Q9
mcq
1 mark
The slope of the straight line perpendicular to x-axis is :
- A. 1
- C. ∞
- D. -1
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Q13
mcq
If the sum and mean of a data are 407 and 11 respectively, then the number of observations in the data are:
- A. 37
- B. 4477
- C. 396
- D. 418
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Q14
mcq
If a letter is chosen at random from the English alphabets {a, b, ..., z}, then the probability that the letter chosen precedes x:
- A. \(\frac{12}{13}\)
- B. \(\frac{1}{13}\)
- C. \(\frac{23}{26}\)
- D. \(\frac{3}{26}\)
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Q15
short answer
If $B \times A = \{(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)\}$, find $A$ and $B$.
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Q17
short answer
Find $x$ so that $x^{16}$, $x^{112}$ and $x^{115}$ are consecutive terms of a Geometric Progression.
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Q19
short answer
Determine the nature of roots for the following quadratic equation:
$$2x^2-x-1=0$$
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Q20
short answer
In the figure AD is the bisector of $\angle BAC$, if $AB=10$ cm, $AC=14$ cm and $BC=6$ cm. Find $BD$ and $DC$.
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Q21
short answer
A cat is located at the point $(-6,-4)$ in $xy$ plane. A bottle of milk is kept at $(5,11)$. The cat wishes to consume the milk travelling through shortest possible distance. Find the equation of the path it needs to take the milk.
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Q22
short answer
If the straight lines $12y=-(P13)x112$, $12x-7y=16$ are perpendicular then find $P$.
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Q23
short answer
Prove that
$$\frac{\sec \theta - \sin \theta}{\cot \theta} = \frac{\sin \theta}{\sin \theta \cos \theta}$$
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Q24
short answer
The radius of a conical tent is 7 m and height is 24 m. Calculate the length of the canvas used to make the tent if the width of the rectangular canvas is 4 m.
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Q25
short answer
If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.
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Q26
short answer
Find the range and co-efficient of range of the following data:
63, 89, 98, 125, 79, 108, 117, 68
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Q27
short answer
A and B are two candidates seeking admission to IIT. The probability that A getting selected is 0.5 and the probability that both A and B getting selected is 0.3. Prove that probability of B being selected is at the most 0.8.
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Q28
short answer
If $p^2 \times q^1 \times r^4 \times s^3 = 3,15,000$ then find $p, q, r$ and $s$.
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Q29
long answer
Let $f : A \to B$ be a function defined by $f(x)=\frac{1}{2}x$. Where $A=\{2,4,6,10,12\}$, $B=\{0,1,2,4,5,9\}$. Represent $f$ by:
(i) set of ordered pairs
(ii) a table
(iii) an arrow diagram
(iv) a graph
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Q30
short answer
The houses of a street are numbered from 1 to 49. Senthil’s house is numbered such that the sum of numbers of the houses prior to Senthil’s house is equal to the sum of the numbers of the houses following Senthil’s house. Find Senthil’s house number.
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Q31
short answer
Find the sum to $n$ terms of the series 515515551.....
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Q41
short answer
Two unbiased dice are rolled once. Find the probability of getting: (i) a doublet (equal numbers on both dice) (ii) the product as a prime number (iii) the sum as a prime number (iv) the sum as 1
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Q42
short answer
Let A={x∈W/x < 3}, B={x∈N/1 < x ≤ 5} and C={3, 5, 7} verify that A×(B∪C)=(A×B)∪(A×C).
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