Any point on the X-axis is of the form
Question: Any point on the X-axis is of the form (a)(x, y) (b)(0, y) (c)(x, 0) (d)(x, x) Solution: (c)Every point on the X-axis has its y-coordinate equal to zero. i.e., y=0 Hence, the general form of every point on X-axis is (x, 0)....
Read More →The graph of the linear equation
Question: The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point (a)(2,0) (b)(0, 3) (c)(3,0) (d)(0, 2) Solution: (d)Since, the graph of linear equation 2x + 3y = 6 cuts the Y-axis. So, we put x = 0 in the given equation 2x+ 3y = 6, we get 2 x 0+ 3y = 6 = 3y = 6 y=2. Hence, at the point (0, 2), the given linear equation cuts the Y-axis....
Read More →Evaluate each of the following when x = 2, y = −1.
Question: Evaluate each of the following when x = 2, y = 1. $(2 x y) \times\left(\frac{x^{2} y}{4}\right) \times\left(x^{2}\right) \times\left(y^{2}\right)$ Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $(2 x y) \times\left(\frac{x^{2} y}{4}\right) \times\left(x^{2}\right) \times\left(y^{2}\right)$ $=\left(2 \times \frac{1}{4}\right) \times\left(x \times x^{2} \times x^{2}\right) \...
Read More →Any solution of the linear equation
Question: Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form (a) $\left(-\frac{9}{2}, m\right)$. (b) $\left(n,-\frac{9}{2}\right)$ (c) $\left(0,-\frac{9}{2}\right)$ (d) $(-9,0)$ Solution: (a)The given linear equation is 2x + 0y + 9 = 0 = 2x + 9 = 0 = 2x = -9 =x= -9/2 and y can be any real number.Hence, (-9/2 , m) is the required form of solution of the given linear equation....
Read More →Choose the correct answer of the following question:
Question: Choose the correct answer of the following question: In the given figure, a tower $A B$ is $20 \mathrm{~m}$ high and $B C$, its shadow on the ground is $20 \sqrt{3} \mathrm{~m}$ long. The sun's altitude is (a) 30 (b) 45 (c) 60 (d) none of these Solution: Let the sun's altitude beWe have, $\mathrm{AB}=20 \mathrm{~m}$ and $\mathrm{BC}=20 \sqrt{3} \mathrm{~m}$ In $\Delta \mathrm{ABC}$, $\tan \theta=\frac{\mathrm{AB}}{\mathrm{BC}}$ $\Rightarrow \tan \theta=\frac{20}{20 \sqrt{3}}$ $\Rightar...
Read More →If (2, 0) is a solution of the linear equation 2x + 3y = k,
Question: If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is (a)4 (b)6 (c)5 (d)2 Solution: (a)Since, (2, 0) is a solution of the given linear equation 2x + 3y = k, then put x =2 and y= 0 in the equation.= 2 (2) + 3 (0) = k = k = 4Hence, the value of k is 4....
Read More →Express each of the following product as a monomials and verify the result for x = 1, y = 2:
Question: Express each of the following product as a monomials and verify the result for x = 1, y = 2: $\left(\frac{4}{9} a b c^{3}\right) \times\left(-\frac{27}{5} a^{3} b^{2}\right) \times\left(-8 b^{3} c\right)$ Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $\left(\frac{4}{9} a b c^{3}\right) \times\left(-\frac{27}{5} a^{3} b^{2}\right) \times\left(-8 b^{3} c\right)$ $=\left\{\l...
Read More →The equation 2x+ 5y = 7 has a unique solution,
Question: The equation 2x+ 5y = 7 has a unique solution, if x and y are (a)natural numbers (b)positive real numbers (c)real numbers (d)rational numbers Solution: (a)In natural numbers, there is only one pair i.e., (1, 1) which satisfy the given equation but in positive real numbers, real numbers and rational numbers there are many pairs to satisfy the given linear equation....
Read More →The linear equation 2 x-5 y=7 has
Question: The linear equation $2 x-5 y=7$ has (a) a unique solution (b) two solutions (c) infinitely many solutions (d) no solution Solution: (c)In the given equation 2x 5y = 7, for every value of x, we get a corresponding value of y and vice-versa. Therefore, the linear equation has infinitely many solutions....
Read More →Choose the correct answer of the following question
Question: Choose the correct answer of the following question A pole casts a shadow of length $2 \sqrt{3} \mathrm{~m}$ on the ground when the sun's elevation is $60^{\circ}$. The height of the pole is (a) $4 \sqrt{3} \mathrm{~m}$ (b) $6 \mathrm{~m}$ (c) $12 \mathrm{~m}$ (d) $3 \mathrm{~m}$ Solution: Let AB be the pole and BC be its shadow.We have, $\mathrm{BC}=2 \sqrt{3} \mathrm{~m}$ and $\angle \mathrm{ACB}=60^{\circ}$ In $\Delta \mathrm{ABC}$ $\tan 60^{\circ}=\frac{\mathrm{AB}}{\mathrm{BC}}$ $...
Read More →Express each of the following product as a monomials and verify the result for x = 1, y = 2:
Question: Express each of the following product as a monomials and verify the result for x = 1, y = 2: $\left(-\frac{4}{7} a^{2} b\right) \times\left(-\frac{2}{3} b^{2} c\right) \times\left(-\frac{7}{6} c^{2} a\right)$ Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $\left(-\frac{4}{7} a^{2} b\right) \times\left(-\frac{2}{3} b^{2} c\right) \times\left(-\frac{7}{6} c^{2} a\right)$ $=\...
Read More →Express each of the following product as a monomials and verify the result for x = 1, y = 2:
Question: Express each of the following product as a monomials and verify the result for x = 1, y = 2: $\left(\frac{2}{5} a^{2} b\right) \times\left(-15 b^{2} a c\right) \times\left(-\frac{1}{2} c^{2}\right)$ Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $\left(\frac{2}{5} a^{2} b\right) \times\left(-15 b^{2} a c\right) \times\left(-\frac{1}{2} c^{2}\right)$ $=\left\{\frac{2}{5} \t...
Read More →Choose the correct answer of the following question:
Question: Choose the correct answer of the following question: The lengths of a vertical rod and its shadow are in the ratio $1: \sqrt{3}$. The angle of elevation of the sun is (a) 30 (b) 45 (c) 60 (d) 90 Solution: Let AB be the rod and BC be its shadow; and be the angle of elevation of the sun. We have, $\mathrm{AB}: \mathrm{BC}=1: \sqrt{3}$ Let $\mathrm{AB}=x$ Then, $\mathrm{BC}=x \sqrt{3}$ In $\triangle \mathrm{ABC}$, $\tan \theta=\frac{\mathrm{AB}}{\mathrm{BC}}$ $\Rightarrow \tan \theta=\fra...
Read More →Express each of the following product as a monomials and verify the result for x = 1, y = 2:
Question: Express each of the following product as a monomials and verify the result for x = 1, y = 2: $\left(\frac{1}{8} x^{2} y^{4}\right) \times\left(\frac{1}{4} x^{4} y^{2}\right) \times(x y) \times 5$ Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $\left(\frac{1}{8} x^{2} y^{4}\right) \times\left(\frac{1}{4} x^{4} y^{2}\right) \times(x y) \times 5$ $=\left(\frac{1}{8} \times \f...
Read More →Choose the correct answer of the following question:
Question: Choose the correct answer of the following question:The length of the shadow of a tower standing on level ground is foundto be 2xmetres longer when the sun's elevation is 30 than when it was45. The height of the tower is (a) $(2 \sqrt{3} x) \mathrm{m}$ (b) $(3 \sqrt{2} x) \mathrm{m}$ (c) $(\sqrt{3}-1) x \mathrm{~m}$ (d) $(\sqrt{3}+1) x \mathrm{~m}$ Solution: Let CD =hbe the height of the tower.We have, $\mathrm{AB}=2 x, \angle \mathrm{DAC}=30^{\circ}$ and $\angle \mathrm{DBC}=45^{\circ...
Read More →Express each of the following product as a monomials and verify the result for x = 1, y = 2:
Question: Express each of the following product as a monomials and verify the result for x = 1, y = 2:(xy3)(yx3) (xy) Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $\left(-x y^{3}\right) \times\left(y x^{3}\right) \times(x y)$ $=(-1) \times\left(x \times x^{3} \times x\right) \times\left(y^{3} \times y \times y\right)$ $=(-1) \times\left(x^{1+3+1}\right) \times\left(y^{3+1+1}\right...
Read More →Evaluate
Question: Evaluate (8x2y6) (20xy) forx= 2.5 andy= 1. Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $\left(-8 x^{2} y^{6}\right) \times(-20 x y)$ $=\{(-8) \times(-20)\} \times\left(x^{2} \times x\right) \times\left(y^{6} \times y\right)$ $=\{(-8) \times(-20)\} \times\left(x^{2+1}\right) \times\left(y^{6+1}\right)$ $=160 x^{3} y^{7}$ $\therefore\left(-8 x^{2} y^{6}\right) \times(-20 ...
Read More →Choose the correct answer of the following question:
Question: Choose the correct answer of the following question:If a l.5-m-tall girl stands at a distance of 3 m from a lamp post and casts ashadow of length 4.5 m on the ground, then the height of the lamp post is(a) 1.5 m (b) 2 m (c) 2.5 m (d) 2.8 m Solution: Let AB be the lamp post; CD be the girl and DE be her shadow.We have, $\mathrm{CD}=1.5 \mathrm{~m}, \mathrm{AD}=3 \mathrm{~m}, \mathrm{DE}=4.5 \mathrm{~m}$ Let $\angle \mathrm{E}=\theta$ In $\Delta \mathrm{CDE}$, $\tan \theta=\frac{\mathrm{...
Read More →Evaluate
Question: Evaluate (2.3a5b2) (1.2a2b2) whena= 1 andb= 0.5. Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $\left(2.3 a^{5} b^{2}\right) \times\left(1.2 a^{2} b^{2}\right)$ $=(2.3 \times 1.2) \times\left(a^{5} \times a^{2}\right) \times\left(b^{2} \times b^{2}\right)$ $=(2.3 \times 1.2) \times\left(a^{5+2}\right) \times\left(b^{2+2}\right)$ $=2.76 a^{7} b^{4}$ $\therefore\left(2.3 a^...
Read More →Plot the points A (1, – 1) and B (4, 5).
Question: Plot the points A (1, 1) and B (4, 5). (i)Draw the line segment joining these points. Write the coordinates of a point on this line segment between the points A and B. (ii)Extend this line segment and write the coordinates of a point on this line which lies outside the line segment AB. Solution: In point A(1, -1), x-coordinate is positive and y-coordinate is negative, so it lies in IV quadrant. In point B(4, 5), both coordinates are positive, so it lies in I quadrant. On plotting these...
Read More →Find the value of
Question: Find the value of (5x6) (1.5x2y3) (12xy2) whenx= 1,y= 0.5. Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $\left(5 x^{6}\right) \times\left(-1.5 x^{2} y^{3}\right) \times\left(-12 x y^{2}\right)$ $=\{5 \times(-1.5) \times(-12)\} \times\left(x^{6} \times x^{2} \times x\right) \times\left(y^{3} \times y^{2}\right)$ $=\{5 \times(-1.5) \times(-12)\} \times\left(x^{6+2+1}\right...
Read More →Choose the correct answer of the following question:
Question: Choose the correct answer of the following question:From the top of a cliff 20 m high, the angle of elevation of the top of atower is found to be equal to the angle of depression of the foot of thetower. The height of the tower is(a) 20 m (b) 40 m (c) 60 m (d) 80 m Solution: Let AB be the cliff and CD be the tower.We have, $\mathrm{AB}=20 \mathrm{~m}$ Also, $\mathrm{CE}=\mathrm{AB}=20 \mathrm{~m}$ Let $\angle \mathrm{ACB}=\angle \mathrm{CAE}=\angle \mathrm{DAE}=\theta$ In $\Delta \math...
Read More →From the given figure, answer the following questions
Question: From the given figure, answer the following questions (i)Write the points whose abscissa is 0. (ii)Write the points whose ordinate is 0. (iii)Write the points whose abscissa is 5, Solution: (i)We know that, the point whose abscissa is 0 will lie on Y-axis. So, the required points whose abscissa is 0 are A, L and O. (ii)We know that, the point whose ordinate is 0 will lie on X-axis. So, the required points, whose ordinate is 0 are G,l and O. (iii)Here, abscissa -5 is negative, which sho...
Read More →Write down the product of −
Question: Write down the product of 8x2y6and 20xy. Verify the product forx= 2.5,y= 1. Solution: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$. We have: $\left(-8 x^{2} y^{6}\right) \times(-20 x y)$ $=\{(-8) \times(-20)\} \times\left(x^{2} \times x\right) \times\left(y^{6} \times y\right)$ $=\{(-8) \times(-20)\} \times\left(x^{2+1}\right) \times\left(y^{6+1}\right)$ $=-160 x^{3} y^{7}$ $\therefore\left...
Read More →Plot the points P(1, 0), Q(4, 0) and 5(1, 3).
Question: Plot the points P(1, 0), Q(4, 0) and 5(1, 3). Find the coordinates of the point R such that PQRS is a square. Solution: In point P( 1, 0), y-coordinate is zero, so it lies on X-axis. In point Q(4, 0), y-coordinate is zero so it lies on X-axis. In point S (1, 3), both coordinates are positive, so it lies in I quadrant. On plotting these points, we get the following graph. Now, take a point R on the graph such that PQRS is a square. Then, all sides will be equal i.e., PQ = QR= RS = PS. S...
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