Question 1 :
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 3 :
The value of $\cos \theta$ increases as $\theta$ increases. True or False?
Question 4 :
Evaluate : $sin 25° cos 65° + cos 25° sin 65°$
Question 5 :
If $\tan 2A = \cot \begin{pmatrix}A – 18^{\circ}\end{pmatrix}$, where 2A is an acute angle, find the value of A.
Question 6 :
The difference between two numbers is 26 and one number is three times the other. Find them.
Question 7 :
Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3, 2x – 3y = 2 and x + 2y = 8.
Question 8 :
The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pencil box.
Question 9 :
A pair of linear equations is inconsistent, if it has ___________.
Question 10 :
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Question 11 :
An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
Question 12 :
Can we write every positive integer in the form 4q + 2, where q is an integer ?
Question 14 :
The sum or difference of a rational and an irrational number is _____________.
Question 15 :
State true or false: From the fundamental theorem of arithmetic, we can say that every composite number can be expressed as a product of primes.
Question 16 :
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 distances of the point from the poless.
Question 17 :
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foof is 45°. Determine the height of the tower.
Question 18 :
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 yr, she prefers to have a slide whose top is at a height of 1.5 m and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m and inclined at an angle of 60° to the ground. What should be the length of the slides in each case?
Question 19 :
As observed from the top of a 75 m high lighthouse from the sea level, the Angles of depression of two ships are 30° and 45°. If one ship is exactly behind the ofher on the same side of the lighthouse, then find the distance between the two ships.
Question 20 :
The Angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.
Question 21 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c1a273b230584979a76.PNG' />
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as given above. Determine the mode number of letters in the surnames.
Question 22 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c16273b230584979a72.PNG' />
The above given frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the mode.
Question 23 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0f273b230584979a6a.PNG' />
The above distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Find the mode of the data.
Question 24 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0f273b230584979a69.PNG' />
The above table shows the ages of the patients admitted in a hospital during a year. Find the mean of the data given above.
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c03273b230584979a5b.PNG' />
Find median for the above given data.
Question 26 :
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 27 :
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.
Question 28 :
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c3b273b230584979a9c.JPG' />
In the above image, an oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.
Question 30 :
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 31 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6e273b230584979ad9.PNG' />
In the above fig, D is a point on hypotenuse AC of ∆ABC, such that BD ⊥AC, DM ⊥ BC and DN ⊥ AB. Which of these is correct : (i) $DM^2$ = $DN . MC$ (ii) $DN^2 = DM . AN$
Question 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba6273b2305849799e9.png' />
State True or False: In the above figure, OB is the perpendicular bisector of the line segment DE, FA is perpendicular to OB and FE intersects OB at the point C. Then we can say that $\frac{1}{OA}+\frac{1}{OB}=\frac{1}{OC}$
Question 33 :
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 34 :
For going to a city B from city A, there is a route via city C such that AC is perpendicular to CB, AC = 2 x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.
Question 35 :
Diagonals of a trapezium PQRS intersect each other at the point O, PQ is parallel to RS and PQ = 3 RS. Find the ratio of the areas of triangles POQ and ROS.
Question 36 :
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 37 :
The area of the square that can be inscribed in a circle of radius 8 cm is
Question 38 :
The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is it true or false?
Question 39 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb6273b2305849799fd.png' />
Find the area of the shaded region in the above figure , if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC$=$40^{\circ}$.
Question 40 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc2273b230584979a0d.png' />
From the above image , calculate the area of the designed region common between the two quadrants of circles of radius 8 cm each.
Question 41 :
State True / False, to construct a triangle similar to a given ∆ABC with its sides $\frac{7}{3}$ of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points $B_1 , B_2 , ...., B_7$ are located at equal distances on $BX, B_3$ is joined to C and then a line segment $B_6C'$ is drawn parallel to $B_3C$ where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC.
Question 42 : <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 43 :
Can we construct a triangle similar to a given triangle as per the given scale factor ?
Question 44 :
If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, Is it TRUE or FALSE that $AQ = \frac { 1 } { 2 } ( BC + CA + AB )$.
Question 45 :
State true or false. Division of a line segment internally in a given ratio is possible.
Question 46 :
Find the coordinates of the points of trisection of the line segment joining $\left(4, -1\right)$ and $\left(-2, -3\right)$.
Question 47 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd5273b230584979a26.JPG' />
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the above image. Niharika runs $\frac{1}{4}$ th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$ th the distance AD on the eighth line and posts a red flag. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
Question 48 :
Find the ratio in which the y-axis divides the line segment joining the points $\left(5, – 6\right)$ and $\left(–1, – 4\right)$.
Question 49 :
Find the distance between the points (0, 0) and (36, 15).
Question 50 :
Find the area of the quadrilateral whose vertices, taken in order, are $\left(– 4, – 2\right)$, $\left(– 3, – 5\right)$, $\left(3, – 2\right)$ and $\left(2, 3\right)$.
Question 51 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b35273b230584979954.jpg' />
In the above figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.
Question 52 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b39273b230584979959.jpg' />
In the above figure, if arcs are drawn with centres A, B, C and D intersects in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. Find the area of the shaded region (Use $\pi=3.14$).
Question 53 :
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding major sector.(Use $\pi$=3.14)
Question 54 :
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is it true or false?
Question 55 :
Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.
