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If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?

Given There are 24 children, each will get 5 chocolate Find out We have to find the number of chocolates ... View Article

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig.) . Show that (i) ΔABE ΔACF (ii) AB = AC, i.e., ABC is an isosceles triangle.

Solution Given Altitudes BE and CF to sides AC and AB are equal To Prove (i) ΔABE ≅ ΔACF (ii)... View Article

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠ POA is equal to (A) 50° (B) 60° (C) 70° (D) 80°

option (A) 50° From quadrilateral OAPB, OA is perpendicular to PA and OB is perpendicular to PB i.e. OA ⊥ PA... View Article

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (i) 2x²– 3x + 5 = 0 (ii) 3x² – 4√3x + 4 = 0 (iii) 2x² – 6x + 3 = 0

(i) 2x2 – 3x + 5 = 0 On comparing the equation with ax2 + bx + c = 0, we get a = 2, b = -3 and c = 5 We... View Article

A godown measures 40 m×25m×15 m. Find the maximum number of wooden crates each measuring 1.5m×1.25 m×0.5 m that can be stored in the godown.

Given Length of the godown, l = 40 m The breadth of the godown,b= 25m Height of godown, h = 15 m Length... View Article

The radii of two circles are 8 cm and 6 cm, respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Given The radii of the two circles are 8 cm and 6 cm Find out We have to find out... View Article

The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

Solution Let the number of boys be ‘7n’ and girls be ‘5n’. According to the given details the equation becomes... View Article

Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

Given equations 5x – y = 5—(i) 3x – y = 3—(ii) From equation (i) y = 5x – 5... View Article

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Given, The following observations have been arranged in ascending order. If the median of the data is 63, 29, 32,... View Article

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is (A) 2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4

The answer is (C) ΔABC and ΔBDE are two equilateral triangle. D is the midpoint of BC. BD = DC... View Article

A random survey of the number of children of various age groups playing in a park was found as follows: Draw a histogram to represent the data above.

Solution The width of the class intervals in the given data is varying in nature. Also, The area of a... View Article

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

Solution Given Perimeter of rectangular swimming pool = 154 m Find out We hBve to determine the length and the... View Article

A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

each side of cube is 7 cm. So, the radius = 7/2 cm. Surface area of solid=T.S.A of cube-Area of circle+... View Article

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 (i) red? (ii) not red?

Given that A bag contains 3 red balls and 5 black balls. Find out The probability that the ball is... View Article

The circumference of the base of cylindrical vessel is 132cm and its height is 25cm. How many litres of water can it hold? (1000 cm3 = 1L) (Assume π = 22/7)

Given Circumference of the base of cylindrical vessel = 132 cm Height of vessel, h = 25 cm Find out... View Article

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig.) . If ∠AOB = 30°, find the area of the shaded region.

Solution Radius of the larger circle, R = 21 cm Radius of the smaller circle, r = 7 cm Angle... View Article

Find the roots of the following quadratic equations by factorisation: (i) x² – 3x – 10 = 0 (ii) 2x² + x – 6 = 0 (iii) √2 x² + 7x + 5√2 = 0 (iv) 2x² – x + 1/8 = 0 (v) 100x² – 20x + 1 = 0

(i) x2 – 3x – 10 =0 On solving LHS we get, =>x2 – 5x + 2x – 10 =>x(x – 5) + 2(x – 5) =>(x – 5)(x + 2)... View Article

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Solution Given AB = CD i.e. two equal chords. To Prove AB = CD Proof From ΔAOB and ΔCOD, OA... View Article

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Let us say that the diameter of the earth is “d”. Hence, the radius of the earth will be d/2 The... View Article

Suppose you drop a die at random on the rectangular region shown in Fig. What is the probability that it will land inside the circle with diameter 1m?

At first, calculate the area of the rectangle and the area of the circle. Here, the area of the rectangle... View Article

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