← Combined Technical (NG)
Past Questions
Mouldboard plough is a___________ implement.
A)
seed drill
B)
planking
C)
primary tillage
D)
secondary tillage
A mouldboard plough is designed to cut, lift, and invert the soil. This process is used to break up compacted soil, bury crop residue, and prepare the land for the first time after harvest, which defines 'primary tillage'.
Reasoning for other options:
- (a) Seed drill: This is a planting implement used for sowing seeds, not for ploughing.
- (b) Planking: This is a leveling or smoothing operation performed after tillage.
- (d) Secondary tillage: This refers to operations like harrowing, cultivating, or leveling that refine the seedbed after the primary tillage has already been completed. A mouldboard plough is too aggressive for secondary tillage.
Tillage or ploughing 25-30 cm deep is:
A)
Medium deep ploughing
B)
Medium ploughing
C)
Deep ploughing
D)
Shallow ploughing
In agronomy, tillage depth is categorized based on the depth of soil inversion and aeration.
1. **Shallow Tillage/Ploughing**: Typically involves depths of 5-15 cm. It is used for seedbed preparation or weed control without disturbing deeper soil layers.
2. **Medium Ploughing**: Generally refers to depths between 15-20 cm, common for standard primary tillage in many crops.
3. **Deep Ploughing**: This involves tillage at depths of 25-30 cm or more. Deep ploughing is specifically employed to break 'hard pans' (compacted soil layers), improve water infiltration, and bring nutrients from deeper layers to the surface. It is often done once in several years or during the preparation of land for deep-rooted crops.
Since the question specifies a depth of 25-30 cm, it falls under the category of Deep Ploughing.
The Seed Act was enacted by the parliament on:
A)
29 December, 1986
B)
29 December, 1996
C)
29 December, 1966
D)
29 December, 1976
The Seeds Act was enacted by the Parliament of India in 1966 to regulate the quality of seeds sold in India to ensure that farmers have access to high-quality, certified seeds to improve agricultural productivity. Specifically, the Act was passed and received assent on December 29, 1966.
- Option (a) 1986: Incorrect. This date does not correspond to the enactment of the Seeds Act.
- Option (b) 1996: Incorrect. This is 30 years after the actual enactment.
- Option (d) 1976: Incorrect. This is 10 years after the actual enactment.
Therefore, the correct date is 29 December, 1966.
___________ is used to increase panicle exertion of CMS lines in hybrid rice.
A)
Nitrogen
B)
Gibberellic acid
C)
Cytokinin
D)
Ethylene
In hybrid rice production using the Cytoplasmic Male Sterility (CMS) system, a common physiological problem is 'panicle exertion failure' or 'incomplete exertion.' This occurs when the panicle remains trapped within the leaf sheath (flag leaf), preventing the pollen from the pollinator (restorer line) from reaching the stigma of the CMS line, thereby reducing seed set and yield. Gibberellic acid (GA3) is a plant growth regulator known for promoting internode elongation. Applying GA3 to CMS lines stimulates the elongation of the peduncle, ensuring that the panicle is fully exerted from the boot leaf, which facilitates efficient pollination.
Why other options are incorrect:
- Nitrogen (a): While nitrogen is essential for overall growth and biomass, it does not specifically trigger the rapid internode elongation required for panicle exertion in the same targeted manner as GA3.
- Cytokinin (c): Cytokinins primarily promote cell division and shoot branching, but they do not promote the longitudinal elongation of the stem/peduncle.
- Ethylene (d): Ethylene is generally associated with fruit ripening, senescence, and growth inhibition (triple response), which would not help in pushing the panicle out of the leaf sheath.
Height and base of a right angled triangle are 24 cm and 18 cm find the length of its hypotenuse.
A)
24cm
B)
30cm
C)
15cm
D)
18cm
To find the hypotenuse of a right-angled triangle, we use the Pythagoras Theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c² = a² + b².
Given:
Height (a) = 24 cm
Base (b) = 18 cm
Step-by-step calculation:
1. Square the height: 24² = 576
2. Square the base: 18² = 324
3. Add the squares: 576 + 324 = 900
4. Find the square root of the sum: √900 = 30
Therefore, the length of the hypotenuse is 30 cm.
Alternative Method (Using Pythagorean Triples):
Divide both sides by their greatest common divisor (6):
24/6 = 4
18/6 = 3
This forms a 3-4-5 right triangle. Multiplying the hypotenuse ratio (5) by the common divisor (6) gives: 5 * 6 = 30 cm.
Comparison with options:
- Option a (24cm) is equal to the height, which is impossible as the hypotenuse must be the longest side.
- Option c (15cm) and Option d (18cm) are shorter than the height, which is mathematically impossible for a hypotenuse.
In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. The angle B is-
A)
120°
B)
60°
C)
90°
D)
45°
To find the angle B in ΔABC, we can use the Law of Cosines or check if the sides satisfy the Pythagorean theorem.
Given sides:
AB (c) = 6√3 cm
AC (b) = 12 cm
BC (a) = 6 cm
Let's check if the square of the longest side (AC) is equal to the sum of the squares of the other two sides (AB and BC):
AC² = 12² = 144
AB² + BC² = (6√3)² + 6²
AB² + BC² = (36 * 3) + 36
AB² + BC² = 108 + 36 = 144
Since AC² = AB² + BC², the triangle satisfies the Pythagorean theorem. According to the converse of the Pythagorean theorem, ΔABC is a right-angled triangle with the right angle opposite to the hypotenuse AC. Therefore, angle B = 90°.
Alternatively, using the Law of Cosines for angle B:
cos(B) = (AB² + BC² - AC²) / (2 * AB * BC)
cos(B) = (108 + 36 - 144) / (2 * 6√3 * 6)
cos(B) = 0 / (72√3) = 0
B = cos⁻¹(0) = 90°.
Out of the following, which is the Pythagorean triplet?
A)
(1,5, 10)
B)
(3,4, 5)
C)
(2, 2, 2)
D)
(5,5, 2)
A Pythagorean triplet consists of three positive integers (a, b, c) such that they satisfy the Pythagorean theorem: a² + b² = c², where 'c' is the largest number (the hypotenuse).
Let's test each option:
Option (a): (1, 5, 10)
1² + 5² = 1 + 25 = 26
10² = 100
Since 26 ≠ 100, this is not a Pythagorean triplet.
Option (b): (3, 4, 5)
3² + 4² = 9 + 16 = 25
5² = 25
Since 25 = 25, this satisfies the theorem. This is the most basic and well-known Pythagorean triplet.
Option (c): (2, 2, 2)
2² + 2² = 4 + 4 = 8
2² = 4
Since 8 ≠ 4, this is not a Pythagorean triplet.
Option (d): (5, 5, 2)
(Note: The largest number must be the hypotenuse, so we check 2² + 5² = 4 + 25 = 29, which is not 5²=25. Or if we take 5 as the hypotenuse: 2² + 5² = 29 ≠ 25).
Since no combination satisfies a² + b² = c², this is not a Pythagorean triplet.
Therefore, option (b) is the correct answer.
(sin A - cos A)² is equal to
A)
1 + 2sinAcosA
B)
1 - 2sinAcosA
C)
2sinAcosA - 1
D)
2sinAcosA + 1
To solve the expression (sin A - cos A)², we use the algebraic identity (a - b)² = a² - 2ab + b².
Step 1: Apply the identity to the trigonometric expression:
(sin A - cos A)² = (sin A)² - 2(sin A)(cos A) + (cos A)²
Step 2: Rearrange the terms:
= (sin² A + cos² A) - 2sin A cos A
Step 3: Use the fundamental trigonometric identity sin² A + cos² A = 1:
= 1 - 2sin A cos A
Comparing this result with the given options:
- Option (a) 1 + 2sinAcosA is the expansion of (sin A + cos A)².
- Option (b) 1 - 2sinAcosA matches our result.
- Option (c) 2sinAcosA - 1 is the negative of our result.
- Option (d) 2sinAcosA + 1 is incorrect.
If r is the radius of the sphere, then the surface area of the sphere is given by;
A)
4πr
B)
2πr²
C)
πr²
D)
4πr²
The surface area of a sphere is defined as the total area of the exterior surface of the sphere. Mathematically, the formula for the surface area (A) of a sphere with radius 'r' is A = 4πr².
Analysis of options:
- Option (a) 4πr: This is not a standard formula for area (it lacks the squared dimension required for area).
- Option (b) 2πr²: This represents the curved surface area of a hemisphere (half a sphere).
- Option (c) πr²: This is the formula for the area of a circle (a 2D cross-section of the sphere).
- Option (d) 4πr²: This is the correct standard geometric formula for the total surface area of a sphere.
Evaluate (cosec θ + cot θ)(cosec θ - cot θ).
A)
0
B)
1
C)
2
D)
3
The given expression is in the form of (a + b)(a - b), which is a standard algebraic identity known as the difference of squares: (a + b)(a - b) = a² - b².
Step 1: Apply the identity to the trigonometric expression:
(cosec θ + cot θ)(cosec θ - cot θ) = cosec² θ - cot² θ
Step 2: Use the fundamental trigonometric identity relating cosecant and cotangent:
We know that 1 + cot² θ = cosec² θ.
Step 3: Rearrange the identity to find the value of cosec² θ - cot² θ:
cosec² θ - cot² θ = 1
Therefore, the value of the expression is 1.
Analysis of options:
- Option (a) 0 is incorrect because the difference between the squares of cosec θ and cot θ is constant (1), not zero.
- Option (b) 1 is correct based on the Pythagorean identity.
- Option (c) 2 and (d) 3 are incorrect as they do not satisfy the trigonometric identity.
What is the value of sin 0° + cos 0°?
A)
0
B)
2
C)
1
D)
∞
To solve the expression sin 0° + cos 0°, we use the standard trigonometric values for the angle 0°:
1. The value of sin 0° is 0. (In a unit circle, the sine represents the y-coordinate, which is 0 at 0 radians/degrees).
2. The value of cos 0° is 1. (In a unit circle, the cosine represents the x-coordinate, which is 1 at 0 radians/degrees).
Substituting these values into the expression:
sin 0° + cos 0° = 0 + 1 = 1.
Analysis of options:
- Option (a) 0 is incorrect because it only considers the value of sin 0°.
- Option (b) 2 is incorrect as it does not match the sum of the trigonometric values.
- Option (c) 1 is correct.
- Option (d) ∞ is incorrect as both functions are defined and finite at 0°.
If ΔPQR ~ ΔXYZ and ∠P=50°, ∠Q=60°, then ∠Y is:
A)
50°
B)
60°
C)
70°
D)
80°
Option B is correct: 60°.
Find the value of cos 135°.
A)
1/2
B)
√2
C)
-√2
D)
-1/√2
To find the value of cos 135°, we can use trigonometric identities.
1. **Quadrant Analysis**: The angle 135° lies in the Second Quadrant (between 90° and 180°). In the second quadrant, the cosine function is negative.
2. **Reference Angle**: The reference angle for 135° is calculated as:
Reference Angle = 180° - 135° = 45°.
3. **Calculation**:
cos(135°) = -cos(45°)
We know that cos(45°) = 1/√2 (or √2/2).
Therefore, cos(135°) = -1/√2.
**Analysis of Options**:
- Option (a) 1/2: This is the value of cos 60°.
- Option (b) √2: This is impossible as the value of cosine cannot exceed 1.
- Option (c) -√2: This is impossible as the value of cosine cannot be less than -1.
- Option (d) -1/√2: This is the correct value based on the second quadrant property and the reference angle of 45°.
If ΔPQR is an equilateral triangle and PQ = 6 cm, then the area of ΔPQR is:
A)
18cm²
B)
9√3 cm²
C)
36cm²
D)
27√3 cm²
Step-by-step solution:
1. **Identify the given information**: The triangle ΔPQR is an equilateral triangle, meaning all three sides are equal. The side length (s) is given as PQ = 6 cm.
2. **Recall the formula for the area of an equilateral triangle**: The area (A) is calculated using the formula: A = (√3 / 4) * s².
3. **Substitute the given value**:
A = (√3 / 4) * (6)²
A = (√3 / 4) * 36
4. **Simplify the expression**:
A = √3 * (36 / 4)
A = 9√3 cm².
Analysis of options:
- Option (a) 18cm²: Incorrect. This is likely obtained by incorrectly using (1/2 * base * height) without calculating the correct height of the triangle.
- Option (b) 9√3 cm²: Correct. Matches the calculated result.
- Option (c) 36cm²: Incorrect. This is simply the square of the side length (s²).
- Option (d) 27√3 cm²: Incorrect. This would be the result if the side length were 6√3 or if the formula was applied incorrectly.
Which of the following is a coordinate point on the y-axis?
A)
(0, 1)
B)
(1, 0)
C)
(1, 1)
D)
(0, 0)
In a 2D Cartesian coordinate system, a point is represented as (x, y).
1. For a point to lie on the y-axis, its horizontal distance from the origin must be zero. Therefore, the x-coordinate must be 0.
2. Analyzing the options:
- Option (a) (0, 1): The x-coordinate is 0. This point lies exactly on the y-axis at a height of 1 unit. This is the correct answer.
- Option (b) (1, 0): The y-coordinate is 0. This point lies on the x-axis.
- Option (c) (1, 1): Neither coordinate is 0. This point lies in the first quadrant.
- Option (d) (0, 0): This is the origin. While it technically lies on both axes, in the context of multiple-choice questions identifying a specific axis point, a point with a non-zero y-value and zero x-value is the definitive answer for 'a point on the y-axis'. However, (0, 1) is the most distinct example of a point specifically on the y-axis.
The area of a rhombus whose vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is:
A)
12 sq.units
B)
24sq.units
C)
30sq.units
D)
32 sq.units
To find the area of a rhombus given its vertices, the most efficient method is to use the formula for the area of a rhombus: Area = (1/2) * d1 * d2, where d1 and d2 are the lengths of the diagonals.
Step 1: Identify the vertices.
Let A = (3, 0), B = (4, 5), C = (-1, 4), and D = (-2, -1).
Step 2: Calculate the lengths of the diagonals.
Diagonal 1 (AC) connects (3, 0) and (-1, 4):
d1 = √[(-1 - 3)² + (4 - 0)²]
d1 = √[(-4)² + (4)²] = √[16 + 16] = √32 = 4√2 units.
Diagonal 2 (BD) connects (4, 5) and (-2, -1):
d2 = √[(-2 - 4)² + (-1 - 5)²]
d2 = √[(-6)² + (-6)²] = √[36 + 36] = √72 = 6√2 units.
Step 3: Calculate the area.
Area = (1/2) * d1 * d2
Area = (1/2) * (4√2) * (6√2)
Area = (1/2) * 24 * (√2 * √2)
Area = (1/2) * 24 * 2
Area = 24 sq. units.
Alternatively, using the Shoelace Formula for the area of a polygon:
Area = 1/2 |(x1y2 + x2y3 + x3y4 + x4y1) - (y1x2 + y2x3 + y3x4 + y4x1)|
Area = 1/2 |(3*5 + 4*4 + (-1)*(-1) + (-2)*0) - (0*4 + 5*(-1) + 4*(-2) + (-1)*3)|
Area = 1/2 |(15 + 16 + 1 + 0) - (0 - 5 - 8 - 3)|
Area = 1/2 |(32) - (-16)|
Area = 1/2 |32 + 16| = 1/2 * 48 = 24 sq. units.
Therefore, option (b) is correct.
Corresponding sides of two similar triangles are in the ratio of 2:3. If the area of the small triangle is 48 cm², then the area of large triangle is:
A)
230 cm²
B)
106 cm²
C)
107 cm²
D)
108 cm²
According to the properties of similar triangles, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
1. Given: Ratio of corresponding sides = 2:3
2. Therefore, the ratio of their areas = (2)² : (3)² = 4 : 9
3. Let the area of the small triangle be A1 and the area of the large triangle be A2.
4. We are given A1 = 48 cm².
5. Using the ratio: A1 / A2 = 4 / 9
6. Substitute the value of A1: 48 / A2 = 4 / 9
7. Solve for A2: A2 = (48 * 9) / 4
8. A2 = 12 * 9 = 108 cm².
Comparing this result to the options:
- Option a (230 cm²), b (106 cm²), and c (107 cm²) are mathematically incorrect based on the theorem of similar triangles.
A circle has a number of tangents equal to -
A)
0
B)
1
C)
2
D)
Infinite
A tangent to a circle is defined as a straight line that touches the circle at exactly one point. By definition, every single point on the circumference of a circle can serve as a point of tangency. Since a circle consists of an infinite number of points along its boundary (circumference), and a unique tangent can be drawn at each of these points, there are an infinite number of tangents that can be drawn to a circle.
Analysis of options:
- Option (a) 0: Incorrect, as tangents clearly exist for any circle.
- Option (b) 1: Incorrect, as you can draw tangents at any point on the circle, not just one.
- Option (c) 2: Incorrect; while only two tangents can be drawn from a single point *outside* the circle, the question asks for the total number of tangents the circle *has* in total.
- Option (d) Infinite: Correct, because there are infinite points on the circumference.
If the area of a circle is 154 cm², then its perimeter is -
A)
11cm
B)
22cm
C)
44cm
D)
55cm
Step-by-step solution:
1. **Given**: Area of the circle (A) = 154 cm².
2. **Formula for Area**: The area of a circle is given by the formula A = πr², where 'r' is the radius.
3. **Find the Radius (r)**:
154 = (22/7) * r²
r² = (154 * 7) / 22
r² = 7 * 7
r² = 49
r = √49 = 7 cm.
4. **Formula for Perimeter (Circumference)**: The perimeter of a circle is given by the formula P = 2πr.
5. **Calculate Perimeter**:
P = 2 * (22/7) * 7
P = 2 * 22
P = 44 cm.
Comparing this result to the options:
- Option (a) 11cm is incorrect.
- Option (b) 22cm is incorrect (this is only πr).
- Option (c) 44cm matches our calculation.
- Option (d) 55cm is incorrect.
From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, find the distance of point P from the foot of the tower is:
A)
149m
B)
156m
C)
173m
D)
200m
1. Identify the given values:
- Height of the tower (Opposite side, h) = 100 m
- Angle of elevation (θ) = 30°
- Distance from point P to the foot of the tower (Adjacent side, d) = ?
2. Use the trigonometric ratio for tangent, which relates the opposite side to the adjacent side:
tan(θ) = Opposite / Adjacent
tan(30°) = 100 / d
3. Substitute the known value of tan(30°):
tan(30°) = 1/√3 (approximately 0.57735)
1/√3 = 100 / d
4. Solve for d:
d = 100 * √3
Using the value of √3 ≈ 1.732:
d = 100 * 1.732 = 173.2 m
5. Comparing the result with the given options, 173.2 m rounds to 173 m.
Option (a) 149m, (b) 156m, and (d) 200m are mathematically incorrect based on the tangent ratio for 30°.
Sin(90° - x) equals to _
A)
cosx
B)
cotx
C)
cosec x
D)
secx
This question is based on the trigonometric complementary angle identities. In trigonometry, the complementary angle identity for the sine function states that the sine of an angle is equal to the cosine of its complement. Mathematically, this is expressed as: sin(90° - θ) = cos(θ).
Applying this to the given problem:
1. We are given the expression sin(90° - x).
2. According to the complementary angle formula, sin(90° - x) = cos(x).
Evaluating the other options:
- Option b (cot x): cot x is equal to tan(90° - x).
- Option c (cosec x): cosec x is the reciprocal of sin x, not the complement.
- Option d (sec x): sec x is equal to cosec(90° - x).
Therefore, the correct identity is cosx.
The area of the square whose perimeter is 45.2 cm:
A)
250.43 cm²
B)
127.69 cm²
C)
142 cm²
D)
64.8 cm²
Step-by-step solution:
1. **Identify the given information**: The perimeter (P) of the square is 45.2 cm.
2. **Formula for the perimeter of a square**: P = 4 × side (s).
3. **Calculate the length of one side**:
s = P / 4
s = 45.2 / 4
s = 11.3 cm
4. **Formula for the area of a square**: Area (A) = side² (s²).
5. **Calculate the area**:
A = (11.3)²
A = 11.3 × 11.3 = 127.69 cm².
Comparing this result to the options:
- Option (a) 250.43 cm² is incorrect.
- Option (b) 127.69 cm² matches our calculation exactly.
- Option (c) 142 cm² is incorrect.
- Option (d) 64.8 cm² is incorrect.
If sin θ=1/2 and cos θ= √3/2, then what is the value of tan θ?
A)
1/3
B)
√3/3
C)
√3
D)
1/2
To find the value of tan θ, we use the fundamental trigonometric identity: tan θ = sin θ / cos θ.
Given:
sin θ = 1/2
cos θ = √3/2
Substituting these values into the formula:
tan θ = (1/2) / (√3/2)
To divide by a fraction, we multiply by its reciprocal:
tan θ = (1/2) * (2/√3)
the 2s cancel out, leaving:
tan θ = 1/√3
To rationalize the denominator, multiply both the numerator and the denominator by √3:
tan θ = (1 * √3) / (√3 * √3) = √3/3.
Verification of options:
- Option (a) 1/3 is incorrect.
- Option (b) √3/3 is the rationalized form of 1/√3, which is correct.
- Option (c) √3 is the value of cot θ in this case, not tan θ.
- Option (d) 1/2 is the value of sin θ, not tan θ.
The line y = 2x - 1 intersects the y-axis at the point:
A)
(0, -1)
B)
(1,9)
C)
(0, 1)
D)
(-1, 0)
To find where a line intersects the y-axis (the y-intercept), we must set the x-coordinate to 0, because every point on the y-axis has an x-value of 0.
Step-by-step calculation:
1. Given the equation of the line: y = 2x - 1
2. Substitute x = 0 into the equation:
y = 2(0) - 1
y = 0 - 1
y = -1
3. The point of intersection is therefore (x, y) = (0, -1).
Analysis of options:
- Option (a) (0, -1) matches our calculation.
- Option (b) (1, 9) is incorrect; if x=1, y=2(1)-1=1, not 9.
- Option (c) (0, 1) is incorrect; this would be the intercept if the equation were y = 2x + 1.
- Option (d) (-1, 0) is the x-intercept (where y=0), not the y-intercept.
If two triangles are similar, then their corresponding sides are:
A)
Equal
B)
Proportional
C)
Unequal
D)
Parallel
In geometry, two triangles are defined as 'similar' (denoted by the symbol ~) if they have the same shape but not necessarily the same size. For two triangles to be similar, two conditions must be met: 1. Their corresponding angles must be equal. 2. Their corresponding sides must be in the same ratio, which means they are proportional. For example, if triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF.
Analysis of options:
- (a) Equal: This describes 'congruent' triangles, which are a specific subset of similar triangles where the ratio is 1:1. Not all similar triangles are equal in size.
- (b) Proportional: This is the defining characteristic of similarity for sides.
- (c) Unequal: While sides may be unequal, this is not a mathematical property or requirement; they must follow a specific ratio.
- (d) Parallel: Parallelism refers to the relationship between lines in a plane, not the relationship between corresponding sides of two different triangles.