Mathematics Standard - Outside Delhi set 1 2019-2020 English Medium Class 10 Question Paper Solution

The sum of exponents of prime factors in the prime-factorisation of 196 is ______.

3

4

5

2

Euclid’s division Lemma states that for two positive integers a and b, there exists unique integer q and r satisfying a = bq + r, and ______.

0 < r < b

0 < r ≤ b

0 ≤ r < b

0 ≤ r ≤ b

The zeroes of the polynomial x² – 3x – m (m + 3) are ______.

m, m + 3

– m, m + 3

m, – (m + 3)

– m, – (m + 3)

The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is ______.

`- 14/3`

`2/5`

5

10

The roots of the quadratic equation x² – 0.04 = 0 are ______.

± 0.2

± 0.02

0.4

2

The common difference of the A.P. `1/p, (1 - p)/p, (1 - 2p)/p`, ... is ______.

1

`1/p`

–1

`- 1/p`

The n^th term of the A.P. a, 3a, 5a, ... is ______.

na

(2n – 1)a

(2n + 1)a

2na

The point P on x-axis equidistant from the points A(–1, 0) and B(5, 0) is ______.

(2, 0)

(0, 2)

(3, 0)

(2, 2)

The co-ordinates of the point which is reflection of point (–3, 5) in x-axis are ______.

(3, 5)

(3, –5)

(–3, –5)

(–3, 5)

If the point P(6, 2) divides the line segment joining A(6, 5) and B(4, y) in the ratio 3 : 1, then the value of y is ______.

4

3

2

1

In figure, MN || BC and AM : MB = 1 : 2, then `(ar(ΔAMN))/(ar(ΔABC))` = ______.

In given figure, the length PB = ______ cm.

In ΔABC, AB = `6sqrt(3)` cm, AC = 12 cm and BC = 6 cm, then B = ______.

Two triangles are similar if their corresponding sides are ______.

The value of (tan 1° tan 2° ...... tan 89°) is equal to ______.

In figure, the angles of depressions from the observing positions O₁ and O₂ respectively of the object A are ______.

If sin A + sin² A = 1, then find the value of the expression (cos² A + cos⁴ A).

In the following figure is a sector of circle of radius 10.5 cm. Find the perimeter of the sector. `("Take"  π = 22/7)`

If a number x is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3, then find the probability of x² < 4.

What is the probability that a randomly taken leap year has 52 Sundays?

Find the class-marks of the classes 10 – 25 and 35 – 66.

A die is thrown once. What is the probability of getting a prime number? 

Answer the following question:

1. How many of the above ten, are not polynomials?   [1]
2. How man of the above ten, are quadratic polynomials?   [1]

In the following figure, ABC and DBC are two triangles on the same base BC. If AD intersects B at O, show that `(ar(ΔABC))/(ar(ΔDBC)) = (AO)/(DO)`

In the following figure, if AD ⊥ BC, then prove that AB² + CD² = BD² + AC².

Prove that `1 + (cot^2 α)/(1 + "cosec"  α) = "cosec"  α`

Show that tan⁴θ + tan²θ = sec⁴θ – sec²θ

The volume of a right circular cylinder with its height equal to the radius is `25 1/7` cm³. Find the height of the cylinder.

A child has a die whose six faces shows the letters as given below:

\[\boxed{\text{A}}\]\[\boxed{\text{B}}\]\[\boxed{\text{C}}\]\[\boxed{\text{D}}\]\[\boxed{\text{E}}\]\[\boxed{\text{A}}\]

The die is thrown once. What is the probability of getting (i) A? (ii) D?

Compute the mode for the following frequency distribution:

If 2x + y = 23 and 4x – y = 19, find the values of (5y – 2x) and `(y/x - 2)`.

Solve for x: `1/(x + 4) - 1/(x + 7) = 11/30, x ≠ - 4, 7`.

Show that the sum of all terms of an A.P. whose first term is a, the second term is b and the let term is c is equal to `((a + c)(b + c - 2a))/(2(b - a))`.

Solve the equation: 1 + 4 + 7 + 10 + ... + x = 287.

In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduce by 200 km/hr and time of flight increased by 30 minutes. Find the original duration of flight.

If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y – 10 = 0, find the value of k.

Find the area of triangle ABC with A(1, –4) and the mid-points of sides through A being (2, –1) and (0, –1).

In the following figure, if ΔABC ∼ ΔDEF and their sides of lengths (in cm) are marked along them, then find the lengths of sides of each triangle.

If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, prove that `AQ = 1/2 (BC + CA + AB)`

If `sin θ + cos θ = sqrt(2)`, prove that tan θ + cot θ = 2.

The area of a circular play ground is 22176 cm². Find the cost of fencing this ground at the rate of 50 per metre.

Prove that `sqrt(5)` is an irrational number. 

It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?

Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle.

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then construct another triangle whose sides are `3/4` times the corresponding sides of the first triangle.

From a point on the ground, the angles of elevation of the bottom and the top of a tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

Find the area of the shaded region in figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

Find the curved surface area of the frustum of a cone, the diameters of whose circular ends are 20 m and 6 m and its height is 24 m.

The mean of the following frequency distribution is 18. The frequency f in the class interval 19 – 21 is missing. Determine f.

The following table gives production yield per hectare of wheat of 100 farms of a village:

Change the distribution to a 'more than' type distribution and draw its ogive.