The following is the Solved Question Paper of 1st Preparatory for SSLC Students of Dharwad.
MATH1001-QPS01
Solution
1st Preparatory Math Question Paper - 01 Solution
- Dharwad District
- Choose the correct Answer: [8×1=8]
- Common difference of A.P. -5, -1, 3, 7,... is __________.
- -4
- 4
- 2
- 3
- If pair of linear equations in two variable X & Y a1x+b1y+c1=0 & a2x+b2y+c2=0 are intersecting lines, then, __________.
- $\frac{a_1}{a_2}=\frac{b_1}{b_2}$
- $\frac{a_1}{a_2}\neq\frac{b_1}{b_2}$
- $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
- $\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}$
- The co-ordinates of the origin are, __________.
- (1, 1)
- (2, 2)
- (3,3)
- (0, 0)
- The number of zeroes in the following figure are, __________.
- 4
- 2
- 3
- 5
- Discriminant of $ax^2+bx+c=0$ is __________.
- $b^2+4a$
- $b^2-4a$
- $-\frac{b}{a}$
- $b^2-4ac$
- If $sin A = \frac{3}{5}$ then the value of $cos A$ is __________.
- $\frac{4}{5}$
- $\frac{3}{4}$
- $\frac{4}{3}$
- $\frac{5}{4}$
- If the probability of an event is p(E) then the value of p(Ē) is __________.
- p(Ē)=1+p(E)
- p(Ē)=1-p(E)
- p(Ē)=1×p(E)
- p(Ē)=1/p(E)
- The Total Surface Area of the cylinder is __________.
- $\pi r l$
- $2\pi r h $
- $ 2\pi r(r+h)$
- $ 2\pi r(r+l)$
Solution:
$$\begin{align} d=a_2-a_1&=a_3-a_2\\ (-1)-(-5)&=(3)-(-1)\\ -1+5&=3+1\\ 4&=4\\ \therefore d&=4\\ \end{align} $$Answer: B)
Solution:
We know that, for intersecting lines,Answer: B)
$\frac{a_1}{a_2}\neq\frac{b_1}{b_2}$
Solution:
We know that, co-ordinates of origin on a Cartesian co-ordinate system is (0, 0).Answer: D)
Solution:
Zeroes are the points at which a given curve crosses the x-axis.Answer: C)
In the given figure the curve crosses x-axis at 3 distinct points.
∴Zeroes = 3
Solution:
We know that,Answer: D)
Discriminant=Δ$=b^2-4ac$
Solution:
We know that,Answer: A)
$$ \begin{align} sin A &= \frac{Opp.Side}{Hypotenuse}\\ sin A &= \frac{3}{5}\\ \end{align}\\ \therefore \text{Opposite Side=3 &}\\ \text{Hypotenuse=5}\\ $$ By Pythagorean Triplets we know that the Adjacent side should be 4.
$$ (Hypotenuse)^2=(Opp.Side)^2+(Adj.Side)^2\\ \begin{align} (Hypotenuse)^2-(Opp.Side)^2&=(Adj.Side)^2\\ 5^2-3^2&=(Adj.Side)^2\\ \sqrt{25-9}&=Adj.Side\\ \sqrt{16}&=Adj.Side\\ \therefore 4&=Adj.Side\\\\ \end{align}$$ Hence, $$ \begin{align} cos A &= \frac{Adj.Side}{Hypotenuse}\\ cos A &= \frac{4}{5}\\ \end{align} $$
Solution:
We know that,Answer: B)
p(E)+p(Ē)=1
∴p(Ē)=1-p(E)
Solution:
We know that,Answer: C)
$$\begin{align} TSA(Cylinder)&=CSA(Cylinder)+2\times Area(CircularBase)\\ TSA(Cylinder)&=2\pi r h + 2\times (\pi r^2)\\ TSA(Cylinder)&=2\pi r \times(h+r)\\ \therefore TSA(Cylinder)&=2\pi r \times(r+h)\\ \end{align}$$
- Common difference of A.P. -5, -1, 3, 7,... is __________.
- Very Short Answers: [6×1=6]
- If 'a' is the first term & 'd' is the common difference of an AP, then the nth term is __________.
- If x+y=14 & x-y=4, then the value of x is __________.
- A tangent to a circle intersects it in __________ points.
- Area of the sector of angle θ is __________.
- The product of zeroes of (x2-3) is __________.
- If r1 & r2 are the radii of frustum of a cone of height 'h' then its slant height l=__________.
Solution:
We know that,Answer: $a_n=a+(n-1)d$
$$a_n=a+(n-1)d$$
Solution:
Solving Eqn (1) & Eqn (2), we get,Answer: x=9
$$\begin{matrix} x&+&y&=&14\\ x&-&y&=&4\\ \hline 2x & & &=&18\\ \end{matrix}$$ Therefore, $$\begin{align} 2x&=18\\ \require{cancel}x=\frac{\cancelto{9}{18} }{\cancel2}\\ x&=9\\ \end{align}$$
Solution:
We know that,Answer: one point
Tangent is a line segment which touches a circle at one and one point only.
Hence tangent intersects a circle at one point.
Solution:
We know that,Answer: $\frac{\theta}{360}\times\pi r^2$
$$Area(Sector)&=\frac{\theta}{360}\times\pi r^2\\$$
Solution:
We know that,Answer: -3
Product of zeroes = αβ = $\frac{c}{a}$
Our equation is $x^2-3$, where a=1 & c=-3
Hence, Product of zeroes = $\frac{-3}{1}$ =-3
- Answer the following questions: [16×2=32]
- In the adjoining figure ΔABC & ΔAMP are two right triangles, right angled at B & M respectively;
Prove that $\frac{CA}{PA}=\frac{BC}{MP}$ - A ladder 10m long reaches a window 8m above the ground. Find the distance of the foot of the ladder from the base of the wall.
- The difference between two numbers is 26 and one number is three times the other; Find them.
- Find the area of the shaded region in the figure given below. If ABCD is a square of side 14cm and APD & BPD are semicircles.
- Draw a circle of radius 4cm from a point 8cm away from its center, construct the pair of tangents to the circle.
- Find the distance between the pairs of points (2, 3) & (4, 1).
- Find the ratio in which the line segment joining the points (-3,10) & (6,-8) is divided by (-1,6).
- Use Euclid's division algorithm to find the HCF of 135 & 225.
- Show that $5-\sqrt{3}$ is irrational.
- Divide the polynomial p(x) by the polynomial g(x) and find the quotient, remainder when $p(x)=x^3-3x^2+5x-3$ and $g(x)=x^2-2$.
- Find the zeroes of $x^2-2$. If $p(x)=3x^3-5x^2-11x-3, find p(-1)$.
- Find the roots of the quadratic equation $3x^2-5x+2=0$ using the quadratic formula.
- If cotθ=7/8 then find the value of $\frac{(1+sin\theta)(1-sin\theta)}{(1+cos\theta)(1-cos\theta)}$
- Find the value of $[sin 60^\circ . cos 30^\circ + sin 30^\circ . cos 60^\circ ]$.
- A die is thrown once, find the probability of getting a prime number.
- A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of the same radius, the total height of the toy is 15.5cm. Find the total surface area of the toy.
- In the adjoining figure ΔABC & ΔAMP are two right triangles, right angled at B & M respectively;
- Answer the following: [6×3=18]
- Prove that the lengths of tangents drawn from an external point to a circle are equal.
OR
Two tangents TP & TQ are drawn to a circle with center 'O' from an external point 'T'; prove that the ∠PTQ=∠OPQ - Construct a triangle similar to the given triangle ABC with its sides equal to 5/3 of the corresponding sides of the triangle ABC whose lengths are 5cm, 6cm & 7cm.
- The difference of the squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Find the roots of the equation $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}$. - Draw the less than type ogive curve for the given data.
C.I f 38-40 3 40-42 5 42-44 9 44-46 14 46-48 28 48-50 32 50-52 35 - Determine the mode of the following data.
C.I f 0-20 10 20-40 35 40-60 52 60-80 61 80-100 38 100-120 29
OR
Determine the median of the following data.CI f 0-10 7 10-20 14 20-30 13 30-40 12 40-50 20 50-60 11 60-70 15 70-80 8
- A drinking glass is in the shape of a frustum of a cone of height 14cm. The diameters of its two circular ends are 4cm & 2cm; Find the capacity of the glass.
OR
A cone of height 24cm and the radius of the base 6cm is made up of modelling clay. A child reshapes it in the form os a sphere. Find the radius of the sphere.
- Prove that the lengths of tangents drawn from an external point to a circle are equal.
- Answer the following questions: [4×4=16]
- Find the sum of first 24 terms of the list of numbers whose nthterm is an=3+2n.
OR
If the sum of the first 7 terms of an AP is 49 and that of the 17 terms is 289. Find the sum of the first 'n' terms. - Prove that the ratio of the area of two similar triangles is equal to the square of the ratio of their corresponding sides.
- Solve them graphically, x+3y=6 & 2x-3y=12.
- The angles of elevation of the top of a tower from two points at a distance of 4m & 9m from the base of the tower and the same straight line with it are complementary. Prove that the height of the tower is 6m.
- Find the sum of first 24 terms of the list of numbers whose nthterm is an=3+2n.
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