In a right circular cone, the cross-section made by a plane parallel to the base is a
Question: In a right circular cone, the cross-section made by a plane parallel to the base is a(a) sphere(b) hemisphere(c) circle(d) a semicircle Solution: (c) circleIn a right circular cone, the cross-section made by a plane parallel to the base is acircle....
Read More →During conversion of a solid from one shape to another, the volume of the new shape will
Question: During conversion of a solid from one shape to another, the volume of the new shape will(a) decrease(b) increase(c) remain unaltered(d) be doubled Solution: (c) remain unalteredDuring conversion of a solid from one shape to another, the volume of the new shape willremain unaltered....
Read More →A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left is called
Question: A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left is called (a) a cone(b) a sphere(c) a cylinder(d) frustum of a cone Solution: (d) frustum of a coneA cone is cut by a plane parallel to its base and the upper part is removed. The part that is left is calledfrustum of a cone....
Read More →If A be a square matrix such that
Question: If $A$ be a square matrix such that $|a d j A|=|A|^{2}$, then the order of $A$ is____________ Solution: Given: $A$ is a square matrix $|\operatorname{adj} A|=|A|^{2}$ As we know, $|\operatorname{adj} A|=|A|^{n-1}$, where $n$ is the order of $A$ $\Rightarrow|A|^{2}=|A|^{n-1}$ $\Rightarrow 2=n-1$ $\Rightarrow n=3$ Hence, the order of $A$ is $\underline{3}$....
Read More →A plumbline (sahul) is a combination of
Question: Aplumbline (sahul)is a combination of (a) a hemisphere and a cone(b) a cylinder and a cone(c) a cylinder and frustum of a cone(d) a cylinder and a sphere Solution: (a) a hemisphere and a coneA plumbline (sahul) is a combination ofa hemisphere and a cone....
Read More →A plumbline (sahul) is a combination of
Question: Aplumbline (sahul)is a combination of (a) a hemisphere and a cone(b) a cylinder and a cone(c) a cylinder and frustum of a cone(d) a cylinder and a sphere Solution: (a) a hemisphere and a coneA plumbline (sahul) is a combination ofa hemisphere and a cone....
Read More →If one of the zeroes of the cubic
Question: If one of the zeroes of the cubic polynomial ax3+ bx2+ cx + d is zero, the product of then other two zeroes is (a) $\frac{-c}{a}$ (b) $\frac{c}{a}$ (c) 0 (d) $\frac{-b}{a}$ Solution: (b) Let p(x) =ax3+ bx2+ cx + d Given that, one of the zeroes of the cubic polynomial p(x) is zero. Let , and are the zeroes of cubic polynomial p(x), where a = 0. We know that, Sum of product of two zeroes at a time $=\frac{C}{a}$ $\Rightarrow \quad \alpha \beta+\beta \gamma+\gamma \alpha=\frac{c}{a}$ $\Ri...
Read More →A certain sum amounts to Rs 5832 in 2 years at 8% compounded interest.
Question: A certain sum amounts to Rs 5832 in 2 years at 8% compounded interest. Find the sum. Solution: Let the sum be P. Thus, we have : $\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$ $5,832=\mathrm{P}\left(1+\frac{8}{100}\right)^{2}$ $5,832=1.1664 \mathrm{P}$ $\mathrm{P}=\frac{5,832}{1.1664}$ = 5,000 Thus, the required sum is Rs 5,000 ....
Read More →The shape of the gilli used in a gilli-danda game is a combination of
Question: The shape of thegilliused in agilli-dandagame is a combination of (a) a cone and a cylinder(b) two cylinders(c) two cones and a cylinder(d) two cylinders and a cone Solution: (c) two cones and a cylinderThe shape of the gilli used in a gilli-dandagame is a combination oftwo cones and a cylinder....
Read More →Find the rate at which a sum of money will become four times the original amount in 2 years,
Question: Find the rate at which a sum of money will become four times the original amount in 2 years, if the interest is compounded half-yearly. Solution: Let the rate percent per annum be $\mathrm{R}$. Then, $\mathrm{A}=\mathrm{P}(1+\mathrm{R})^{2 \mathrm{n}}$ $4 \mathrm{P}=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{4}$ $\left(1+\frac{\mathrm{R}}{200}\right)^{4}=4$ $\left(1+\frac{\mathrm{R}}{200}\right)=1.4142$ $\frac{\mathrm{R}}{200}=0.4142$ $\mathrm{R}=82.84$ Thus, the required rate is...
Read More →The number of polynomials having zeroes as -2 and 5 is
Question: The number of polynomials having zeroes as -2 and 5 is (a) 1 (b) 2 (c) 3 (d) more than 3 Solution: (d) Let p (x) = ax2+ bx + c be the required polynomial whose zeroes are -2 and 5. $\therefore \quad$ Sum of zeroes $=\frac{-b}{a}$ $\Rightarrow$$\frac{-b}{a}=-2+5=\frac{3}{1}=\frac{-(-3)}{1}$...(i) and product of zeroes $=\frac{c}{a}$ $\Rightarrow \quad \frac{c}{a}=-2 \times 5=\frac{-10}{1}$ .....(ii) From Eqs. (i) and (ii), $a=1, b=-3$ and $c=-10$ $\therefore$ $p(x)=a x^{2}+b x+c=1 \cdot...
Read More →The shape of a glass (tumbler) is usually in the form of
Question: The shape of aglass (tumbler)is usually in the form of (a) a cylinder(b) frustum of a cone(c) a cone(d) a sphere Solution: (b) frustum of a coneThe shape of a glass (tumbler) is usually in the form offrustum of a cone....
Read More →Find the rate at which a sum of money will double itself in 3 years,
Question: Find the rate at which a sum of money will double itself in 3 years, if the interest is compounded annually. Solution: Let the rate percent per annum be $R$. Then, $\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$ $2 \mathrm{P}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{3}$ $\left(1+\frac{\mathrm{R}}{100}\right)^{3}=2$ $\left(1+\frac{\mathrm{R}}{100}\right)=1.2599$ $\frac{\mathrm{R}}{100}=0.2599$ $\mathrm{R}=25.99$ Thus, the required rate is $25.99 \%$ per...
Read More →A surahi is a combination of
Question: Asurahiis a combination of (a) a sphere and a cylinder(b) a hemisphere and a cylinder(c) a cylinder and a cone(d) two hemispheres Solution: (a) a sphere and a cylinderA surahi is a combination ofa sphere and a cylinder....
Read More →Find the rate percent per annum,
Question: Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in an year and a half, interest being compounded six monthly. Solution: Let the rate percent per annum be $\mathrm{R}$. Because interest is compounded every six months, n will be 3 for $1.5$ years. Now, $\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{\mathrm{n}}$ $2,315.25=2,000\left(1+\frac{\mathrm{R}}{200}\right)^{3}$ $\left(1+\frac{\mathrm{R}}{200}\right)^{3}=\frac{2,315.25}{2,000}$ $\left(1+\frac{\mathrm{...
Read More →If the zeroes of the quadratic polynomial
Question: If the zeroes of the quadratic polynomial xz+ (a +1)* + b are 2 and -3, then (a) a = -7, b = -1 (b) a = 5,b = -1 (c) a=2, b = -6 (d)a=0,b = -6 Solution: (d) Let $p\{x)=x^{2}+(a+1) x+b$ Given that, 2 and $-3$ are the zeroes of the quadratic polynomial $p(x)$. $\therefore \quad p(2)=0$ and $p(-3)=0$ $\Rightarrow \quad 2^{2}+(a+1)(2)+b=0$ $\Rightarrow \quad 4+2 a+2+b=0$ $\Rightarrow \quad 2 a+b=-6 \quad \ldots$ (i) and $\quad(-3)^{2}+(a+1)(-3)+b=0$ $\Rightarrow \quad 9-3 a-3+b=0$ $\Righta...
Read More →Kamala borrowed from Ratan a certain sum at a certain rate for two years simple interest.
Question: Kamala borrowed from Ratan a certain sum at a certain rate for two years simple interest. She lent this sum at the same rate to Hari for two years compound interest. At the end of two years she received Rs 210 as compound interest, but paid Rs 200 only as simple interest. Find the sum and the rate of interest. Solution: Let the sum be Rs P and the rate of interest be R\%. We know that Kamla paid Rs 200 as simple interest. $\therefore 200=\frac{\operatorname{PR}(2)}{100}$ $\mathrm{PR}=1...
Read More →A funnel is a combination of
Question: Afunnelis a combination of (a) a cylinder and a cone(b) a cylinder and a hemisphere(c) a cylinder and frustum of a cone(d) a cone and hemisphere Solution: (c) a cylinder and frustum of a coneA funnel is a combination of a cylinder and frustum of a cone....
Read More →A shuttlecock used for playing badminton is a combination of
Question: Ashuttlecockused for playing badminton is a combination of (a) cylinder and a hemisphere(b) frustum of a cone and a hemisphere(c) a cone and a hemisphere(d) a cylinder and a sphere Solution: (b) frustum of a cone and a hemisphereA shuttlecock used for playing badminton is a combination offrustum of a cone and a hemisphere....
Read More →A cylindrical pencil sharpened at one end is a combination of
Question: Acylindrical pencilsharpened at one end is a combination of(a) a cylinder and a cone(b) a cylinder and frustum of a cone(c) a cylinder and a hemisphere(d) two cylinders Solution: (a) a cylinder and a coneA cylindrical pencil sharpened at one end is a combination ofa cylinder and a cone....
Read More →Find the rate percent per annum if Rs 2000 amount to Rs 2662 in
Question: Find the rate percent per annum if Rs 2000 amount to Rs 2662 in $1 \frac{1}{2}$ years, interest being compounded half-yearly? Solution: Let the rate of interest be $\mathrm{R} \%$. Then, $\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$ $2,662=2,000\left(1+\frac{\mathrm{R}}{100}\right)^{3}$ $\left(1+\frac{\mathrm{R}}{100}\right)^{3}=\frac{2,662}{2,000}$ $\left(1+\frac{\mathrm{R}}{100}\right)^{3}=1.331$ $\left(1+\frac{\mathrm{R}}{100}\right)^{3}=(1.1)^{3}$ $\left...
Read More →A quadratic polynomial,
Question: A quadratic polynomial, whose zeroes are -3 and 4, is (a) $x^{2}-x+12$ (b) $x^{2}+x+12$ (c) $\frac{x^{2}}{2}-\frac{x}{2}-6$ (d) $2 x^{2}+2 x-24$ Solution: (c) Let $a x^{2}+b x+c$ be a required polynomial whose zeroes are $-3$ and 4 . Then, sum of zeroes $=-3+4=1$ $\left[\because\right.$ sum of zeroes $\left.=\frac{-b}{a}\right]$ $\Rightarrow$ $\frac{-b}{a}=\frac{1}{1} \Rightarrow \frac{-b}{a}=-\frac{(-1)}{1}$ ... (i) and product of zeroes $=-3 \times 4=-12$ $\left[\because\right.$ prod...
Read More →A cylindrical vessel with internal diameter 10 cm and height 10.5 cm
Question: A cylindrical vessel with internal diameter 10 cm and height 10.5 cm isfull of water. A solid cone of base diameter 7 cm and height 6 cm iscompletely immersed in water. Find the volume of water(i) displacedout of the cylinder(ii) left in the cylinder. Solution: We have, Internal radius of the cylindrical vessel, $R=\frac{10}{2}=5 \mathrm{~cm}$, Height of the cylindrical vessel, $H=10.5 \mathrm{~cm}$, Radius of the solid cone, $r=\frac{7}{2}=3.5 \mathrm{~cm}$ and Height of the solid con...
Read More →If A and B are two square matrices of the same order
Question: If $A$ and $B$ are two square matrices of the same order such that $B=-A^{-1} B A$, then $(A+B)^{2}=$ Solution: Given: $B=-A^{-1} B A$ $\Rightarrow A B=-A A^{-1} B A$ $\Rightarrow A B=-I B A$ $\Rightarrow A B=-B A$ Now, $(A+B)^{2}=A^{2}+A B+B A+B^{2}$ $=A^{2}-B A+B A+B^{2} \quad(\because A B=-B A)$ $=A^{2}+B^{2}$ Hence, $(A+B)^{2}=\underline{A}^{2}+B^{2}$....
Read More →At what rate percent compound interest per annum will Rs 640
Question: At what rate percent compound interest per annum will Rs 640 amount to Rs 774.40 in 2 years? Solution: Let the rate of interest be $\mathrm{R} \%$. Then, $\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$ $774.40=640\left(1+\frac{\mathrm{R}}{100}\right)^{2}$ $\left(1+\frac{\mathrm{R}}{100}\right)^{2}=\frac{774.40}{640}$ $\left(1+\frac{\mathrm{R}}{100}\right)^{2}=1.21$ $\left(1+\frac{\mathrm{R}}{100}\right)^{2}=(1.1)^{2}$ $\left(1+\frac{\mathrm{R}}{100}\right)=1.1...
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