$ABC ~ $\Delta$PQR,with $\frac{BC}{QR}=\frac{1}{3}$. Then,$\frac{area\ of\ PRQ}{area\ of\ BCA}$ is equal to
Question 79 :
State true or false:
If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.
Question 80 :
State True or False: A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR= 6 cm and PB = 4 cm. Then AB is parallel to QR.
Question 81 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c66273b230584979acf.PNG' />
In the above fig, sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆ PQR. Is ∆ABC ~ ∆PQR ?
Question 82 :
D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ ABC. Find the ratio of the areas of ∆ DEF and ∆ ABC.
Question 83 :
It is given that $\Delta$ABC ~ $\Delta$DFE, $\angle$A =30°, $\angle$C = 50°, AB = 5 cm, AC = 8 cm and DF= 7.5 cm. Then, which of the following is true?
Question 85 :
State True or False: In $\Delta$ ABC, AB = 24 cm, BC = 10 cm and AC = 26 cm. Then this is a right angled traingle.
Question 86 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c50273b230584979ab5.PNG' />
In the above fig, BL and CM are medians of a triangle ABC right angled at A. $X(BL^2 + CM^2)$ = $Y (BC)^2$. What is the value of X and Y ?
Question 87 :
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Question 88 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb7273b2305849799fe.png' />
In the above figure , find the area of the shaded region if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Question 89 :
Find the area of the major sector of a circle with radius 4 cm and of angle $30^{\circ}$.
Question 90 :
The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period $6\ :\ 05\ am$ and $6\ :\ 40\ am$ .
Question 91 :
If the areas of two sectors of two different circles are equal, then their corresponding arc lengths will be equal. Is it true or false?
Question 92 :
The numerical value of the area of a circle is greater than the numerical value of its circumference. Is it true or false?
Question 93 :
Area of a sector of a circle of radius 36 cm is 54 $\pi\ cm^2$ . Find the length of the corresponding arc of the sector.
Question 94 :
The area of a square inscribed in a circle of diameter $p\ cm$ is $p^2\ cm^2$. Is it true or false?
Question 95 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bad273b2305849799f2.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the red scoring region.
Question 96 :
Is the area of the largest circle that can be drawn inside a rectangle of length $a\ cm$ and breadth $b\ cm$ $\left(a>b\right)$ is $\pi\ b^2\ cm^2$ ?
Question 97 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc7273b230584979a14.JPG' />
In the above fig. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?
Question 98 :
30th term of the AP: 10, 7, 4, . . . , is
Question 99 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 100 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 101 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
Question 102 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?
Question 103 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 104 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc8273b230584979a15.JPG' />
In the above fig. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
Question 105 :
Find the sum of the following AP: 34 + 32 + 30 + . . . + 10
Question 106 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc6273b230584979a13.JPG' />
In the above fig. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in above figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?
Question 107 :
In a right triangle ABC in which $\angle B = 90^{\circ}$, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Does the tangent to the circle at P bisects BC?
Question 108 :
State true or false. Tangent is perpendicular to the radius through the point of contact.
Question 109 :
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
Question 110 :
What is the common point of a tangent to a circle and the circle called?
Question 111 :
Two concentric circles are of radii 5 cm and 3 cm . Find the length of the chord of the larger circle which touches the smaller circle .
Question 112 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bce273b230584979a1d.JPG' />
In the above figure , a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively . Find the side AC.
Question 113 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4d273b230584979974.PNG' />
In the above figure, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is
Question 114 :
A line and a circle in the same plane can co-exist in _______ different ways.
Question 115 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b44273b230584979968.PNG' />
In the above figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of $50^{\circ}$ with PQ, then $\angle POQ$ is equal to
Question 116 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b49273b23058497996f.PNG' />
In the above figure, tangents PQ and PR are drawn to a circle such that $\angle RPQ = 30^{\circ}$. A chord RS is drawn parallel to the tangent PQ. What is the value of $\angle RQS$?
Question 117 :
The value of $\cos \theta$ increases as $\theta$ increases. True or False?
Question 119 :
(1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ____
Question 123 :
If A, B and C are interior angles of a triangle ABC, then $\sin\begin{pmatrix}\frac{B+C}{2}\end{pmatrix}\ne\cos\begin{pmatrix}\frac{A}{2}\end{pmatrix}$. TRUE or FALSE ?
Question 125 :
Express $\sin 67^{\circ} + \cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.
Question 127 :
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Question 128 :
The cost of 2 pencils and 3 erasers is Rs. 9 and the cost of 4 pencils and 6 erasers is Rs. 18. Find the cost of each pencil and each eraser.
Question 129 :
For which value of k will the following pair of linear equations have no solution? $3x + y = 1; (2k – 1)x + (k – 1) y = 2k + 1$
Question 130 :
Solve the following pair of linear equations by the substitution method : $0.2x + 0.3y = 1.3 ; 0.4x + 0.5y = 2.3$
Question 131 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations intersect at a point, are parallel or coincident: $6x – 3y + 10 = 0 ; 2x – y + 9 = 0$
Question 132 :
From the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0, find the area of the quadrilateral formed by the lines and the x–axis.
Question 133 :
For what values of k will the following pair of linear equations have infinitely many solutions? $kx + 3y – (k – 3) =0 ; 12x + ky – k =0$
Question 134 :
Solve the pair of equations: $\frac{2}{x} + \frac{3}{y} = 13 ; \frac{5}{x} - \frac{4}{y} = -2$
Question 135 :
Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Which of these represent this situation algebraically?
Question 136 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{5}{x-1} + \frac{1}{y-2} = 2 ; \frac{6}{x-1} - \frac{3}{y-2} = 1$.
Question 137 : The number of zeroes lying between –2 to 2 of the polynomial f (x), whose graph is given below, is
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b61273b23058497998f.PNG' />
Question 138 :
If sinθ = $\frac{1}{3}$,then the value of ($9 cot^{2}θ + 9$) is
Question 139 :
A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is $\frac{11}{20}$ and that of blue ball is $\frac{1}{5}$ then the number of black balls is
Question 140 : In the adjoining figure, ∆ ABC is circumscribing a circle. Then, the length of BC is <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b63273b230584979991.PNG' />
Question 141 :
The discriminant of the quadratic equation $3\sqrt{3}x^2 + 10x + \sqrt{3} = 0$ is
Question 142 : From each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in figure. The area of the remaining (shaded) portion is <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b67273b230584979997.PNG' />
Question 143 :
The smallest value of k for which the equation $x^{2} + kx + 9 = 0$ has real roots, is
Question 144 :
If for some angle θ, cot 2θ = $\frac{1}{\sqrt{3}}$ then the value of sin3θ, where 2θ $\leq$ 90º is
Question 145 :
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where
Question 146 :
The coordinates of the points P and Q are (4, –3) and (–1, 7). Then the abscissa of a point R on the line segment PQ such that $\frac{PR}{PQ}$ = $\frac{3}{5}$ is
Question 147 :
A bag contains 3 red balls, 5 white balls and 7 black balls. What is the probability that a ball drawn from the bag at random will be neither red nor black?
Question 148 :
Which of the following cannot be the probability of an event?
Question 149 : Consider the data:
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b72273b2305849799a5.jpg' />
The difference of the upper limit of the median class and the lower limit of the modal class is
Question 150 : In the following distribution :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b8e273b2305849799c8.PNG' />
The number of families having income range (in Rs) 16000 – 19000 is
Question 151 :
When a die is thrown, the probability of getting an odd number less than 3 is
Question 152 : The times, in seconds, taken by 150 atheletes to run a 110 m hurdle race are tabulated below :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b71273b2305849799a4.jpg' />
The number of atheletes who completed the race in less then 14.6 seconds is :
Question 153 :
A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
Question 154 : For the following distribution:
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b70273b2305849799a3.jpg' />
The modal class is
Question 155 :
The probability that a non leap year selected at random will contain 53 sundays is
Question 156 :
If n is the total number of observations, locate the class whose cumulative frequency is greater than (and nearest to) $\frac{n}{2}$.Is it TRUE or FALSE that, this class is called the median class.
Question 157 :
A mason constructs a wall of dimensions 270cm× 300cm × 350cm with the bricks each of size 22.5cm × 11.25cm × 8.75cm and it is assumed that $\frac{1}{8}$ space is covered by the mortar. Then the number of bricks used to construct the wall is
Question 158 :
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.
Question 160 :
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter.A full barrel of ink in the pen is used up on writing 3300 words on an average.How many words can be written in a bottle of ink containing one fifth of a litre?
Question 161 :
A spherical steel ball is melted to make eight new identical balls.Then, the radius of each new ball be $\frac{1}{8}$th the radius of the original ball.
Question 162 :
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length of the wire, assuming the density of copper to be 8.88 g per $cm^3$ .
Question 163 :
Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Question 164 :
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Question 165 :
A cistern, internally measuring $150 cm\times 120 cm\times 110 cm$, has 129600 $cm^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being $22.5 cm\times 7.5 cm\times 6.5 cm$.
Question 166 :
A wall 24 m long, 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 $\frac{1}{10}$th of the volume of the wall, then find the number of bricks used in constructing the wall.
Question 168 :
Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n.
Question 169 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 170 :
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Question 171 :
Find the sum of the first 15 terms in $a_n = 9 – 5n$
Question 172 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Question 173 :
In an AP, given $a = 3, n = 8, S = 192$, find d.
Question 174 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.
Question 175 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?
Question 176 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc3273b230584979a0e.JPG' />
In the above fig, find the missing value corresponding to (iii)
Question 177 :
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.
Question 178 :
The angle formed by the line of sight with the horizontal when the point on the object which is being viewed is above the horizontal level , is known as ________
Question 179 :
From a point P on the ground the angle of elevation of the top of a 10 m tall building is $30^{\circ}$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is $45^{\circ}$. Find the length of the flagstaff and the distance of the building from the point P respectively. (You may take $\sqrt3 = 1.732$)
Question 180 :
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 8 m. Find the height of the tree.
Question 181 :
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are $30^{\circ}$ and $45^{\circ}$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Question 182 :
An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is $45^{\circ}$. What is the height of the chimney?
Question 183 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf9273b230584979a51.PNG' />
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$. After some time, the angle of elevation reduces to $30^{\circ}$ (see above figure). Find the distance travelled by the balloon during the interval.
Question 184 :
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ}$, respectively. Find the height of the poles and the distances of the point from the poles respectively.
Question 185 :
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^{\circ}$. Find the length of the string, assuming that there is no slack in the string.
Question 186 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf8273b230584979a50.PNG' />
A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ}$. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ}$ (see figure above). Find the height of the tower and the width of the canal.
Question 187 :
A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is
Question 188 :
A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, then find the length of the wire.
Question 189 :
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Question 190 :
A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm, 5 cm and 4 cm. The radius of each the conical depressions is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.
Question 191 :
Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 95 cm. Compare the capacity of the tank with that of the sump. (Use $\pi$ = 3.14)
Question 192 :
A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8 cm. The height of the cone is
Question 193 :
A rectangular water tank of base 11 m × 6 m contains water upto a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank.
Question 194 :
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $cm^2$.
Question 195 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2a273b230584979a87.JPG' />
In the above image, rasheed got a playing top (lattu) as his birthday present, which surprisingly had false colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the approximate area he has to colour. (Take $\pi$ = $\frac{22 }{7}$ )
Question 196 :
Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
