Mark (✓) against the correct answer
Question: Mark (✓) against the correct answer Ifx48yis exactly divisible by 9, then the least value of (x+y) is (a) 4 (b) 0 (c) 6 (d) 7 Solution: (c) 6 When a number is divisible by 9, the sum of its digits is also divisible by 9. $x+4+8+y=12+(x+y)$ For $12+(x+y)$ to be divisible by 9 : $12+(x+y)=18 \Rightarrow(x+y)=6$...
Read More →A cone is cut through a plane parallel
Question: A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called (a) a frustum of a cone (b) cone (c) cylinder (d) sphere Solution:...
Read More →Mark (✓) against the correct answer
Question: Mark (✓) against the correct answer If 6x5 is exactly divisible by 9, then the least value ofxis (a) 1 (b) 4 (c) 7 (d) 0 Solution: (c) 7 When a number is divisible by 9, the sum of the digits is also divisible by 9. $6+x+5=11+x$ To be divisible by 9 : $11+x=18 \Rightarrow x=7$...
Read More →A shuttle cock used for playing badminton
Question: A shuttle cock used for playing badminton has the shape of the combination of (a) a cylinder and a sphere (b) a cylinder and a hemisphere (c) a sphere and a cone (d) frustum of a cone and a hemisphere Solution: (d) Because the shape of the shuttle cock is equal to sum of frustum of a cone and hemisphere....
Read More →Mark (✓) against the correct answer
Question: Mark (✓) against the correct answer If 7x8 is exactly divisible by 3, then the least value ofxis (a) 3 (b) 0 (c) 6 (d) 9 Solution: (b) 0 If a number is exactly divisible by 3, the sum of its digits is also divisible by 3. $7+x+8=15+x$ $15+x$ can be divisible by 3 even if $x$ is equal to 0 ....
Read More →The shape of a gilli,
Question: The shape of a gilli, in the gilli-danda game (see figure) is a combination of (a) two cylinders (b) a cone and a cylinder (c) two cones and a cylinder (d) two cylinders and a cone Solution:...
Read More →Find the values of A, B, C when
Question: Find the values ofA,B,Cwhen Solution: Now, $B \neq A=1$ and $\left(1+B^{2}\right)$ is a single digit number. $\therefore B=2$ $C=\left(1+B^{2}\right)=(1+4)=5$ $\therefore A=1, B=2$ and $C=5$...
Read More →The shape of a glass (tumbler)
Question: The shape of a glass (tumbler) (see figure) is usually in the form of (a) a cone (b) frustum of a cone (c) a cylinder (d) a sphere Solution: (b)We know that, the shape of frustum of a cone is So, the given figure is usually in the form of frustum of a cone....
Read More →Replace A, B, C by suitable numerals:
Question: Replace A, B, C by suitable numerals: Solution: Here, $A-6=6$ $\Rightarrow A=2$ (with 1 being borrowed) $B=3$ Since $7 \times 9=63, C=9$ $\therefore A=2, B=3$ and $C=9$...
Read More →A plumbline (sahul) is the
Question: A plumbline (sahul) is the combination of (see figure) (a) a cone and a cylinder (b) a hemisphere and a cone (c) frustum of a cone and a cylinder (d) sphere and cylinder Solution:...
Read More →Replace A, B, C by suitable numerals:
Question: ReplaceA,B,Cby suitable numerals: Solution: $A-8=3$ This implies that 1 is borrowed. $11-8=3$ $\Rightarrow A=1$ Then, $7-B=9$ 1 is borrowed from 7. $\therefore 16-B=9$ $\quad \Rightarrow B=7$ Further, $5-C=2$ But 1 has been borrowed from $5 .$ $\therefore 4-C=2$ $\Rightarrow C=2$ $\therefore A=1, B=7$ and $C=2$...
Read More →A surahi is the combination of
Question: A surahi is the combination of (a) a sphere and a cylinder (b) a hemisphere and a cylinder (c) two hemispheres (d) a cylinder and a cone Solution: (a)Because the shape of surahi is...
Read More →A cylindrical pencil sharpened at
Question: A cylindrical pencil sharpened at one edge is the combination of (a) a cone and a cylinder (b) frustum of a cone and a cylinder (c) a hemisphere and a cylinder (d) two cylinders Solution: (a)Because the shape of sharpened pencil is...
Read More →Which of the following numbers are divisible by 9?
Question: Which of the following numbers are divisible by 9? (i) 524618 (ii) 7345845 (iii) 8987148 Solution: A number is divisible by 9 if the sum of the digits is divisible by 9....
Read More →The sum of the digits of a 2-digit number is 6.
Question: The sum of the digits of a 2-digit number is 6. The number obtained by interchanging its digits is 18 more than the original number. Find the original number. Solution: Let the two numbers of the two-digit number be 'a' and 'b'. $a+b=6$ ....(1) The number can be written as $(10 a+b)$. After interchanging the digits, the number becomes $(10 b+a)$. $(10 a+b)+18=(10 b+a)$ $9 a-9 b=-18$ $a-b=-2$ ..(2) Adding equations (1) and (2): $2 a=4 \Rightarrow a=2$ Using $a=2$ in equation (1): $b=6-a...
Read More →Find the difference of the areas of a sector
Question: Find the difference of the areas of a sector of angle 120 and its corresponding major sector of a circle of radius 21 cm. Solution: Given that, radius of the circle (r) = 21 cm and central angle of the sector AOBA () = 120 So, area of the circle $=\pi r^{2}=\frac{22}{7} \times(21)^{2}=\frac{22}{7} \times 21 \times 21$ $=22 \times 3 \times 21=1386 \mathrm{~cm}^{2}$ Now, area of the minor sector $A O B A$ with central angle $120^{\circ}$ $=\frac{\pi r^{2}}{360^{\circ}} \times \theta=\fra...
Read More →Find all possible values of y for which the 4-digit number 64y3 is divisible by 9.
Question: Find all possible values ofyfor which the 4-digit number 64y3 is divisible by 9. Also, find the numbers. Solution: For a number to be divisible by 9, the sum of the digits must also be divisible by 9. $6+4+y+3=13+y$ For this to be divisible by 9 : $y=5$ The number will be 6453 ....
Read More →Find all possible values of x for which the 4-digit number 320x is divisible by 3.
Question: Find all possible values ofxfor which the 4-digit number 320xis divisible by 3. Also, find the numbers. Solution: If a number is divisible by 3, then the sum of the digits is also divisible by 3. $3+2+0+x=5+x$ must be divisible by 3 . This is possible in the following cases: (i) $x=1$ $\therefore 5+x=6$ Thus, the number is 3201 . (ii) $x=4$ $\therefore 5+x=9$ Thus, the number is 3204 . (iii) $x=7$ $\therefore 5+x=12$ Thus, the number is 3207 ....
Read More →Find the difference of the areas of two segments
Question: Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of 90 at the centre. Solution: Let the radius of the circle be r $\therefore$$O A=O B=r \mathrm{~cm}$ Given that, length of chord of a circle, $A B=5 \mathrm{~cm}$ and central angle of the sector $A O B A(\theta)=90^{\circ}$ Now, in $\triangle A O B$ $(A B)^{2}=(O A)^{2}+(O B)^{2}$ [by Pythagoras theorem] $(5)^{2}=r^{2}+r^{2}$ $\Rightarrow$ $2 r^{2}=25$ $\therefore$ $r=\fra...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer If the 4-digit numberx27yis exactly divisible by 9, then the least value of (x+y) is (a) 0 (b) 3 (c) 6 (d) 9 Solution: (d) 9 If a number is divisible by 9, then the sum of the digits is divisible by 9. $x+2+7+y=(x+y)+9$ For this to be divisible by 9 , the least value of $(x+y)$ is 0 . But for x+y = 0, x and y both will be zero. Since x is the first digit, it can never be 0. x + y + 9 = 18 or x + y = 9...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer If the 4-digit numberx27yis exactly divisible by 9, then the least value of (x+y) is (a) 0 (b) 3 (c) 6 (d) 9 Solution: (d) 9 If a number is divisible by 9, then the sum of the digits is divisible by 9. $x+2+7+y=(x+y)+9$ For this to be divisible by 9, the least value of(x+y)is0(x+y)is0. But for x+y = 0, x and y both will be zero. Since x is the first digit, it can never be 0. x + y + 9 = 18 or x + y = 9...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer If 1A2B5 is exactly divisible by 9, then the least value of (A+B) is (a) 0 (b) 1 (c) 2 (d) 10 Solution: (b) 1 For a number to be divisible by 9, the sum of the digits must also be divisible by 9. $1+A+2+B+5=(A+B)+8$ The number will be divisible by 9 if $(A+B)=1$....
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer Ifx4y5zis exactly divisible by 9, then the least value of (x+y+z) is (a) 3 (b) 6 (c) 9 (d) 0 Solution: (c) 9 A number is divisible by 9 if the sum of the digits is divisible by 9. $x+4+y+5+z=9+(x+y+z)$ The lowest value of $(x+y+z)$ is equal to 0 for the number x4y5z to be divisible by 9 . In this case, all x, y and z will be 0. But x is the first digit, so it cannot be 0. x+4+y+5+z = 18 or x+y+z+9 = 18 or x+y+z = 9...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer Ifx7y5 is exactly divisible by 3, then the least value of (x+y) is (a) 6 (b) 0 (c) 4 (d) 3 Solution: (d) 3 When a number is divisible by 3, the sum of the digits must also be divisible by 3. $x+7+y+5=(x+y)+12$ This sum is divisible by 3 if x+y+12 is 12 or 15. For x+y+12 = 12: x+y=0 But x+y cannot be 0 because then x and y both will have to be 0. Since x is the first digit, it cannot be 0. x+y+12 = 15 or x+y = 15-12=3...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer If 4xy7 is exactly divisible by 3, then the least value of (x+y) is (a) 1 (b) 4 (c) 5 (d) 7 Solution: (a) 1 If a number is divisible by 3, the sum of the digits is also divisible by 3. $4+x+y+7=11+(x+y)$ For the sum to be divisible by 3 : $11+(x+y)=12 \Rightarrow(x+y)=1$...
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