# Solved papers for 10th Class Mathematics Solved Paper - Mathematics 2017 Delhi Set-I

### done Solved Paper - Mathematics 2017 Delhi Set-I

• question_answer1) The ratio of the height of a tower and the length of its shadow on the ground is $\sqrt{3}:1$. What is the angle of elevation of the sun?

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• question_answer2) Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

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• question_answer3)

 A number is chosen at random from the numbers$3,\text{ }2,\text{ }1,\text{ }0,\text{ }1,\text{ }2,\text{ }3$. What will be the probability that square of this number is less then or equal to 1?

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• question_answer4) If the distance between the points $(4,k)$ and $(1,0)$ is 5, then what can be the possible values of k?

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• question_answer5) Find the roots of the quadratic equation $\sqrt{2}{{x}^{2}}+7x+5\sqrt{2}=0$.

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• question_answer6) Find how many integers between 200 and 500 are divisible by 8?

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• question_answer7) Prove that tangents drawn at the ends of a diameter of a circle are parallel to each other.

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• question_answer8) Find the value of k for which the equation ${{x}^{2}}+k(2x+k-1)+2=0$ has real and equal roots.

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• question_answer9) Draw a line segment of length 8 cm and divide it internally in the ratio $4:5$.

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• question_answer10)

 In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If$PA=12\text{ }cm,\text{ }QC=QD=3\text{ }cm$, then find $PC+PD$.

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• question_answer11) If ${{m}^{th}}$ term of an A.P. is $\frac{1}{n}$ and ${{n}^{th}}$ term is $\frac{1}{m}$, then find the sum of its first mn terms.

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• question_answer12) Find the sum of n terms of the series $\left( 4-\frac{1}{n} \right)+\left( 4-\frac{2}{n} \right)+\left( 4-\frac{3}{n} \right)+.......$

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• question_answer13) If the equation $(1+{{m}^{2}}){{x}^{2}}+2mcx+{{c}^{2}}-{{a}^{2}}=0$ has equal roots then show that ${{c}^{2}}={{a}^{2}}(1+{{m}^{2}})$.

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• question_answer14) The $\frac{3}{4}th$ part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

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• question_answer15)

 In the given figure, OACB is a quadrant of a circle with centre O and radius $3.5\text{ }cm.$ If $OD=2\text{ }cm$, find the area of the shaded region.

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• question_answer16) Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that $\angle PTQ=2\angle OPQ.$

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• question_answer17) Show that $\Delta \,ABC$, where $A(-2,0),B(2,0),C(0,2)$ and $\Delta \text{ }PQR$ where $P(-4,0),Q(4,0),R(0,4)$ are similar triangles.

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• question_answer18) The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and ($3,\text{ }2$). If the third vertex is $\left( \frac{7}{2},y \right)$, find the value of y.

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• question_answer19)

 Two different dice are thrown together. Find the probability that the numbers obtained (i) have a sum less than 7 (ii) have a product less than 16 (iii) is a doublet of odd numbers.

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• question_answer20) A moving boat is observed from the top of a $150\text{ }m$ high cliff moving away from the cliff. The angle of depression of the boat changes from $60{}^\circ$ to $45{}^\circ$ in 2 minutes. Find the speed of the boat in m/h.

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• question_answer21) Construct an isosceles triangle with base $8\text{ }cm$ and altitude$4\text{ }cm$. Construct another triangle whose sides are $\frac{2}{3}$ times the corresponding sides of the isosceles triangle.

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• question_answer22) Prove that the lengths of tangents drawn from an external point to a circle are equal.

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• question_answer23)

 The ratio of the sums of first m and first n terms of an A. P. is ${{m}^{2}}:{{n}^{2}}$. Show that the ratio of its mth and nth terms is $2(m-1):(2n-1)$.

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• question_answer24) Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

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• question_answer25) If $a\ne b\ne 0$, prove that the points $(a,{{a}^{2}}),(b,{{b}^{2}})(0,0)$ will not be collinear.

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• question_answer26) The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height Find the ratio of the volumes of the two parts.

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• question_answer27)

 Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25.

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• question_answer28) A chord PQ of a circle of radius 10 cm subtends an angle of $60{}^\circ$ at the centre of circle. Find the area of major and minor segments of the circle.

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• question_answer29) The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is $30{}^\circ$ and the angle of depression of its shadow in water of lake is $60{}^\circ$. Find the height of the cloud from the surface of water.

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• question_answer30)

 In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O? are centres of the circles. Find the area of shaded region.

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• question_answer31) In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be height of standing water used for irrigating the park. Write your views on recycling of water.

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